A Chronicle of Mathematical Milestones: The Mathematical Calendar 1527561429, 9781527561427

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A Chronicle of Mathematical Milestones

A Chronicle of Mathematical Milestones: The Mathematical Calendar By

Nataliya Ivanova

A Chronicle of Mathematical Milestones: The Mathematical Calendar By Nataliya Ivanova This book first published 2024 Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2024 by Nataliya Ivanova All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN (10): 1-5275-6142-9 ISBN (13): 978-1-5275-6142-7

TABLE OF CONTENTS

Chapter One ................................................................................................. 1 January Chapter Two .............................................................................................. 33 February Chapter Three ............................................................................................ 62 March Chapter Four .............................................................................................. 89 April Chapter Five ............................................................................................ 121 May Chapter Six .............................................................................................. 150 June Chapter Seven.......................................................................................... 179 July Chapter Eight ........................................................................................... 209 August Chapter Nine............................................................................................ 236 September Chapter Ten ............................................................................................. 261 October Chapter Eleven ........................................................................................ 292 November Chapter Twelve ....................................................................................... 322 December

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Table of Contents

Conclusive Remarks ................................................................................ 351 References ............................................................................................... 352

CHAPTER ONE JANUARY

January, 1 1748 - Death of Johann Bernoulli, Swiss mathematician (b. 1667). 1787 - Death of Jose Anastacio da Cunha, Portuguese mathematician (b. 1744). 1796 - Death of Alexandre-Theophile Vandermonde, French mathematician (b. 1735). 1800 - Cauchy's father was elected Secretary of the Senate in France. The young Cauchy used a corner of his father's office in the Luxembourg Palace for his own desk. There, Lagrange and Laplace would often meet him. [11] 1803 - Birthdate of Guglielmo Libri Carucci dalla Sommaja, Italian count and mathematician (d. 1869). 1862 - Death of Mikhail Ostrogradsky, Ukrainian mathematician and physicist (b. 1801). 1878 - Birthdate of Agner Krarup Erlang, Danish mathematician, statistician, and engineer (d. 1929). 1894 - Birthdate of Satyendra Nath Bose, Indian physicist and mathematician (d. 1974). 1902 - Death of Lothar Heffter (b. 1862). 1905 - Birthdate of Stanislaw Mazur, Ukrainian-Polish mathematician (d. 1981). 1912 - Birthdate of Boris Vladimirovich Gnedenko, Russian mathematician and historian (d. 1995). 1922 - Death of Wooster Woodruff Beman, American mathematician, philologist, and historian of mathematics (b. 1850). 1923 - Birthdate of Alexander (Smbat) Abian, Iranian-born ArmenianAmerican mathematician (d. 1999). 1923 - Birthdate of Daniel E. Gorenstein, American mathematician (d. 1992). 1938 - Hungary issued a stamp portraying Pope Sylvester II, Archbishop of Astrik (also known as mathematician Gerbert of Aurillac). 1940 - The first item was added to MathSciNet.

2

Chapter One

1995 - Death of Eugene Wigner, Hungarian-American physicist and mathematician, and Nobel Prize laureate (b. 1902). 1996 - Death of Gertrude Blanch, American mathematician (b. 1897).

January, 2 1539 - Zuan Antonio de Bassano, a bookseller who frequently traveled between Milan and Venice (he took messages between Cardano and Tartaglia), wrote to Tartaglia: “Master Niccolo Tartaglia, I have been directed to you by a worthy man, a physician of Milan, named Master Girolamo Cardano, who is a very great mathematician. And because he has understood that you have been engaged in disputation with Master Fior, putting to him for a wager certain question that could only be answered by knowing the general rule for resolving the case of the cubic, which general rule you had found by your own discovery. Therefore his excellency prays you that you will kindly make known to him the rule discovered by you, and if you think it will make it public under your name in his present work, but if you do not think fit that it should be published he will keep it secret.” 1663 - The Republic of Venice offered Stefano Degli Angeli a professorship of mathematics at the University of Padua, a post Galileo had held earlier. 1690 - The Hamburg Mathematical Society was founded. 1803 - Birthdate of Guglielmo Libri Carucci dalla Sommaja, Italian mathematician (d. 1869). 1822 - Birthdate of Rudolf Clausius, Polish-German physicist, and mathematician (d. 1888). 1892 - Day of death of George Biddell Airy, English mathematician, and astronomer (b. 1801). 1905 - Birthdate of Lev Genrikhovich Schnirelmann, Soviet mathematician (d. 1938). 1923 - Birthdate of Philip J. Davis, American academic applied mathematician, and writer. 1938 - Birthdate of Anatoly Mykhailovych Samoilenko, Ukrainian mathematician (d. 2020). 1940 - Birthdate of Sathamangalam Ranga Iyengar Srinivasa Varadhan, Indian-American mathematician. 1947 - Matt Weinstock's column in the Los Angeles Daily News began: "Readers of Esquire magazine [January 1948] ... are slowly losing their minds over a story by Martin Gardner" entitled the "No-Sided

January

3

Professor." This story is the first time that the Mobius strip, a one-sided surface, was used in a piece of fantasy. 1992 - Day of death of Brian Kuttner, British mathematician (b. 1908).

January, 3 1641 - Day of death of Jeremiah Horrocks, English astronomer, and mathematician (b. 1618). 1657 - Fermat posed two problems involving S(n), the sum of the proper divisors of n: (i) find a cube n such that n+S(n) is a square, and (ii) find a square n such that n+S(n) is a cube. 1777 - Birthdate of Louis Poinsot, French mathematician, and physicist (d. 1859). 1891 - Day of death of John Casey, Irish mathematician (b. 1820). 1892 - Day of death of Heinrich Eduard Schroeter, German mathematician (b. 1829). 1912 - Day of death of Jacob Amsler, Swiss mathematician (b. 1823). 1917 - Birthdate of Yurii Alekseevich Mitropolskiy, Ukrainian mathematician (d. 2008). 1920 - Day of death of Zygmunt Janiszewski, Polish mathematician (b. 1888). 1921 - Birthdate of Isabella Bashmakova, Russian historian of mathematics (d. 2005). 1921 - Birthdate of Jean-Louis Koszul, French mathematician (d. 2018). 1927 - Day of death of Carl David Tolme Runge, German physicist, and mathematician (b. 1856). 1943 - Barbara Lee Wilson wrote to Einstein for advice on how to stop being anxious about her performance in math class. Her letter began as: "Most of the girls in my room have heroes which they write fan mail to. You + my uncle, who is in the Coast Guard, are my heroes." 1956 - Israel issued the world's first postage stamp picturing Albert Einstein. 1970 - Yuri Matiyasevich completes the proof of Hilbert's 10th Problem. 1975 - Birthdate of Danica McKellar, American actress, mathematical writer, and mathematician. 1977 - Apple Computer Corporation is incorporated by Stephen Jobs and Stephen Wozniak. 1989 - Day of death of Sergei Sobolev, Soviet mathematician (b. 1909). 2011 - Day of death of Anatoliy Volodymyrovych Skorokhod, SovietUkrainian mathematician (b. 1930).

4

Chapter One

2018 - On this day it was announced that the Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 277,232,917 - 1, having 23,249,425 digits.

January, 4 1567 - Birthdate of François d'Aguilon, Belgian Jesuit mathematician (d. 1617). 1643 - Birthdate of Isaac Newton, English mathematician, and physicist (d. 1727). 1752 - Day of death of Gabriel Cramer, Swiss mathematician, and physicist (b. 1704). 1826 - Day of death of Nikolai Fuss, Swiss mathematician (b. 1755). 1831 - Galois was expelled from the Ecole Normale for his political views. 1845 - Giusto Bellavitis was appointed, via a competitive examination, a full professor of descriptive geometry at the University of Padua. 1848 - Birthdate of Heinrich Suter, Swiss historian of mathematics (d. 1922). 1890 - Birthdate of Raymond Woodard Brink, American mathematician (d. 1973). 1913 - Birthdate of Sixto Rios Garcia, Spanish mathematician (d. 2008). 1948 - Birthdate of Alexander Bogomolny, Soviet-born Israeli American mathematician (d. 2018). 1950 - Day of death of Virgil Snyder, American mathematician (b. 1869). 1961 - Day of death of Erwin Schrödinger, Austrian theoretical physicist (b. 1887). 2005 - Day of death of Frank Harary, American mathematician (b. 1921).

January, 5 1665 - The first volume of the Journal des Savants appeared in Paris. It was the first academic journal to publish scientific material. 1723 - Birthdate of Nicole-Reine Lepaute, French astronomer, and mathematician (d. 1788). 1838 - Birthdate of Camille Jordan, French mathematician (d. 1922). 1846 - Möbius, in a letter to Apelt, says that he has a copy of Grassmann's Ausdehnungslehre but failed to read beyond the first sheets [36]. 1853 - The term "first derivative" first used as a noun in English in a paper "On the General Law of the Transformation of Energy" by William John Macquorn Rankine read before the Philosophical Society of Glasgow.

January

5

1855 - Birthdate of Gyula Valyi, Hungarian mathematician, and theoretical physicist (d. 1913). 1865 - Birthdate of Julio Garavito Armero, Colombian astronomer, mathematician, and engineer (d. 1920). 1871 - Birthdate of Federigo Enriques, Italian mathematician (d. 1946). 1871 - Birthdate of Gino Fano, Italian mathematician (d. 1952). 1874 - In a letter to Dedekind, Cantor asked “Can a surface (say a square that includes the boundary) be uniquely referred to a line (say a straight line segment that includes the endpoints) so that for every point on the surface there is a corresponding point of the line and, conversely, for every point of the line, there is a corresponding point of the surface? I think that answering this question would be no easy job, despite the fact that the answer seems so clearly to be 'no' that proof appears almost unnecessary." [117]. 1884 - Birthdate of Arnaud Denjoy, French mathematician (d. 1974). 1899 - Day of death of Ezra Otis Kendall, American professor, astronomer, and mathematician (b. 1818). 1900 - Minkowski responds to Hilbert (who had asked his opinion about possible topics for Hilbert's talk at the Second International Conference of Mathematicians in Paris) saying, “Most alluring would be the attempt at a look into the future and listing the problems on which mathematicians should try themselves during the coming century. With such a lecture, you could have people talking about your lecture decades later." [139]. 1909 - Birthdate of Stephen Cole Kleene, American mathematician, and computer scientist (d. 1994). 1913 - Birthdate of Max Erich (Eric) Reissner, German-American civil engineer, and mathematician (d. 1996). 1951 - Day of death of Joseph Fels Ritt, American mathematician (b. 1893). 1970 - Day of death of Max Born, German physicist, and mathematician, Nobel Prize laureate (b. 1882). 1987 - Day of death of Josif Zakharovich Shtokalo, Soviet mathematician, and historian of mathematics (b. 1897). 1994 - Day of death of David Robert Bates, Irish mathematician, and physicist (b. 1916).

January, 6 1561 - Birthdate of Thomas Fincke, Danish mathematician, and physicist (d. 1656).

6

Chapter One

1607 - Guidobaldo Marchese del Monte, Italian mathematician, philosopher, and astronomer (b. 1545). 1654 - Birthdate of Jakob Bernoulli, Swiss mathematician (d. 1705). 1689 - Day of death of Seth Ward, English bishop, mathematician, and astronomer (b. 1617). 1699 - Newton wrote to Flamsteed, probably alluding to Bernoulli's challenge of the brachistochrone problem, "I do not love... to be dunned and teezed by foreigners about Mathematical things..." [180]. 1807 - Birthdate of Joseph Petzval, German-Hungarian mathematician, and physicist (d. 1891). 1819 - Gauss, in a letter to his former student, Christian Ludwig Gerling, describes how he came to his construction of the 17-gon while still in bed. 1841 - Birthdate of Friedrich Otto Rudolf Sturm, German mathematician (d. 1919). 1883 - Birthdate of Francisco Jose Duarte, Venezuelan mathematician (d. 1972). 1886 - Adhémar Jean Claude Barré de Saint-Venant, French mechanician, and mathematician (b. 1797). 1900 - Gottlob Frege wrote to David Hilbert: "Suppose we know that the propositions (1) A is an intelligent being, (2) A is omnipresent, (3) A is omnipotent, together with all their consequences did not contradict one another; could we infer from this that there was an omnipotent, omnipresent, intelligent being?" [47]. 1918 - Day of death of Georg Cantor, German mathematician, and philosopher (b. 1845). 1920 - Day of death of Hieronymus Georg Zeuthen, Danish mathematician (b. 1839). 1922 - Day of death of Jakob Rosanes, Ukrainian-German mathematician, and chess player (b. 1842). 1930 - Day of death of Eduard Study, German mathematician (b. 1862). 1953 - Day of death of Giovanni Enrico Eugenio Vacca, Italian mathematician, and historian of science (b. 1872). 2018 - ij day (is about the 'golden ratio.' The next date that aligns is not for another hundred years, on 6 Jan 2118 (1/6/18).

January, 7 1451 - University of Glasgow was founded. 1610 - Galileo Galilei discovered the first three moons of Jupiter, or the Medicean Stars, as he called them.

January

7

1734 - Leonhard Euler and Katharina Gsell were married*. 1810 - Gauss wrote to his friend Bessel: "This winter I am teaching two courses for three listeners, of whom one is only modestly prepared, one scarcely modestly prepared, and the third lacks preparation as well as ability. These are the onera of a mathematical professor." 1859 - Birthdate of Marie Georges Humbert, French mathematician (d. 1921). 1871 - Birthdate of Émile Borel, French mathematician, and politician (d. 1956). 1886 - Nature Magazine quotes from Sylvester's inaugural address at Oxford related to his meeting with Poincaré: "What Briggs said of logarithmes may be said almost in the same words of the subject of this lecture, “This most excellent help to geometry which, being found out, one wonders nobody else fount it out before; when now known, it is so easy." 1893 - Day of death of Josef Stefan, Slovenian physicist, and mathematician (b. 1835). 1904 - Birthdate of Gordon Thomas Whyburn, American mathematician (d. 1969). 1907 - Birthdate of Raymond Edward Alan Christopher Paley, English mathematician (d. 1933). 1935 - Day of death of Ivan Vsevolodovich Meshchersky, Soviet mathematician (b. 1859). 1943 - Einstein replies to the January 3 letter of Barbara Lee Wilson: " Do not worry about your difficulties in Mathematics. I can assure you mine are still greater." 1947 - History of Mathematics department established at Brown University. 1974 - Day of death of Charles Alfred Coulson, British applied mathematician, theoretical chemist, and religious author (b. 1910). 1981 - Cathleen S. Morawetz became the first female to deliver the (54th) Gibbs Lecture entitled "The mathematical approach to the sound barrier." 1989 - Day of death of John Frank Adams, English mathematician (b. 1930). 1998 - Day of death of Richard Hamming, American mathematician. 2012 - Day of death of Herbert Wilf, American mathematician (b. 1931). 2016 - The 49th Mersenne prime 274 207 281 - 1 is discovered. *

Gottlob Juncker wrote a poem celebrating the wedding: Who would have thought it, That our Euler should be in love? Day and night he thought constantly,

8

Chapter One

How he wanted more to calculate numbers, His profound learned sense was free.

January, 8 1642 - Day of death of Galileo Galilei, Italian physicist, mathematician, astronomer, and philosopher (b. 1564). 1713 - A complete copy of the report Commercium Epistolicum D. Johannis Collins et aliorum de analysi promota (on the priority of Newton in discovering calculus) was laid before the Royal Society; and Newton, as president, ordered a copy to be delivered to each person of the Committee appointed for this purpose, to examine it before publication [22]. 1730 - In a letter to Goldbach, Euler admits that he is unable to do anything with Fermat's theorem [104]. He also first presents an integral representation of the interpolating function of the factorials. Today we would write this as . 1746 - Of his early reception in Berlin, Euler wrote to the Basel-born chaplain Johann Caspar Wettstein: “I can do just what I wish [in my research]... The king calls me his professor, and I think I am the happiest man in the world." 1816 - Sophie Germain did not appear at the awards ceremony for a prize offered by the Institut de France on the mathematical theory of elastic surfaces. 1829 - Birthdate of Heinrich Eduard Schroeter, German mathematician (d. 1892). 1852 - Birthdate of Giovanni Frattini, Italian mathematician (d. 1925). 1869 - The term "variety" arose as a translation by E. Beltrami (inspired by Gauss) of the German term "Mannigfaltigkeit" used by Riemann; nowadays, this term is usually translated as "manifold". The following correspondence, from Aldo Brigaglia to Steven Kleiman, contains more details: "I believe the usage of the word 'varieta' by Italian geometers arose from the (unpublished) Italian translation of Riemann's Habilitationsvortrag, which was later translated into French by J. Houel and published in the Italian journal Annali. Indeed, Beltrami wrote to Houel on 8 January 1869: 'J'ai traduit Mannigfaltigkeit par varieta, dans le sens de multitudo variarum rerum...' And later, on 14 February 1869, he wrote: 'Je croirais toujours convenable de traduire Mannigfaltigkeit par variété: j'ai remarque que Gauss, dans ses Mémoires sur les résidus biquadratiques appelle en latin varietas la même chose qui, dans les comptes-rendus rédiges par

January

9

lui-même en allemand dans les Gelehrte Anzeige, est désignée par Mannigfaltigkeit.' [13, 149]". 1888 - Birthdate of Richard Courant, German-American mathematician (d. 1972). 1889 - Dr. Herman Hollerith received patent no. 395,782 for the first tabulating machine [81]. 1917 - Birthdate of Leonard E. Gillman, American mathematician (d. 2009). 1924 - Birthdate of Paul Moritz Cohn, German-British mathematician (d. 2006). 1931 - Birthdate of Andrew Browder, American mathematician (d. 2019). 1939 - Birthdate of Alan Wilson, English mathematician. 1942 - Birthdate of Stephen W. Hawking, English theoretical physicist. 1947 - Norbert Wiener refused to address a Harvard symposium on computers because they were used “for war work” and announced he would not publish work "which may do damage in the hands of irresponsible militarists." 1952 - Birthdate of Peter McCullagh, Irish mathematician. 1968 - Day of death of Charles Loewner, American mathematician (b. 1893).

January, 9 1621 - J. Welles writes to Henry Briggs at Merton College in Oxford to offer help in the construction of logarithms for base ten [143]. 1757 - Day of death of Louis Bertrand Castel, French mathematician, and philosopher (b. 1688). 1799 - Day of death of Maria Gaetana Agnesi, Italian mathematician, and philosopher (b. 1718). 1839 - Thomas Henderson announced the first stellar parallax [75]. 1864 - Birthdate of Vladimir Steklov, Russian mathematician, and physicist (d. 1926). 1873 - Birthdate of Hans Blichfeldt, American mathematician (d. 1945). 1916 - Birthdate of Peter Twinn, English mathematician, and entomologist (d. 2004). 1922 - Graustein, at a meeting of the Harvard Division of Mathematics, read the letter by an official of an American "organization for the assistance of German and Austrian science" (probably the "Emergency Society for German and Austrian Science and Art"), asking for advice as to possible support for the Jahrbuch [158].

10

Chapter One

1930 - Birthdate of Jacob Theodore (Jack) Schwartz, American mathematician, and computer scientist (d. 2009). 1937 - Nature publishes a poetic version of the generalization to N dimensions of Descartes' theorem on Apollonian circles by Thorold Gosset* (see the June 20 entry for a poetic version of the original theorem). 1956 - The Soviet Union issued a stamp commemorating the tenth anniversary of the death of Alexei N. Krylov (1863-1945), mathematician, and naval architect.

1973 - Day of death of Harry Schultz Vandiver, American mathematician (b. 1882). 1975 - Day of death of Pyotr Novikov, Soviet mathematician (b. 1901). 1989 - Day of death of Marshall Harvey Stone, American mathematician (b. 1903). *

The Kiss Precise (generalized) by Thorold Gosset And let us not confine our cares To simple circles, planes and spheres, But rise to hyper ats and bends Where kissing multiple appears, In n-ic space the kissing pairs Are hyperspheres, and Truth declares, As n + 2 such osculate Each with an n + 1 fold mate The square of the sum of all the bends Is n times the sum of their squares.

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11

January, 10 1833 - Day of death of Adrien-Marie Legendre, French mathematician (b. 1752). 1844 - George Boole submitted his first paper to the Philosophical Transactions of the Royal Society. 1854 - Riemann presents a paper to the philosophical faculty at Gऺttingen in which he described the Euclidean plane geometry and solid geometry, respectively, as two- and three-dimensional examples of what we now call Riemann spaces with zero curvature. Saying that the space is curved, rather than flat or Euclidean, is another way of saying that the familiar properties of Euclidean geometry (such as the Pythagorean theorem) do not hold. He went on to suggest that all physical laws become simpler when expressed in higher dimensions [111]. 1875 - Birthdate of Issai Schur, German mathematician (d. 1941). 1891 - Birthdate of Heinrich Behmann, German mathematician (d. 1970). 1905 - Birthdate of Ruth Moufang, German mathematician (d. 1977). 1906 - Birthdate of Grigore Constantin Moisil, Romanian mathematician, computer pioneer (d. 1973). 1929 - Day of death of Karl Heun, German mathematician (b. 1859). 1938 - Birthdate of Donald Knuth, American computer scientist, and mathematician. 1941 - Day of death of Issai Schur, Belarusian-German mathematician (b. 1875). 1944 - Day of death of Thomas Scott Fiske, American mathematician (b. 1865). 1949 - Birthdate of Ann Watkins, American mathematician. 1984 - Day of death of Lancelot Stephen Bosanquet, British mathematician (b. 1903). 1988 - Postage stamps for Euclid and Newton are issued by the Maldive Islands.

12

Chapter One

January, 11 1545 - Birthdate of Guidobaldo Marchese del Monte, Italian mathematician, philosopher, and astronomer (d. 1607). 1672 - Newton presented his telescope to the Royal Society of London. At the same meeting, he was elected a Fellow of the Royal Society. 1707 - Birthdate of Vincenzo Riccati, Italian mathematician, and physicist (d. 1775). 1734 - Birthdate of Achille-Pierre Dionis du Sejour, French mathematician, astronomer, and politician (d. 1794). 1750 - Birthdate of Isaac Milner, British mathematician (d. 1820). 1757 - Day of death of Louis Bertrand Castel, French mathematician (b. 1688). 1775 - Gaspard Monge presented a memoir before the Académie des Sciences in which he made use of two planes of projection in his descriptive geometry. 1787 - Friedrich Wilhelm Herschel discovered the first two moons of Uranus, Titania and Oberon. 1825 - Birthdate of William Spottiswoode, English mathematician, and physicist (d. 1883). 1826 - Birthdate of Giuseppe Battaglini, Italian mathematician (d. 1894). 1845 - Birthdate of Albert Victor Backlund, Swedish mathematician, and physicist (d. 1912). 1858 - In his letter to Engels, Marx writes: “I am so damnedly held up by mistakes in calculation in the working out of the economic principles that out of despair I intend to master algebra promptly. Arithmetic remains foreign to me. But I am again shooting my way rapidly along the algebraic route." [113]. 1902 - Popular Mechanics magazine is published for the first time. 1903 - Day of death of Henry William Watson, English mathematician (b. 1827). 1911 - The "Kaiser Wilhelm Society for the Advancement of Science" was founded in Berlin. This became the present Max Planck Society. 1914 - Birthdate of George Brinton Thomas Jr., American mathematician (d. 2006). 1915 - The Times of London ran a column entitled “A Mathematical War" on the importance and use of mathematics in warfare [7]. 1941 - Day of death of Emanuel Lasker, German mathematician, philosopher, and chess player (b. 1868). 1947 - Day of death of Edward Ross, Scottish mathematician (b. 1881).

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13

1949 - Day of death of Torsten Carleman, Swedish mathematician (b. 1892). 2018 - Day of death of Michael Atiyah, British-Lebanese mathematician (b. 1929).

January, 12 1665 - Day of death of Pierre de Fermat, French mathematician, and lawyer (b. 1601). 1721 - John Hadley presented at a meeting of the Royal Society a reflecting telescope that magnified 200 times and was made according to Newton's plan. 1820 - Founding of the Royal Astronomical Society of England. 1828 - The term "equations modulaires" (modular equations) appears first in a letter written by Jacobi to Legendre. 1853 - Birthdate of Gregorio Ricci-Curbastro, Italian mathematician (d. 1925). 1906 - Birthdate of Kurt Hirsch, German-British mathematician (d. 1986). 1909 - Day of death of Hermann Minkowski, Lithuanian-German mathematician (b. 1864). 1915 - Birthdate of Herbert Ellis Robbins, American mathematician, and statistician (d. 2001). 1920 - Ramanujan wrote to Hardy about his discovery of mock theta functions [1]. 1946 - Day of death of Jean-Louis Loday, French mathematician (d. 2012). 1996 - Day of death of Joachim Nitsche, German mathematician (b. 1926). 1996 - Day of death of Bartel Leendert van der Waerden, Dutch mathematician, and historian of mathematics (b. 1903). 2004 - Day of death of Olga Ladyzhenskaya, Russian mathematician (b. 1921). 2018 - Day of death of Jean-Louis Koszul, French mathematician (b. 1921).

January, 13 1659 - Hendrik van Heuraet sent Frans van Schooten his rectification of the semi-cubical parabola. 1852 - William Rowan Hamilton wrote to August De Morgan: “I see that either you or I – but I hope it will be you – must write, sometime or

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Chapter One

another, a history of the square root of –1." (See January 18 entry for De Morgan's reply) [121]. 1868 - Birthdate of Donald McIntosh, Scottish mathematician (d. 1957). 1876 - Birthdate of Luther Pfahler Eisenhart, American mathematician (d. 1965). 1876 - Birthdate of Erhard Schmidt, German mathematician (d. 1959). 1900 - Birthdate of Gertrude Cox, American statistician (d. 1978). 1902 - Birthdate of Karl Menger, Austrian-American mathematician from the Vienna Circle (d. 1985). 1911 - A. V. Vasil'ev gave a lecture entitled "Non-Euclidean Geometry and the Non-Aristotelian Logic." This is his claim to the discovery of three-valued logics. 2013 - Day of death of Chia-Chiao Lin, Chinese-American mathematician (b. 1916).

January, 14 1650 - Descartes' lectures started in Stockholm during the coldest winter for over 60 years (the cold caused fatal pneumonia a few days later) [163]. 1679 - Day of death of Jacques de Billy, French mathematician (b. 1602). 1684 - Birthdate of Johann Matthias Hase, German mathematician, astronomer, and cartographer (d. 1742). 1687 - Day of death of Nicholas (Nikolaus) Mercator (b. 1620). 1742 - Day of death of Edmond Halley, English astronomer, geophysicist, mathematician, meteorologist, and physicist (b. 1656). 1753 - Day of death of George Berkeley, English mathematician (b. 1685). 1814 - Day of death of Charles Bossut, French mathematician (b. 1730). 1819 - Birthdate of James Cockle, English mathematician (d. 1895). 1858 - Arthur Cayley's A Memoir on the Theory of Matrices is read at the Royal Society. 1874 - Day of death of Ernst Wilhelm Grebe, German mathematician (b. 1804). 1887 - Birthdate of Hugo Steinhaus, Polish mathematician (d. 1972). 1898 - Day of death of Charles Lutwidge Dodgson (aka Lewis Carroll), English novelist, poet, and mathematician (b. 1832). 1901 - Birthdate of Alfred Tarski, Polish-American mathematician and philosopher (d. 1983). 1901 - Day of death of Charles Hermite, French mathematician (b. 1822). 1912 - Day of death of Arnold Droz-Farny, Swiss mathematician (b. 1856).

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15

1914 - Day of death of Benjamin Osgood Peirce, American mathematician (b. 1854). 1924 - Birthdate of Linards Eduardovich Reizins, Soviet mathematician (d. 1991). 1931 - Day of death of William Ernest Johnson, British logician (b. 1858). 1970 - Day of death of William Feller, Croatian-American mathematician (b. 1906). 1978 - Day of death of Kurt Gödel, Austrian-American mathematician and philosopher (b. 1906). 1980 - Robert J. Griess, Jr. announced that he had constructed the conjectured sporadic simple group F1 known as the monster. This group consists of 808,017,424,794,512,875,886,459,904,961,710,757, 005,754,368,000,000 square matrices each of size 196,883 by 196,883. This led to the completion of the classification of the finite simple groups. [62]. 1993 - Germany issued a postage stamp for the 350 years of Newton’s birthday.

2014 - Day of death of Milutin Dostanic, Serbian mathematician (b. 1958). 2020 - Zentralblatt MATH announces that zbMATH becomes an openaccess platform.

January, 15 1704 - Birthdate of Johann Castillon, Italian mathematician (d. 1791). 1717 - Birthdate of Matthew Stewart, Scottish geometer (d. 1785). 1790 - Day of death of John Landen, English mathematician (b. 1719). 1814 - Birthdate of Ludwig Schlai, Swiss mathematician (d. 1895). 1827 - Gauss wrote to his friend Schumacher that his ideas on nonEuclidean Geometry, published in a book review in 1816, were "besmirched with mud" by critics. 1850 - Birthdate of Sofia Kovalevskaya, Russian-Swedish mathematician and physicist (d. 1891). 1866 - The first Annual General Meeting of the London Mathematical Society was held [140].

Chapter One

16

1876 - Birthdate of Robert Bell, Scottish mathematician (d. 1963). 1883 - Birthdate of James Mercer, British mathematician (d. 1932). 1891 - The first bimagic square (where the numbers form a magic square, and when replaced by their squares, still form a magic square) was published in France [105], with only half of the numbers shown as a problem for the readers. The square is: 56

8 20

26

18 48

13 5

15

64 30

63 55

61

12

11

60 50

58 27

37

10 4

41

42 62

9 29

45 39

51

3

The solution was published on February 1, 1891. 1913 - Ramanujan sent his first letter to Hardy. In the pages that followed Ramanujan's one-page cover letter, he provides at least 11 more pages (at least two of which are now lost) containing technical results in topics ranging from work on infinite series and the gamma function, the distribution of prime numbers, hypergeometric series, continued fractions, elliptic functions, Bromwich's infinite series, divergent functions, a discussion of the Bernoulli numbers, and more. [172].

January

17

1918 - Noether gave a lecture before the Mathematical Society in Göttingen, entitled "Über Invarianten beliebiger Differentialausdrücke" (On invariants of arbitrary differential forms) [38]. 1925 - Birthdate of James Laurie Snell, American mathematician (d. 2011). 1945 - Day of death of Wilhelm Wirtinger, Austrian-German mathematician (b. 1865). 1950 - John Nash’s paper “Equilibrium Points in n-Person Games" was published by the National Academy of Sciences of the USA [122]. 1958 - Day of death of Aurel Wintner, Hungarian-American mathematician (d. 1903). 1973 - Day of death of Ivan Petrovsky, Soviet mathematician (b. 1901). 2001 - Wikipedia was formally launched on January 15, 2001, by Jimmy Wales and Larry Sanger, using the concept and technology of a wiki pioneered in 1995 by Ward Cunningham.

January, 16 1777 - Euler last attended a meeting of the St. Petersburg Academy on this date; later on, he was communicating with the Academy via assistants only [150]. 1801 - Birthdate of Thomas Clausen, Danish mathematician, and astronomer (d. 1885). 1826 - Niels Abel wrote to his former teacher Bernt Holmboe: "The divergent series are the invention of the devil." [93]. 1832 - Janos Bolyai's pioneering work The Absolutely True Science of Space was published and sent to Gauss for the second time. 1834 - Day of death of Jean Nicolas Pierre Hachette, French mathematician (b. 1769). 1865 - Founding of the London Mathematical Society. 1906 - Birthdate of Erich Kahler, German mathematician (d. 2000). 1910 - Richard Courant was scheduled to be examined for his Ph.D. by Hilbert in mathematics, Voight in physics, and Husserl in philosophy. 1913 - Srinivasa Ramanujan, a 23-year-old clerk in Madras, India, wrote G. H. Hardy, Professor at Cambridge, sending "a few examples of my theorems" and asking for advice. 1922 - Day of death of Pierre Rene Jean Baptiste Henri Brocard, French mathematician (b. 1845). 1925 - Birthdate of Germund Dahlquist, Swedish mathematician (d. 2005). 1939 - When around 1938-1939 voices were raised in the AMS that cast doubts on the objectivity of the abstracts in Zentralblatt, the

18

Chapter One

mathematician Arthur B. Coble wrote in a letter to G. D. Birkhoff: "Unless it would appear in the future that the reviews in the Zentralblatt are biased, I can see no reason why the Society should take any steps in the matter... I might add that the only recent criticism of a Zentralblatt review that I have heard was from an American author who complained that the American referee had completely missed the point of his article. In other words, even under the most favorable circumstances, the abstract journal will sometimes be at fault." [158].

January, 17 1492 - Birthdate of Adam Ries, German mathematician (d. 1559). 1574 - Birthdate of Robert Fludd, English physician, astrologer, and mathematician (d. 1637). 1618 - Day of death of Luca Valerio, Italian mathematician (b. 1552). 1670 - Day of death of Jean Leurechon, French Jesuit priest, and mathematician (b. 1591). 1775 - Day of death of Vincenzo Riccati, Italian mathematician, and physicist (b. 1707). 1798 - Birthdate of Isidore Auguste Marie Francois Xavier Comte, French philosopher, and mathematician (d. 1857). 1831 - Galois submitted his work on the theory of equations following the advice of Simeon Poisson. 1881 - Birthdate of Antoni Lomnicki, Polish mathematician (d. 1941). 1858 - Birthdate of Gabriel Xavier Paul Koenigs, French mathematician (d. 1931). 1905 - Birthdate of Dattaraya Ramchandra Kaprekar, Indian mathematician (d. 1986). 1913 - Birthdate of Shaun Wylie, British mathematician (d. 2009). 1954 - Day of death of Leonard Eugene Dickson, American mathematician (b. 1874). 1974 - Hewlett-Packard (HP) introduced the first programmable calculator, the HP-65. 2000 - Day of death of Eugene Ehrhart, French mathematician (b. 1906).

January, 18 1758 - Day of death of François Nicole, French mathematician (b. 1683). 1802 - Gauss read in the newspaper that Olbers had rediscovered Ceres. Gauss wrote to Olbers to get his observations, which was the beginning of their friendship.

January

19

1844 - John Thomas Graves communicated to Sir William Hamilton his theorem respecting sums of eight squares. This is the basis of his work on Octonions. 1852 - De Morgan replied to Hamilton's January 13th letter: “As for a history of the square root of –1, it would be no small job to do it well from the Hindus downwards." Neither Hamilton nor De Morgan ever wrote such a history... [121] 1856 - Birthdate of Luigi Bianchi, Italian mathematician (d. 1928). 1865 - In a letter to Hirst, two days after the founding of the London Mathematical Society, Bompas expressed the hope that “if you meet any mathematician now, you always ask him to join us" [140]. 1873 - Day of death of Pierre Charles François Dupin, French mathematician (b. 1784). 1880 - Birthdate of Paul Ehrenfest, Austrian and Dutch physicist, and mathematician (d. 1933). 1897 - The Indiana Pi Bill, aiming to change the value of ʌ to 3 (and several other numbers, it seems), was first introduced. 1901 - Birthdate of Ivan Petrovsky, Soviet mathematician (d. 1973). 1908 - Birthdate of Jacob Bronowski, Polish-English mathematician, historian, and television host (d. 1974). 1963 - Day of death of Edward Charles Titchmarsh, English mathematician (b. 1899). 1981 - Day of death of Rufus Philip Isaacs, American mathematician (b. 1914).

January, 19 1581 - Andreas Dudith wrote in a letter that observations of the comet of 1577 proved the Aristotelian explanation of comets being accidental exhalations of hot air from the earth that rise in the sublunar sphere is wrong. 1669 - Newton wrote to John Collins to provide a solution to a question about evaluating a series of fractions with a common numerator and denominators in an arithmetic sequence. 1730 - Euler replied to Goldbach with an outline of some of the integral methods he was using to analyze the form of the gamma function. He closed with a note: “I have been able to discover nothing about the observation noticed by Fermat [Fermat's conjecture that is prime]" [151]. 1755 - Day of death of Jean-Pierre Christin, French physicist, mathematician, and astronomer (b. 1683).

20

Chapter One

1833 - Birthdate of Alfred Clebsch, German mathematician (d. 1872). 1851 - Birthdate of Emanuel Czuber, Austrian mathematician (d. 1925). 1879 - Birthdate of Guido Fubini, Italian-American mathematician (d. 1943). 1889 - Oskar Bolza gave his first lecture to a non-German audience. More precisely, he started a series of twenty lectures at Johns Hopkins “on the theory of substitution groups and its application to algebraic equations." This was the first course on Galois theory in this country. 1908 - Birthdate of Aleksandr Gennadievich Kurosh, Soviet mathematician (d. 1971). 1911 - Birthdate of Garrett Birkhoff, American mathematician (d. 1996). 1912 - Birthdate of Leonid Kantorovich, Soviet mathematician and economist, Nobel Prize laureate (d. 1986). 1917 - Birthdate of Graham Higman, English mathematician (d. 2008). 1930 - Day of death of Frank P. Ramsey, British mathematician, philosopher, and economist (b. 1903). 1954 - Day of death of Theodor Kaluza, German mathematician, and physicist (b. 1885). 1984 - Apple introduced the Macintosh computer during a 60-second commercial aired during the Super Bowl. 1986 - The first IBM PC computer virus is released. 2000 - Day of death of Hedy Lamarr, Austrian-American actress, singer, and mathematician (b. 1913). 2001 - Day of death of Paul Olum, American mathematician (b. 1918). 2007 - Day of death of Asger Hartvig Aaboe, American historian of the exact sciences and mathematician (b. 1922). 2016 - The Great Internet Mersenne Prime Search reported the discovery of the new record largest prime number, 274,207,281 - 1.

January, 20 1526 - Birthdate of Rafael Bombelli, Italian mathematician (d. 1572). 1590 - Day of death of Giovanni Battista Benedetti, Italian mathematician (b. 1530). 1633 - Galileo left his home in Florence, Italy, to face the Inquisition in Rome. 1714 - Russian tsar Peter I (the Great) prohibited the dvorians (Russian aristocrats) from getting married unless they passed school courses in arithmetic and geometry. 1760 - Day of death of John Colson, English clergyman, and mathematician (b. 1680).

January

21

1775 - Birthdate of Andre-Marie Ampere, French physicist, and mathematician (d. 1836). 1831 - Birthdate of Edward John Routh, English mathematician (d. 1907). 1834 - Birthdate of William Watson, American mathematician (d. 1915). 1864 - Day of death of Giovanni Antonio Amedeo Plana, Italian astronomer, and mathematician (b. 1781). 1895 - Birthdate of Gabor Szego, Hungarian mathematician (d. 1985). 1904 - Birthdate of Renato Caccioppoli, Italian mathematician (d. 1959). 1939 - Birthdate of Chandra Wickramasinghe, Sri Lankan-English mathematician, astronomer, and biologist. 1971 - Day of death of Jan Arnoldus Schouten, Dutch mathematician (b. 1883). 2001 - Day of death of Crispin St. John Alvah Nash-Williams, BritishCanadian mathematician (b. 1932).

January, 21 1807 - The London Institution received a royal charter signed by King George III to "promote the diffusion of Science, Literature, and the Arts, by means of Lectures and Experiments, and by easy access to an extensive collection of books, both ancient and modern, in all languages." 1827 - Birthdate of Ivan Mikheevich Pervushin, Russian mathematician (d. 1900). 1844 - Augustus De Morgan wrote a confidential letter to Lady Noel Byron about her 28-year-old daughter, Augusta Ada King, the Countess of Lovelace, whom De Morgan had tutored as a private pupil in various areas of advanced mathematics for about eighteen months in the early 1840s. In his letter, while he was at pains to stress that “I have never expressed to Lady Lovelace my opinion of her as a student of these matters" [i.e. mathematics], De Morgan wrote: “I feel bound to tell you that the power of thinking on these matters which Lady L[ovelace] has always shown from the beginning of my correspondence with her has been something so utterly out of the common way for any beginner, man or woman, that this power must be duly considered by her friends, with reference to the question whether they should urge or check her obvious determination to try not only to reach but to get beyond the present bounds of knowledge." 1846 - Birthdate of Pieter Hendrik Schoute, Dutch mathematician (d. 1923).

22

Chapter One

1860 - Birthdate of David Eugene Smith, American mathematician, educator, and editor (d. 1944). 1874 - Birthdate of René-Louis Baire, French mathematician (d. 1932). 1882 - Birthdate of Pavel Florensky, Russian mathematician, and theologian (d. 1937). 1892 - Day of death of John Couch Adams, British mathematician, and astronomer (b. 1819). 1897 - Birthdate of Alexander Weinstein, Russian-American mathematician (d. 1979). 1915 - Birthdate of André Lichnerowicz, French mathematician (d. 1998). 1915 - Birthdate of Yuri Vladimirovich Linnik, Soviet mathematician (d. 1972). 1931 - Day of death of Cesare Burali-Forti, Italian mathematician (b. 1861). 1946 - Day of death of Harry Bateman, English mathematician (b. 1882). 1947 - Birthdate of Dorian M. Goldfeld, American mathematician. 1974 - Day of death of Arnaud Denjoy, French mathematician (b. 1884).

January, 22 1592 - Birthdate of Pierre Gassendi, French mathematician, astronomer, and philosopher (d. 1655). 1673 - Leibniz presents a calculation machine at the Royal Society. 1833 - In his notebook, Gauss introduces the linking number of two knots [175]. 1866 - Birthdate of Gustav de Vries, Dutch mathematician (d. 1934). 1867 - Thomson wrote to Helmholtz: “… a few days ago Tait showed me in Edinburgh a magnificent way of producing [vortex rings]. We sometimes can make one ring shoot through another, illustrating perfectly your description; when one ring passes near another, each is much disturbed and is seen to be in a state of violent vibration for a few seconds, till it settles again into its circular form… The vibrations make a beautiful subject for mathematical work.” 1874 - Birthdate of Leonard Eugene Dickson, American mathematician (d. 1954). 1880 - Birthdate of Frigyes Riesz, Hungarian mathematician (d. 1956). 1889 - Oskar Bolza gave his first lecture to a non-German audience (the first from his twenty lectures “On the theory of substitution groups and its application to algebraic equations") at Johns Hopkins University. 1904 - Day of death of George Salmon, Irish mathematician (b. 1819).

January

23

1921 - Day of death of Marie Georges Humbert, French mathematician (b. 1859). 1922 - Day of death of Camille Jordan, French mathematician, and engineer (b. 1838). 1929 - Birthdate of Walter Volodymyr Petryshyn (Vladimir Petryshin), Ukrainian mathematician. 1936 - Day of death of Ramaswami Aiyar, Indian mathematician (b. 1871). 1951 - Day of death of Harald August Bohr, Danish mathematician (b. 1887). 1987 - Day of death of Patrick du Val, British mathematician (b. 1903).

January, 23 1656 - Blaise Pascal wrote the first of his eighteen Provincial Letters. 1693 - Birthdate of Georg Bernhard Bilfinger, German philosopher, mathematician, statesman (d. 1750). 1719 - Birthdate of John Landen, English mathematician (d. 1790). 1731 - Euler wrote to Schumacher: “It seems to me that it is very disgraceful for me, that I, who up to now have had more salary than the others, shall now be set equal to them... I think that the number of those who have carried [mathematics] as far as I is pretty small in the whole of Europe, and none of them will come for 1000 rubles." 1785 - Day of death of Matthew Stewart, Scottish mathematician (b. 1717). 1806 - Birthdate of Ernst Ferdinand Adolf Minding, Russian mathematician (d. 1885). 1846 - Birthdate of Nikolay Umov, Russian physicist, and mathematician (d. 1915). 1853 - Day of death of Kazimierz Zorawski, Polish mathematician (b. 1853). 1862 - Birthdate of David Hilbert, Russian-German mathematician (d. 1943). 1880 - Birthdate of Friedrich Riesz, Hungarian mathematician (b. 1880). 1883 - The idea of creating the Edinburgh Mathematical Society was announced: A.Y. Fraser and A.J.G. Barclay (mathematics teachers) together with C.G. Knott, the professor of physics at the University of Edinburgh, sent out a letter dated 23 January 1883: “…to gentlemen in Edinburgh, in Cambridge, and throughout Scotland generally..." The letter asked for support for their project: “It is proposed to establish, primarily in connection with the University, a Society for the mutual

24

Chapter One

improvement of its members in the Mathematical Sciences, pure and applied. Amongst the methods by which this object might be attained may be mentioned: Reviews of works both British and Foreign, historical notes, discussions of new problems or new solutions, a comparison of the various systems of teaching in different countries, or any other means tending to the promotion of mathematical Education." 1913 - Andrei Andreyevich Markov addressed the Imperial Academy of Sciences in St. Petersburg, reading a paper “An example of statistical investigation of the text Eugene Onegin concerning the connection of samples in chains" [72]. 1924 - Birthdate of Michael James Lighthill, British mathematician (d. 1998). 1946 - Birthdate of Boris Berezovsky, Russian-English businessman, and mathematician (d. 2013). 1947 - Birthdate of Peter Jephson Cameron, Australian mathematician. 2005 - The first episode of Numb3rs airs on CBS. The show is a standard police procedural with the twist that a mathematics professor is brought on as a consultant to help the FBI solve cases.

2017 - Russian schoolboy, Andrey S. Shchebetov, announced on his website that he had found a sequence of the first 126 numbers (125 of them never reported before) that take exactly 261 steps to reach a 119digit palindrome. This sequence was published in OEIS as A281506. This sequence started with 1,186,060,307,891,929,990 – by then the only publicly known number found by Jason Doucette back in 2005 (see Nov. 30 entry).

January

25

January, 24 1640 - John Pell wrote to Marin Mersenne that Thomas Harriot had found the law of refraction, now known as Snell's law. 1672 - In a letter from John Wallis to Oldenberg, he discusses his joint solution with Huygens of the area between the cissoid and its asymptote. 1679 - Birthdate of Christian Freiherr von Wolff, German philosopher, and mathematician (d. 1754). 1798 - Birthdate of Karl George Christian von Staudt, German mathematician (d. 1867). 1814 - Birthdate of John Colenso, British mathematician (d. 1883). 1863 - Birthdate of August Adler, Czech and Austrian mathematician (d. 1923). 1865 - Day of death of Samuel Hunter Christie, British mathematician (b. 1784). 1891 - Birthdate of Abram Samoilovitch Besicovitch, Russian-British mathematician (d. 1970). 1894 - Cantor wrote to Hermite that “in the realm of the spirit," mathematics had no longer been “the essential love of his soul" for more than 20 years [31]. 1895 - Karl Pearson first uses the term “Binomial Distribution" in Contributions to the Mathematical Theory of Evolution II. Skew Variation in Homogeneous Material, presented to the Royal Society of London. 1902 - Birthdate of Oskar Morgenstern, German-American economist, and mathematician (d. 1977). 1912 - Birthdate of Nils Aall Barricelli, Norwegian-Italian mathematician (d. 1993). 1914 - Birthdate of Vladimir Petrovich Potapov, Soviet mathematician (d. 1980). 1930 - Day of death of Adolf Kneser, German mathematician (b. 1862). 1931 - Birthdate of Lars Hörmander, Swedish mathematician (d. 2012). 1955 - Day of death of Percy John Heawood, British mathematician (b. 1861). 1982 - Day of death of Karol Borsuk, Polish mathematician (b. 1905). 1988 - Day of death of Werner Fenchel, German-Danish mathematician (b. 1905).

January, 25 1635 - Cardinal Richelieu widens the scope of the Paris literary union (established 1625) to the Académie française.

26

Chapter One

1736 - Birthdate of Joseph-Louis Lagrange, Italian-French mathematician, and astronomer (d. 1813). 1812 - Birthdate of William Shanks, English mathematician (d. 1882). 1855 - Birthdate of Karl Friedrich Wilhelm Rohn, German mathematician (d. 1920). 1843 - Birthdate of Karl Hermann Amandus Schwarz, German mathematician (d. 1921). 1870 - Birthdate of Niels Fabian Helge von Koch, Swedish mathematician (d. 1924). 1894 - Day of death of Emil Weyr, Austrian mathematician (b. 1848). 1916 - Birthdate of Frederick Valentine Atkinson, British mathematician (d. 2002). 1916 - Birthdate of Ernest Roland Duncan, New Zealand-born mathematician, Australian headmaster, and American professor (d. 1990). 1918 - F. Klein, at a regular meeting of the Königliche Gesellschaft der Wissenschaften (Royal Society for the Sciences), presented a paper with the title “Frl. E. Noether, Über Differentialformen beliebigen Grades" (On differential forms of arbitrary degree) [38]. 1935 - Day of death of Alfred Loewy, German mathematician (b. 1873). 1973 - Day of death of Wilhelm Ljunggren, Norwegian mathematician (b. 1905). 1995 - Day of death of Stephen Cole Kleene, American mathematician, computer scientist (b. 1909). 1995 - Day of death of Albert William Tucker, Canadian-American mathematician (b. 1905). 2008 - Croatia issued a postage stamp on the 250th anniversary of the Arithmetika Horvatszka, the first arithmetic book in the Croatian language.

2013 - Curtis Cooper of Central Missouri University discovered the 48th known Mersenne prime, 257 885 161 - 1, a 17,425,170-digit number*. 2014 - Day of death of Heini Halberstam, Czech-English mathematician (b. 1926).

January

27

* Helen Arney wrote a Christmas song called Mersenne 48 [6] (released December 30, 2013) In January Professor Curtis Cooper found a number Not an ordinary number, but a number thats humungous. . . ... so I don't want your mulled pies and you can keep your minced wine All I want for Christmas is the world's biggest prime! It's 2 to the power of 57885161 (minus one) Mersenne 48 – the perfect gift for everyone So give me oh give me this Christmas time A seventeen million digit Christmas prime It's rarer than a cracker joke that actually makes you laugh As useful as a pair of roller skates for a giraffe If I had one I could do whatever I like with it Well, anything I want apart from dividing it. . . except by itself and one... 2 to the power of 57885161 (minus one) And if I tried to sing it in hours I'd need one thousand one hundred and eighty-one So give me oh give me this Christmas time A seventeen million digit Christmas prime You can type it and text it or write it and post it, Bake it in bread and then slice it and toast it If you can't calculate it and send it in time I'll accept 16 million decimal places of Pi So give me oh give me this Christmas time A seventeen million digit Christmas prime (One more recursion!) Give me give oh give me this Christmas time A seventeen million digit Christmas prime

January, 26 1126 - Adelard of Bath translated al-Khwarizmi's Astronomical Tables into Latin. 1630 - Day of death of Henry Briggs, English mathematician, and astronomer (b. 1556). 1678 - Philippe de La Hire nominated to the Academy of Sciences in Paris. 1697 - Isaac Newton received and solved Jean Bernoulli's brachistochrone problem. 1697 - Day of death of Georg Mohr, Danish mathematician (b. 1640).

28

Chapter One

1750 - Daniel Bernoulli writes to Euler to complain that d'Alembert's work on the wind had no experimental basis [70]. 1862 - Birthdate of Eliakim Hastings Moore, American mathematician (d. 1932). 1870 - Birthdate of Helge von Koch, Swedish mathematician (d. 1924). 1895 - Day of death of Arthur Cayley, English mathematician (b. 1825). 1929 - Day of death of Constantin Marie Le Paige, Belgian mathematician (b. 1852). 1934 - Birthdate of Lionel March, British mathematician, architect, and digital artist (d. 2018). 1942 - Day of death of Felix Hausdorff, German mathematician (b. 1868). 1945 - Birthdate of John Henry Coates, British mathematician. 1946 - Birthdate of Susan Friedlander, American mathematician. 1947 - Birthdate of Andreas P Huhn, Hungarian mathematician (d. 1985). 1984 - The Fredkin Foundation announced it would award a prize of $100,000 for the first major mathematical discovery made by a computer. 2007 - Day of death of Gregory Maxwell Kelly, Australian mathematician (b. 1930). 2020 - Day of death of Louis Nirenberg, Canadian-born American mathematician (b. 1925).

January, 27 1701 - Birthdate of Charles-Marie de La Condamine, French naturalist, and mathematician (d. 1774). 1715 - Day of death of Caspar (or Kaspar) Neumann, German professor, and clergyman (b. 1648). 1823 - Day of death of Charles Hutton, English mathematician (b. 1737). 1895 - Day of death of James Cockle, English mathematician (b. 1819). 1832 - Birthdate of Charles Lutwidge Dodgson (Lewis Carroll), English novelist, poet, and mathematician (d. 1898). 1860 - Day of death of Janos Bolyai, Romanian-Hungarian mathematician (b. 1802). 1885 - Birthdate of Franciszek Leja, Polish mathematician (d. 1979). 1903 - Birthdate of Howard Percy Robertson, American mathematician (d. 1961). 1947 - Day of death of Alexander Brown, South African mathematician (b. 1877). 1965 - Day of death of Philip Franklin, American mathematician (b. 1898).

January

29

1972 - Day of death of Richard Courant, German-American mathematician (b. 1888). 1993 - Day of death of Nils Aall Barricelli, Norwegian-Italian mathematician (b. 1912). 1995 - Birthdate of Raphael Mitchel Robinson, American mathematician (b. 1911). 2001 - Day of death of Robert Alexander Rankin, Scottish mathematician (b. 1915). 2008 - Day of death of Irene Anne Stegun, American mathematician (b. 1919). 2009 - Tim Gowers began his experiment on the possibility of "massively collaborative mathematics" [56].

January, 28 1540 - Birthdate of Ludolph van Ceulen, German-Dutch mathematician (d. 1610). 1608 - Birthdate of Giovanni Alfonso Borelli, Italian mathematician (d. 1679). 1699 - Gottfried Leibniz was elected as the first foreign member of the French Academy. 1701 - Birthdate of Charles Marie de La Condamine, French mathematician, and geographer (d. 1774). 1724 - The Royal Academy of Sciences was founded in St. Petersburg, Russia, by Peter the Great. 1741 - The first mention of the pentagonal theorem is in a letter from Daniel Bernoulli to Euler. Bernoulli replies to a (lost) letter from Euler writing, "The other problem, to transform (1 - x)(1 - x2) … into 1 - x x2 + x5 + …, follows easily by induction, if one multiplied many factors. The remainder of the series I do not see. This can be shown in a most pleasant investigation, together with tranquil pastime and the endurance of pertinacious labor, all three of which I lack." [95] 1888 - Birthdate of Louis Joel Mordell, British mathematician (d. 1972). 1889 - Day of death of Joseph-Emile Barbier, French astronomer, and mathematician (b. 1839). 1892 - Birthdate of Carlo Emilio Bonferroni, Italian mathematician (d. 1960). 1902 - Carnegie Institute was founded. 1910 - Day of death of Alfredo Capelli, Italian mathematician (b. 1855). 1911 - Birthdate of Robert Schatten, American mathematician (d. 1977).

30

Chapter One

1924 - Birthdate of Wilhelm Paul Albert Klingenberg, German mathematician (d. 2010). 1946 - Day of death of Dmitrii Matveevich Sintsov, Soviet mathematician (b. 1867). 1950 - Day of death of Nikolai Luzin, Soviet mathematician (b. 1883). 1954 - Day of death of Ernest Benjamin Esclangon, French astronomer, and mathematician (b. 1876). 2009 - Day of death of William Moser, Canadian mathematician (b. 1927).

January, 29 1697 - Isaac Newton received two challenge problems from Johann Bernoulli, one of which was the Brachistochrone Problem published in Acta eruditorum the previous June and addressed "to the shrewdest mathematicians in the world." The next day, Newton posted his solution to the Royal Society. When Bernoulli saw the anonymous solution, he recognized it as "ex ungue leonem" (as the lion is recognized by his paw). [180] 1700 - Birthdate of Daniel Bernoulli, Swiss mathematician, and physicist (d. 1782). 1715 - Day of death of Bernard Lamy, French mathematician, and theologian (b. 1640). 1747 - d'Alembert expressed doubt that the logarithms of negative real numbers are imaginary. [30] 1761 - Birthdate of Jose de Mendoza y Rios, Spanish mathematician (d. 1816). 1810 - Birthdate of Ernst Kummer, Polish-German mathematician (d. 1893). 1824 - T. Jefferson wrote to Patrick K. Rogers on the abandonment of fluxional calculus at Cambridge in favor of the Leibnizian notation: "The English generally have been very stationary in later times, and the French, on the contrary, so active and successful, particularly in preparing elementary books, in mathematics and natural sciences, that those who wish for instruction without caring from what nation they get it, resort universally to the latter language. Besides the earlier and invaluable works of Euler and Bezout, we have latterly that of Lacroix in mathematics, of Legendre in geometry, ... to say nothing of the many detached essays of Monge and others, and the transcendent labors of Laplace. I am informed by a highly instructed person recently from Cambridge that the mathematicians of that institution, sensible of being in the rear of those of the continent, and ascribing the cause

January

31

much to their long-continued preference of the geometrical over the analytical methods, which the French have so long cultivated and improved, have now adopted the latter; and that they have also given up the fluxionary for the differential calculus." [45] 1846 - Birthdate of Karol Olszewski, Polish chemist, mathematician, and physicist (d. 1915). 1888 - Birthdate of Sydney Chapman, English mathematician, and geophysicist (d. 1970). 1905 - Day of death of Robert Tucker, English mathematician (b. 1832). 1928 - Birthdate of Joseph Kruskal, American mathematician, and computer scientist (d. 2010). 1970 - Yuri Matiyasevich presents the proof of Hilbert's 10th Problem. [114] 1984 - Day of death of John Macnaghten Whittaker I, British mathematician (b. 1905). 1999 - Day of death of Viktor Aleksandrovich Gorbunov, Soviet mathematician (b. 1950).

January, 30 1619 - Birthdate of Michelangelo Ricci, Italian mathematician (d. 1682). 1755 - Birthdate of Nikolai Fuss, Swiss mathematician (d. 1826). 1805 - Birthdate of Edward Sang, Scottish mathematician (d. 1890). 1830 - In a letter to Laplace, Gauss writes about a "curious problem" that he had been working on for twelve years. He gives the limiting value of the frequency of distribution of positive integers in the continued fraction of a random number (now called the Gauss-Kuzmin distribution) as log2(1+ x). 1865 - Birthdate of Georg Landsberg, German mathematician (d. 1912). 1884 - Sofia Kovalevskaya gives her first university lecture. This was the first regular lecture by a woman at a research institution in any field in modern times. [94] 1897 - Mary Frances Winston, the first American female with a PhD obtained from a German university, was elected to membership in the American Mathematical Society. 1918 - Birthdate of Heinz Rutishauser, Swiss mathematician (d. 1970). 1948 - Birthdate of Miles Reid, English mathematician. 1954 - Day of death of Gino Benedetto Loria, Italian historian of mathematics (b. 1862). 1977 - Day of death of Harry Clyde Carver, American mathematician (b. 1890).

32

Chapter One

1982 - Day of death of Viktor Mikhaylovich Glushkov, Soviet mathematician (b. 1923). 1992 - Day of death of Dom George Frederick James Temple, English mathematician (b. 1901). 1998 - Day of death of Samuel Eilenberg, Polish-American mathematician (b. 1913). 2004 - Item number MR2000000 was added to MathSciNet.

January, 31 1632 - Day of death of Jost Bürgi, Swiss clockmaker, and mathematician (b. 1552). 1715 - Birthdate of Giovanni Francesco Fagnano dei Toschi, Italian mathematician (d. 1797). 1802 - Gauss was elected a corresponding member of the St. Petersburg Academy of Sciences. 1854 - Birthdate of David Emmanuel, Romanian mathematician (d. 1941). 1886 - Birthdate of George Neville Watson, English mathematician (d. 1965). 1903 - Day of death of Norman Macleod Ferrers, English mathematician (b. 1829). 1913 - G.H. Hardy received a parcel of papers from Madras, India, which included a cover letter from Srinivasa Ramanujan. This letter included an introduction to Ramanujan and his precarious situation, a claim about the domain of the gamma function, and a claim about the distribution of prime numbers [172] (see Jan. 16 entry). 1914 - Birthdate of Lev Arkad'evich Kaluznin, Soviet mathematician (d. 1990). 1928 - Birthdate of Heinz Bauer, German mathematician (d. 2002). 1934 - Day of death of Duncan MacLaren Young Sommerville, New Zealand mathematician (b. 1879). 1939 - Hewlett-Packard was founded. 1939 - Joseph Ehrenfried Hofmann was appointed as a professor of the history of mathematics at the University of Berlin. 1945 - Birthdate of Persi Warren Diaconis, American mathematician, and former professional magician. 1973 - Day of death of Noel Bryan Slater, British mathematician, and physicist (b. 1912). 1995 - Day of death of George Robert Stibitz, American mathematician (b. 1904).

CHAPTER TWO FEBRUARY

February, 1 1561 - Birthdate of Henry Briggs, British mathematician (d. 1630). 1634 - Descartes writes to Father Marin Mersenne and explains that he had retracted his book "The World," which supported the Copernican theory, “thus losing four years of my work in order to give full obeisance to the Church... I do not dare to publish my own sentiment." 1673 - G. Leibniz exhibited his calculating machine to the Royal Society. 1840 - Birthdate of William Allen Whitworth, English mathematician, and priest (d. 1905). 1847 - Birthdate of Eduardo Torroja Caballe, Spanish mathematician (d. 1918). 1890 - Birthdate of Jovan Karamata, Serbian mathematician (d. 1967). 1891 - The solution to the first known bimagic square (the numbers form a magic square, and when the numbers are replaced by their squares, they still form a magic square) is published [106]. This solution is 56 33 26 19 15 6 61 44

34 20 43 5 25 55 16 62

8 54 13 35 63 17 42 28

57 48 23 30 2 11 52 37

18 7 64 53 41 36 27 14

47 29 38 12 24 58 1 51

9 59 4 46 50 32 39 21

13 10 49 60 40 45 22 3

1894 - "Nature" magazine publishes Newcomb's speech to the New York Mathematical Society (given on 28 December 1893) with comments on the fourth dimension [16]. 1900 - Birthdate of John Charles Burkill, English mathematician (d. 1993).

34

Chapter Two

1903 - Day of death of Sir George Stokes, Anglo-Irish physicist, mathematician, and politician (b. 1819). 1905 - Birthdate of Ernst Carl Gerlach Stueckelberg, Swiss mathematician, and physicist (d. 1984). 1916 - Birthdate of George Whitelaw Mackey, American mathematician (d. 2006). 1938 - Hans Fitting submitted his last paper titled "Beiträge zur Theorie der Gruppen endlicher Ordnung," which was published in "Jahresbericht der Deutschen Mathematiker-Vereinigung." In this paper, Fitting proved the famous theorem on the nilpotency of the product of two nilpotent normal subgroups. 1970 - Day of death of Alfred Renyi, Hungarian mathematician (b. 1921). 1976 - Day of death of Werner Karl Heisenberg, German physicist, and philosopher (b. 1901).

February, 2 1522 - Birthdate of Lodovico Ferrari, Italian mathematician (d. 1565). 1612 - Day of death of Christopher Clavius, Italian mathematician, leader of the Gregorian calendar reform. 1704 - Day of death of Guillaume de l'Hôpital, French mathematician (b. 1661). 1724 - Goldbach posed a variant of the Diophantine problem (see December 18, 1723 entry) to Daniel Bernoulli: given one number, to find three more so that the pairwise products of any two, plus 1, were squares [20]. 1766 - Birthdate of Timofei Fedorovich Osipovsky, Russian mathematician, physicist, astronomer, and philosopher (d. 1832). 1768 - Day of death of Charles-Étienne Camus, French mathematician (b. 1699). 1768 - Day of death of Robert Smith, English mathematician (b. 1689). 1786 - Birthdate of Jacques Philippe Marie Binet, French mathematician, physicist, and astronomer (d. 1856). 1793 - Birthdate of William Hopkins, English mathematician, and geologist (d. 1866). 1823 - Gauss completes the "Gauss-Markov Theorem" [142]. 1842 - Birthdate of Julian Sochocki, Polish-Russian mathematician (d. 1927). 1845 - Möbius replied to Grassmann (see October 10, 1844 entry) that he is not able to review Grassmann's book Ausdehnungslehre but he had

February

35

contacted a mathematician named Drobisch and hoped that he would write a review [36]. 1849 - Birthdate of Leopold Bernhard Gegenbauer, Austrian mathematician (d. 1903). 1860 - Birthdate of August Gutzmer, German mathematician (d. 1924). 1881 - Birthdate of Gustav Herglotz, German mathematician (d. 1953). 1882 - Birthdate of Joseph Henry Maclagan Wedderburn, ScottishAmerican mathematician (d. 1948). 1883 - Preliminary meeting of the Edinburgh Mathematical Society. 1893 - Birthdate of Cornelius Lanczos, Hungarian mathematician, and physicist (d. 1974). 1896 - Birthdate of Kazimierz Kuratowski*, Polish mathematician, and logician (d. 1980). 1897 - Birthdate of Gertrude Blanch, Russian-American mathematician (d. 1996). 1903 - Birthdate of Bartel van der Waerden, Dutch mathematician, and historian of mathematics. 1911 - Day of death of Hugues Charles Robert Meray, French mathematician (b. 1835). 1950 - Day of death of Constantin Carathéodory, Greek mathematician (b. 1873). 1965 - Day of death of George Neville Watson, English mathematician (b. 1886). 1970 - Day of death of Bertrand Russell, English mathematician, and philosopher, Nobel Prize laureate (b. 1872). 1974 - Day of death of Imre Lakatos, Hungarian-English mathematician, and philosopher (b. 1922). 2005 - Day of death of Edward Maitland Wright, English mathematician (b. 1906). 2011 - Day of death of Rodney Hill, English mathematician (b. 1921). 2018 - Satellogic, a high-resolution Earth observation imaging and analytics company, launched a uSat type micro-satellite named in honor of Maryam Mirzakhani. *

A dedication of Frank Harary's book [71] is To KASIMIR KURATOWSKI, Who gave K5 and K3;3 To those who thought planarity Was nothing but topology.

36

Chapter Two

February, 3 1673 - Leibniz writes to Oldenburg describing his "accidental" meeting with the mathematician John Pell at the house of Robert Boyle. They discussed infinite series [103]. 1692 - De la Pryme recorded in his diary that Newton had a fire in his study that destroyed the manuscript of his Optics. 1737 - Day of death of Tommaso Ceva, Italian mathematician (b. 1648). 1774 - Birthdate of Karl Brandan Mollweide, German mathematician (d. 1825). 1806 - Lagrange presented an attempt to prove Euclid's parallel postulate to the mathematical and physical classes of the Institute National [59]. 1862 - Day of death of Jean-Baptiste Biot, French physicist, astronomer, and mathematician (b. 1774). 1893 - Birthdate of Gaston Julia, Algerian-French mathematician (d. 1978). 1898 - Birthdate of Pavel Urysohn, Soviet mathematician (d. 1924). 1905 - Birthdate of Arne Beurling, Swedish-American mathematician (d. 1986). 1923 - Day of death of Adam Wilhelm Siegmund Gunther, German mathematician (b. 1848). 1929 - Day of death of Agner Krarup Erlang, Danish mathematician, and engineer (b. 1878). 1943 - Day of death of Earle Raymond Hedrick, American mathematician (b. 1876). 1951 - Birthdate of Steven George Krantz, American mathematician. 1956 - Day of death of Émile Borel, French mathematician (b. 1871). 1957 - Birthdate of Eric Lander, American mathematician, geneticist. 1959 - Gödel wrote to Schilpp: "However, I feel I owe you an explanation of why I did not send my paper earlier. The fact is that I have completed several different versions, but none of them satisfies me. It is easy to allege very weighty and striking arguments in favor of my views, but a complete elucidation of the situation turned out to be more difficult than I had anticipated, doubtless as a consequence of the fact that the subject matter is closely related to, and partly identical with, one of the basic problems of philosophy, namely the question of the objective reality of concepts and their relations. On the other hand, because of widely held prejudices, it may do more harm than good to publish half-done work." [110].

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37

February, 4 1615 - Day of death of Giambattista della Porta, Italian playwright, scientist, and mathematician (b. 1535). 1774 - Day of death of Charles Marie de La Condamine, French mathematician, and geographer (b. 1701). 1895 - Day of death of Thomas Kirkman, British self-educated mathematician (b. 1806). 1921 - Birthdate of Lotfi Zadeh, Iranian-American mathematician, computer scientist, and founder of fuzzy logic (d. 2017). 1925 - Birthdate of Christopher Zeeman, English mathematician (d. 2016). 1926 - Birthdate of Jaroslav Hajek, Czech mathematician (d. 1974). 1974 - Day of death of Satyendra Nath Bose, Indian physicist, mathematician (b. 1894). 2004 - Mark Zuckerberg founded Facebook for his fellow students at Harvard University. 2004 - Day of death of Valentina Mikhailovna Borok, Soviet-Ukrainian mathematician (b. 1931).

February, 5 1608 - Birthdate of Gaspar Schott, German mathematician, and physicist (d. 1666). 1676 - I. Newton wrote to Hooke: “What Descartes did was a good step... If I have seen further it is by standing on the shoulders of Giants." 1772 - Laplace presented his first probability memoir to the Académie des Sciences. 1797 - Birthdate of Jean-Marie-Constant Duhamel, French mathematician, and physicist (d. 1872). 1835 - A ceremony to honor “The Genius and Discoveries of Sir Isaac Newton" was organized by the citizens of Lincolnshire. 1840 - The American Statistical Association held its first annual meeting in Boston. 1850 - D. D. Parmalee issued a patent (US Patent # 7074) for the first keydriven adding machine. 1897 - The Indiana State House legislature presented Bill No.246 which effectively gave ʌ the value of 3.2. 1907 - Birthdate of Wilhelm Magnus, German-American mathematician (d. 1990). 1930 - Birthdate of Kazimierz Urbanik, Polish mathematician (d. 2005).

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Chapter Two

1937 - Birthdate of Alar Toomre, Estonian-American astronomer, and mathematician. 1939 - Day of death of Gheorghe Titeica, Romanian mathematician (b. 1873). 1959 - The USSR issued a stamp on the 350th anniversary of Torricelli’s birth.

1980 - Day of death of Nachman Aronszajn, Polish-American mathematician (b. 1907). 1988 - Day of death of Dorothy Lewis Bernstein, American mathematician (b. 1914). 1997 - Day of death of Frederick Justin Almgren, American mathematician (b. 1933).

February, 6 1465 - Birthdate of Scipione del Ferro, Italian mathematician (d. 1526). 1582 - Birthdate of Mario Bettinus, Italian mathematician, astronomer, and philosopher (d. 1657). 1612 - Birthdate of Antoine Arnauld, French mathematician, theologian, and philosopher (d. 1694). 1612 - Day of death of Christopher Clavius, German mathematician, and astronomer (b. 1538). 1672 - Newton wrote to Henry Oldenburg about his optical theories, and Oldenburg published them a few days later in the Philosophical Transactions. 1695 - Birthdate of Nicolaus II Bernoulli, Swiss-Russian mathematician (d. 1726). 1766 - Euler read his paper "A New Method for Comparing the Observation of the Moon to Theory" to the Berlin Academy. The paper proposes numerical techniques for approximating a body's velocity and acceleration [150]. 1848 - Birthdate of Adam Wilhelm Siegmund Gunther, German mathematician (d. 1923).

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39

1916 - Birthdate of John Crank, English mathematician, and physicist (d. 2006). 1930 - Kurt Gödel received his Ph.D. from the University of Vienna for a dissertation that showed the completeness of first-order logic (every valid first-order formula is provable). 1940 - Birthdate of Petr Hajek, Czech mathematician. 1965 - Day of death of Ernst Erich Jacobsthal, German mathematician (b. 1882). 1992 - Day of death of Caius Jacob, Romanian mathematician (b. 1912). 1998 - F.Y.R.O.M. (Former Yugoslav Republic of Macedonia) issued a stamp to commemorate the 2500th anniversary of the death of Pythagoras.

February, 7 E-Day: The holiday gets its name from Euler's number, which starts with 2.7182818. It is celebrated each year, but 2018 was extra special as it included the first four digits in the date — something that won't happen for another 100 years. 1664 - Leibniz earned his master's degree in Philosophy. 1816 - Birthdate of Jean Frenet, French mathematician (d. 1900). 1877 - Birthdate of G. H. Hardy, English mathematician, and geneticist (d. 1947). 1883 - Birthdate of Eric Temple Bell, Scottish mathematician, and mathematical writer. 1885 - David Hilbert earned his Ph.D. from the University of Konigsberg. 1897 - Birthdate of Maxwell Herman Alexander Newman, British mathematician, and codebreaker (d. 1984). 1898 - Birthdate of Charles Wilderman Trigg, American engineer, and mathematician (d. 1989). 1905 - Birthdate of Lucien Alexandre Charles René de Possel, French mathematician, one of the founders of the Bourbaki group (d. 1974). 1948 - Day of death of Poul Heegaard, Danish mathematician (b. 1871).

40

Chapter Two

1969 - Day of death of Hans Rademacher, German-American mathematician (b. 1892). 1975 - Hungary issued a stamp commemorating the bicentenary of the birth of Farkas Bolyai (1775-1856).

2012 - In an interview, Brad Pitt said, "I find all of my performances come down to mathematics in a sense — how do you approach the problem of this character? Sometimes I crack that problem, sometimes I don't." [120]

February, 8 120 - Birthdate of Vettius Valens, Greek astronomer, mathematician, and astrologer (probable d. 175). 412 - Birthdate of Proclus Diadochus, Greek mathematician, and philosopher (d. 485). 1587 - Mary, Queen of Scots, was beheaded after Sir Francis Walsingham conducted a frequency count on Mary's cipher, read her message, and uncovered her plot to assassinate Elizabeth I, Queen of England. 1627 - Birthdate of Jonas Moore, English mathematician, and physicist (d. 1679). 1672 - Isaac Newton's first paper on optics was read before the Royal Society in London. 1700 - Birthdate of Daniel Bernoulli, Dutch-Swiss mathematician, and physicist (d. 1782). 1853 - Birthdate of Alexander Ziwet, German-American mathematician (d. 1928). 1875 - Birthdate of Thomas John l'Anson Bromwich, English mathematician (d. 1929). 1885 - Birthdate of Thomas Bromwich, English mathematician (d. 1929). 1909 - Day of death of Giacinto Morera, Italian engineer, and mathematician (b. 1856). 1913 - Hardy replied to the first letter from Ramanujan (see Jan. 16 and Jan. 31 entries), expressing his interest in Ramanujan's work [172].

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41

1924 - Birthdate of Irving Reiner, American mathematician (d. 1986). 1928 - Birthdate of Ennio de Giorgi, Italian mathematician (d. 1996). 1957 - Birthdate of Karine Chemla, French historian of mathematics and sinologist. 1957 - Day of death of John von Neumann, Hungarian-American mathematician, and physicist (b. 1903). 1964 - Birthdate of Arlie Petters, Belizean-American mathematical physicist. 1978 - The first issue of the CSHPM newsletter (Canadian Society for History and Philosophy of Mathematics) is published. 2005 - Day of death of Germund Dahlquist, Swedish mathematician (b. 1925).

February, 9 1498 - Luca Pacioli was inspired to start his work "Divina Proportione" (and completed it on 14 Dec 1498). 1775 - Birthdate of Farkas Bolyai, Hungarian mathematician (d. 1856). 1880 - Birthdate of Lipot Fejer, Hungarian mathematician (d. 1959). 1883 - Day of death of Henry John Stephen Smith, Irish mathematician (b. 1826).

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Chapter Two

1883 - The first issue of Science was published. The first item in the “Weekly summary of the progress of science" contained a report by Thomas Craig that “Lindemann gave a proof of the fact that ʌ cannot be a root of an equation of any degree with rational coefficients." 1907 - Birthdate of Harold Scott MacDonald Coxeter, English-Canadian mathematician (d. 2003). 1908 - Birthdate of Alexander Dinghas, Turkish mathematician (d. 1974). 1918 - G. Polya and H. Weyl, during a mathematicians' gathering in Zurich, made a bet concerning the future direction of mathematics. Weyl predicted that in the subsequent 20 years, mathematicians would come to realize the total vagueness of notions such as real numbers, sets, and countability, and moreover, that asking about the truth or falsity of the least upper bound property of the real numbers was as meaningful as asking about the truth of the basic assertions of Hegel on the philosophy of nature. 1919 - Birthdate of Irene Anne Stegun, American mathematician (d. 2008). 1937 - Day of death of Francis Sowerby Macaulay, English mathematician (b. 1862). 1945 - Birthdate of Carol Wood, American mathematician. 1970 - Day of death of Leo Moser, Austrian-Canadian mathematician (b. 1921). 1988 - Day of death of Israel Nathan Herstein, Polish-American mathematician (b. 1923). 2003 - Day of death of Masatoshi Gunduz Ikeda, Japanese-Turkish mathematician (b. 1926).

February, 10 1576 - Day of death of Wilhelm Xylander (born Wilhelm Holtzman, graecized to Xylander), translator of Euclid and Diophantus (b. 1532). 1677 - John Collins wrote, “The truth of it is, mathematical learning will not go off without a dowry; the booksellers have lost so much by the works of Drs. Wallis and ... Barrow ... that it is no easy task to persuade booksellers to undertake anything but toys that are mathematical." [125] 1747 - Birthdate of Aida Yasuaki, Japanese mathematician (d. 1817). 1785 - Birthdate of Claude Louis Marie Henri Navier, French mathematician (d. 1836). 1891 - Day of death of Sofia Kovalevskaya, Russian-Swedish mathematician and physicist (b. 1850).

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43

1901 - Birthdate of Richard Dagobert Brauer, German-American mathematician (d. 1977). 1927 - Day of death of Alfred George Greenhill, English mathematician (b. 1847). 1951 - Day of death of George Abram Miller, American mathematician (b. 1863). 1994 - Day of death of Fritz John, German-born American mathematician (b. 1910).

February, 11 1555 - Day of death of Giovanni Antonio Magini, Italian astronomer, astrologer, cartographer, and mathematician (b. 1555). 1626 - Day of death of Pietro Cataldi, Italian mathematician and astronomer (b. 1552). 1635 - Sir Charles Cavendish writes to William Oughtred to thank him for teaching him “the way of calculating the divisions of your gauging rod." He also passes on praise for Oughtred's work, stating that “Clavis" is in great estimation amongst mathematicians at Paris [143]. 1650 - Day of death of René Descartes, French mathematician, and philosopher (b. 1596). 1800 - Birthdate of William Henry Fox Talbot, English inventor, mathematician, chemist, physicist, philologist, and Egyptologist (d. 1877). 1826 - Founding of University College London. 1839 - Birthdate of Josiah Willard Gibbs, American physicist, mathematician (d. 1903). 1854 - Birthdate of Benjamin Osgood Peirce, American mathematician (d. 1914). 1862 - Birthdate of Francis Sowerby Macaulay, English mathematician (d. 1937). 1887 - Birthdate of John Jackson (d. 1958). 1897 - Birthdate of Emil Leon Post, Polish-American mathematician, and logician (d. 1954). 1897 - An Indiana bill to fix the value of ʌ was defeated in the state senate. The bill specified several values for ʌ to simplify computation. 1891 - Birthdate of Ivan Ivanovich Privalov, Soviet mathematician (d. 1941). 1909 - Birthdate of Claude Chevalley, French mathematician (d. 1984). 1915 - Birthdate of Richard Hamming, American mathematician (d. 1998). 1917 - Birthdate of Andrzej Alexiewicz, Polish mathematician (d. 1995).

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Chapter Two

1921 - Birthdate of Yozo Matsushima, Japanese mathematician (d. 1983). 1923 - Day of death of Wilhelm Killing, German mathematician (b. 1847). 1942 - Day of death of Egbert Rudolf van Kampen, Dutch-American mathematician (b. 1908). 1948 - Richard Duffin writes a recommendation for John Nash. 1974 - Day of death of Vladimir Ivanovich Smirnov, Soviet mathematician (b. 1887). 1976 - Day of death of Dorothy Maud Wrinch, British-American mathematician, and biochemist (b. 1894).

February, 12 1535 - Tartaglia discovered a method of solving cubic equations that enabled him to beat Fiore in a contest [142]. 1539 - Cardano wrote to Tartaglia: “I wonder much, dear Master Niccolò, at the unseemly reply you have made to one Zuan Antonio de Bassano, a bookseller... I would remove you from this conceit, as I recently did with Master Zuanne da Coi, that is to say, the conceit of being the first man in the world. Therefore, I would write to you affectionately and pull you out of the notion of thinking yourself so great. I would help you understand, through kindly admonition and your own words, that you are closer to the valley than the mountaintop. In other matters, you may be more skilled and clever than you have shown in your response. I must state, first of all, that I have held you in high esteem. As soon as your book on Artillery appeared, I bought two copies, the only ones Zuan Antonio brought, of which I gave one to Signore the Marquis..." 1804 - Day of death of Immanuel Kant, German philosopher, trained as a mathematician and physicist (b. 1724). 1824 - Goethe mentioned Lagrange in a conversation with Eckermann: “He was a good man and great for just that reason. When a good man is gifted with talent, he will always exert a morally positive influence as an artist, a scientist, a poet, or whatever else it may be" [54]. 1826 - N. Lobachevsky presented a paper to the mathematics and physics departments of Kazan University on his “imaginary geometry" [185]. 1856 - Birthdate of Arnold Droz-Farny, Swiss mathematician (d. 1912). 1870 - Birthdate of Horatio Carslaw, British-Australian mathematician (d. 1954). 1874 - Birthdate of Harold Stanley Ruse, British mathematician (d. 1974). 1908 - Birthdate of Jacques Herbrand, French mathematician, and philosopher (d. 1931).

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45

1914 - Birthdate of Hanna Neumann, German-British-Australian mathematician (d. 1971). 1916 - Day of death of Richard Dedekind, German mathematician, philosopher (b. 1831). 1929 - Birthdate of Alexei I. Kostrikin, Soviet-Russian mathematician (d. 2000). 1958 - Day of death of Douglas Hartree, English mathematician, and physicist (b. 1897). 1960 - Day of death of Oskar Anderson, Russian-German mathematician (b. 1887). 1962 - Day of death of Joseph Jean Camille Pérez, French mathematician (b. 1890). 1974 - Day of death of Vladimir Ivanovich Smirnov, Soviet mathematician (b. 1887). 1977 - Day of death of Ebenezer Cunningham, British mathematician (b. 1881). 1980 - Day of death of Einar Hille, Swedish-American mathematician (b. 1894). 2001 - Day of death of Herbert Ellis Robbins, American mathematician, and statistician (b. 1915). 2019 - Day of death of Arkadiy Onishchik, Soviet-Russian mathematician (b. 1933).

February, 13 1237 - Day of death of Jordanus de Nemore, European mathematician and scientist (b. 1225), probably of German or Italian origin. 1523 - Birthdate of Valentin Naboth, German astronomer and mathematician (d. 1593). 1535 - Tartaglia found a solution for x³ = mx + n [27]. 1632 - Day of death of Philippe van Lansberge, Dutch astronomer and mathematician (b. 1561). 1633 - Galileo arrived in Rome for his trial before the Inquisition for professing the belief that the earth revolves around the sun. 1735 - Birthdate of Alexandre-Theophile Vandermonde, French mathematician (d. 1796). 1748 - Euler wrote that the proof of the Three-Squares Theorem ought to resemble his proof for two squares. Euler mentioned “Fermat's Last Theorem" [104]. 1755 - Euler presented his proof of Fermat's Little Theorem to the Berlin Academy [20].

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Chapter Two

1774 - Day of death of Charles Marie de La Condamine, French explorer, geographer, and mathematician (b. 1701). 1787 - Day of death of Roger Joseph Boscovich, Croatian physicist, astronomer, mathematician, and philosopher (b. 1711). 1805 - Birthdate of Peter Gustav Lejeune Dirichlet, German mathematician (d. 1859). 1809 - The French Academy of Sciences couldn't announce the winner for the prize competition in Galvanism, so they recommended to Napoleon that the prize money should be used to “encourage the mathematical analysis of the experiments made by M. Chladni on the vibration of resonating plates" [25]. 1874 - Day of death of Franz Taurinus, German mathematician (b. 1794). 1882 - Birthdate of Tadeusz Banachiewicz, Polish astronomer, mathematician, and geodesist (d. 1954). 1883 - Day of death of Henry Wilbraham, English mathematician (b. 1825). 1906 - Birthdate of Edward Maitland Wright, English mathematician (d. 2005). 1916 - Mie, in a letter to Hilbert, manifested his general skepticism towards the idea of “general relativity" [97]. 1926 - Birthdate of Tonny Albert Springer, Dutch mathematician (d. 2011). 1947 - Day of death of Erich Hecke, German mathematician (b. 1887). 1956 - Day of death of Jan Lukasiewicz, Polish mathematician and philosopher (b. 1878). 1973 - The German Democratic Republic issued a stamp devoted to Copernicus and his De Revolutionibus, which was published in 1473. 1992 - Day of death of Nikolay Bogolyubov, Soviet mathematician, and physicist (b. 1909). 1980 - Day of death of Marian Rejewski, Polish mathematician, and cryptologist, one of the breakers of the German Enigma (b. 1905). 1997 - Day of death of Mark Krasnosel'skii, Soviet Russian-Ukrainian mathematician (b. 1920). 2018 - Day of death of Valentin Zaitsev, Russian mathematician (b. 1945).

February, 14 1468 - Birthdate of Johannes Werner, German priest, and mathematician (d. 1522). 1614 - Birthdate of John Wilkins, English mathematician (d. 1672).

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47

1744 - Day of death of John Hadley, English mathematician, inventor of the octant (b. 1682). 1747 - Founding of the Ecole nationale des Ponts et Chaussees (The School of Bridges and Roads) in Paris. 1761 - Euler uses his circles (Euler diagrams) for the first time [150]. 1814 - Laplace presented his “Essai philosophique des probabilites" to the Academie des Sciences in Paris. 1832 - C. F. Gauss wrote to C.L. Gerling, “Let me add further that I have received a little work on non-Euclidean geometry from Hungary today, in which I find all my own ideas and results developed with greater elegance, although in a concise form that offers great difficulty to anyone not familiar with the subject. ... I regard this young geometer [Janos] Bolyai as a genius of the first order" [111]. 1839 - Birthdate of Hermann Hankel, German mathematician (d. 1873). 1877 - Birthdate of Edmund Georg Hermann Landau, German mathematician (d. 1938). 1894 - Day of death of Eugene Charles Catalan, Belgian-French mathematician (b. 1814). 1917 - Birthdate of Herbert A. Hauptman, American mathematician and crystallographer, Nobel Prize laureate (d. 2011). 1943 - Day of death of David Hilbert, German mathematician, physicist, and philosopher (b. 1862). 1954 - Birthdate of Vladimir Gershonovich Drinfeld, Soviet-American mathematician. 1973 - Birthdate of Annalisa Buffa, Italian mathematician. 1977 - Birthdate of Anna Erschler, Russian mathematician. 2001 - Day of death of Helmut Wielandt, German mathematician (b. 1910). 2007 - Day of death of James Eells, American-British mathematician (b. 1926). 2019 - Day of death of Simon Phillips Norton, British mathematician (b. 1952).

February, 15 1564 - Birthdate of Galileo Galilei, Italian astronomer, physicist, and mathematician (d. 1642). 1588 - Birthdate of Benjamin Bramer, German architect, and mathematician (d. 1652). 1671 - James Gregory wrote to John Collins that he had found infinite series for the tangent and secant functions.

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Chapter Two

1676 - (5 Feb OS) Newton wrote to Hooke: "What DesCartes did was a good step... If I have seen further it is by standing on ye shoulders of Giants." 1748 - Euler writes to d'Alembert about the pentagonal number theorem. 1839 - Birthdate of Hieronymus Georg Zeuthen, Danish mathematician (d. 1920). 1839 - Birthdate of Christian Gustav Adolph Mayer, German mathematician (d. 1907). 1847 - Day of death of Germinal Pierre Dandelin, Belgian mathematician, and engineer (b. 1794). 1849 - Day of death of Pierre Francois Verhulst, Belgian mathematician (b. 1804). 1850 - Birthdate of Sophie Bryant, Irish mathematician (d. 1922). 1851 - Birthdate of Spiru Haret, Romanian mathematician, astronomer, and politician, 55th Romanian Minister of Internal Affairs (d. 1912). 1861 - Birthdate of Alfred North Whitehead, English mathematician, and philosopher (d. 1947). 1882 - Birthdate of Paul Koebe, German mathematician (d. 1945). 1900 - Day of death of John James Walker, English mathematician (b. 1825). 1915 - Birthdate of Chuan-Chih Hsiung, Chinese-American mathematician (d. 2009). 1940 - Day of death of Otto Toeplitz, Jewish mathematician (b. 1881). 1958 - France issued stamps honoring Joseph Louis Lagrange, Urbain Jean Joseph Leverrier, Jean Bernard Leon Foucault, and Claude Louis Berthollet.

1974 - West Berlin issued a postage stamp for 150th birth anniversary of Kirchhoff.

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49

1980 - The USA issued a stamp honoring the mathematician and astronomer Benjamin Bannecker (1731-1806). 1983 - Grothendieck wrote the following about his mathematical projects: "One reason for my poor answering is that I feel somewhat 'out of the game', and I am keen on not getting caught in any big technical machinery – the machine-building time is over for me now, and I want to be careful not to do more than occasionally throw a very casual glance at the machine-building others pursue, and possibly make a comment or two, without really getting involved" [155]. 1988 - Day of death of Richard Phillips Feynman, American theoretical physicist (b. 1918). 2008 - Day of death of Walter Warwick Sawyer, mathematician, mathematics educator, and author, who taught on several continents (b. 1911).

February, 16 1514 - Birthdate of Georg Joachim Rheticus, German astronomer, and mathematician (d. 1576). 1531 - Day of death of Johannes Stöffler, German mathematician, and astronomer (b. 1452). 1636 - Day of death of Henry Gellibrand, English astronomer, and mathematician (b. 1597). 1698 - Birthdate of Pierre Bouguer, French mathematician, geophysicist, and astronomer (d. 1758). 1745 - Euler, in a letter to Goldbach, shows that numbers represented in two different ways as a sum of two squares must be composite [104]. 1892 - Day of death of Thomas Archer Hirst, English mathematician (b. 1830). 1903 - Birthdate of Beniamino Segre, Italian mathematician (d. 1977). 1903 - Birthdate of Geoffrey Timms, British mathematician, and cryptanalyst (d. 1982). 1937 - Birthdate of Yuri Manin, Soviet-Russian-German mathematician. 1977 - Day of death of Rózsa Péter, Hungarian mathematician (b. 1905). 1980 - Day of death of Edward Copson, English mathematician (b. 1901).

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Chapter Two

1982 - Sweden issued three stamps picturing impossible figures like Penrose Triangles. 1997 - Day of death of Leon Bankoff, American dentist, and mathematician (b. 1908).

February, 17 1600 - Day of death of Giordano Bruno, Italian mathematician, astronomer, and philosopher (b. 1548). 1723 - Birthdate of Tobias Mayer, self-taught German mathematician (d. 1762). 1765 - Birthdate of Sir James Ivory, Scottish mathematician (d. 1842). 1874 - Day of death of Adolphe Quetelet, Belgian astronomer, mathematician, and sociologist (b. 1796). 1890 - Birthdate of Sir Ronald Aylmer Fisher, English-Australian mathematician (d. 1962). 1891 - Birthdate of Abraham Fraenkel, German-Israeli mathematician (d. 1965). 1905 - Day of death of Rózsa Péter, Hungarian mathematician (d. 1977). 1918 - Birthdate of Jacqueline Ferrand, French mathematician (d. 2014). 1947 - Day of death of Ettore Bortolotti, Italian mathematician (b. 1866). 1950 - Birthdate of Viktor Aleksandrovich Gorbunov, Soviet mathematician (d. 1999). 1964 - Day of death of Heinrich Franz Friedrich Tietze Austrian mathematician (b. 1880). 2012 - Day of death of Nicolaas Govert de Bruijn, Dutch mathematician (b. 1918).

February, 18 3102 BCE - According to Aryabhata, the Kali Yuga began. 901 - Day of death of Al-Sabi Thabit ibn Qurra al-Harrani, Mesopotamian scholar, and mathematician (b. 836). 1201 - Birthdate of Khawaja Muhammad ibn Muhammad ibn Hasan Tusi (Nasir al-Din Tusi), Islamic astronomer, and mathematician (d. 1274). 1404 - Birthdate of Leone Battista Alberti, Italian cartographer, and mathematician (d. 1472). 1670 - John Wallis wrote, “Joannes Georgius Pelshower [Regimontanus Borussus] visited me and desired an example of the like; that night, in the dark, without the help of my memory, I proposed to myself a number in 53 places: 2468135791011121411131516182017192122242

February

51

628302325272931, from which I extracted the square root to 27 places: 157103016871482805817152171 proxime. These numbers I did not commit to paper until he visited me again in March of the following year when I dictated them to him from memory." 1727 - Leonhard Euler defended his De Sono essay in a public disputation at the law auditorium at Basel [30]. 1750 - Day of death of Georg Bernhard Bilfinger, German philosopher, mathematician, statesman (b. 1693). 1844 - Birthdate of Jacob Loroth, German mathematician (d. 1910). 1851 - Day of death of Carl Gustav Jacob Jacobi, German mathematician (b. 1804). 1879 - Benjamin Peirce wrote to Arthur V. Gilman, president of Harvard: “I will do the same for young women as I do for young men. I shall take pleasure in providing gratuitous instruction to any person whom I find competent to receive it. I offer no elementary instruction, but only in higher mathematics." 1899 - Day of death of Sophus Lie, Norwegian mathematician (b. 1842). 1900 - Day of death of Eugenio Beltrami, Italian mathematician (b. 1835).

February, 19 1473 - Birthdate of Nicolaus Copernicus, Polish mathematician, and astronomer (d. 1543). 1549 - Andreas Osiander wrote about Michael Stifel: “He has devised new numbers for the alphabet, namely the triangular numbers, and his fantasies are more absurd than before." 1553 - Day of death of Erasmus Reinhold, German astronomer, and mathematician (b. 1511). 1622 - Day of death of Sir Henry Savile, English mathematician (b. 1549). 1672 - Newton published his first work on the new theory of light as a letter in Philosophical Transactions. Huygens, Hooke, and others objected so strongly that he vowed not to publish again. 1799 - Day of death of Jean-Charles de Borda, French mathematician, physicist, and sailor (b. 1733). 1863 - Birthdate of Axel Thue, Norwegian mathematician (d. 1922). 1876 - J. J. Sylvester began his duties at the newly founded Johns Hopkins University in Baltimore, Maryland. 1897 - Day of death of Karl Weierstrass, German mathematician (b. 1815). 1908 - Day of death of Paul Matthieu Hermann Laurent, French mathematician (b. 1841). 1915 - Birthdate of Fritz Joachim Weyl, Swiss mathematician (d. 1977).

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1929 - Day of death of Joseph Valentin Boussinesq, French mathematician, and physicist (b. 1842). 1938 - Day of death of Edmund Georg Hermann Landau, German mathematician (b. 1877). 1946 - Alan Turing presents the “Proposal for the Development in the Mathematics Division of an Automatic Computing Engine (ACE)." 1990 - Day of death of Otto Neugebauer, German-American historian of mathematics (b. 1889).

February, 20 1647 - In a letter to Kenelm Digby, Bernard Frenicle de Bessy said that Fermat found the smallest solution for N up to 150 of equations of the type x2 - Ay2 = 1 and challenged John Wallis to solve the cases N = 151 or 313 [183]. 1762 - Day of death of Tobias Mayer, self-taught German mathematician (b. 1723). 1807 - Sophie Germain writes to Gauss informing him that she is the person who had written to him using the name M. LeBlanc [25]. 1844 - Birthdate of Ludwig Boltzmann, Austrian theoretical physicist (d. 1906). 1860 - Birthdate of Mathias Lerch, Czech mathematician (d. 1922). 1910 - Birthdate of Esther (Klein) Szekeres, Hungarian-Australian mathematician (d. 2005). 1931 - Birthdate of John Willard Milnor, American mathematician. 1947 - Alan Turing suggests testing artificial intelligence with the game of chess in a lecture to the London Mathematical Society. 1955 - Day of death of Arthur Lee Dixon, British mathematician (b. 1867). 1979 - The German Democratic Republic issued a stamp commemorating the centenary of Einstein's birth. 2018 - Day of death of Lionel March, British mathematician, architect, and digital artist (b. 1934).

February, 21 1591 - Birthdate of Girard Desargues, French geometer (d. 1661). 1699 - Newton was elected as the second foreign member of the French Academy. 1728 - Isaac Greenwood began his "Publick" lectures at Harvard that were open to the entire university.

February

53

1912 - Day of death of Émile Michel Hyacinthe Lemoine, French mathematician (b. 1840). 1912 - Day of death of Osborne Reynolds, Irish mathematician (b. 1842). 1932 - Day of death of James Mercer, British mathematician (b. 1883). 1962 - Day of death of Julio Rey Pastor, Spanish mathematician, and historian of science (b. 1888). 1996 - Day of death of Hans-Joachim Bremermann, German-American mathematician, and biophysicist (b. 1926). 2009 - Day of death of Ilya Piatetski-Shapiro, Soviet-Jewish mathematician (b. 1929).

February, 22 1535 - Public discussion about solving cubic equations between Tartaglia and Scipione dal Ferro [27]. 1687 - Day of death of Francesco Lana de Terzi, Italian Jesuit, mathematician, naturalist, and aeronautics pioneer (b. 1631). 1796 - Birthdate of Adolphe Quetelet, Belgian mathematician, astronomer, and sociologist (d. 1874). 1817 - Birthdate of Carl Wilhelm Borchardt, German mathematician (d. 1880). 1824 - Birthdate of Pierre Janssen, French astronomer, and mathematician (d. 1907). 1849 - Birthdate of Nikolay Yakovlevich Sonin, Russian mathematician (d. 1915). 1856 - Birthdate of Micaiah John Muller Hill, English mathematician (d. 1929). 1876 - The Johns Hopkins University was founded. 1880 - Sidney Lanier (1842-1922) read his "Ode to The Johns Hopkins University"* [100]. 1903 - Birthdate of Frank P. Ramsey, English economist, mathematician, and philosopher (d. 1930). 1947 - Birthdate of Yuri Zelinski, Ukrainian mathematician (d. 2017). 1964 - In a letter to van Heijenoort, Gödel remarks on the motivation that led him to the incompleteness theorem: “Perhaps you were puzzled by the fact that once I said an attempted relative consistency proof for analysis led to the proof of the existence of undecidable propositions and another time that the heuristic principle and the first version of the proof were those given in Sect. 7 of my 1934 Princeton lectures. But it was precisely the relative consistency proof which made it necessary to

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formalize either ‘truth’ or ‘provability’ and thereby forced a comparison of the two in this respect." [110]. 1975 - Day of death of Oskar Perron, German mathematician (b. 1880). 1984 - Day of death of Maxwell Herman Alexander Newman, British mathematician, and codebreaker (b. 1897). 1990 - Item number MR1000000 was added to MathSciNet. *

How tall among her sisters, and how fair, – How grave beyond her youth, yet debonair As dawn, 'mid wrinkled Matres of old lands Our youngest Alma Mater modest stands! In four brief cycles round the punctual sun Has she, old Learning's latest daughter, won This grace, this stature, and this fruitful fame. Howbeit she was born Unnoised as any stealing summer morn. From far the sages saw, from far they came And ministered to her, Led by the soaring-genius'd Sylvester That, earlier, loosed the knot great Newton tied, And ung the door of Fame's locked temple wide. As favorable fairies thronged of old and blessed The cradled princess with their several best, So, gifts and dowers meet To lay at Wisdom's feet, These liberal masters largely brought { Dear diamonds of their long-compressed thought, Rich stones from out the labyrinthine cave Of research, pearls from Time's profoundest wave And many a jewel brave, of brilliant ray, Dug in the far obscure Cathay Of meditation deep – With owers, of such as keep Their fragrant tissues and their heavenly hues Fresh-bathed forever in eternal dews – The violet with her low-drooped eye, For learned modesty, – The student snow-drop, that doth hang and pore Upon the earth, like Science, evermore, And underneath the clod doth grope and grope, – The astronomer heliotrope,

February

That watches heaven with a constant eye, – The daring crocus, unafraid to try (When Nature calls) the February snows, – And patience perfect rose. Thus sped with helps of love and toil and thought, Thus forwarded of faith, with hope thus fraught, In four brief cycles round the stringent sun This youngest sister hath her stature won. Nay, why regard The passing of the years? Nor made, nor marr'd, By help or hindrance of slow Time was she: O'er this fair growth Time had no mastery: So quick she bloomed, she seemed to bloom at birth, As Eve from Adam, or as he from earth. Superb oer slow increase of day on day, Complete as Pallas she began her way; Yet not from Jove's unwrinkled forehead sprung, But long-time dreamed, and out of trouble wrung, Fore-seen, wise-plann'd, pure child of thought and pain, Leapt our Minerva from a mortal brain. And here, O finer Pallas, long remain, – Sit on these Maryland hills, and fix thy reign, And frame a fairer Athens than of yore In these blest bounds of Baltimore, – Here, where the climates meet That each may make the other's lack complete, – Where Florida's soft Favonian airs beguile The nipping North, { where nature's powers smile, – Where Chesapeake holds frankly forth her hands Spread wide with invitation to all lands, – Where now the eager people yearn to find The organizing hand that fast may bind Loose straws of aimless aspiration fain In sheaves of serviceable grain, – Here, old and new in one, Through nobler cycles round a richer sun O'er-rule our modern ways, O blest Minerva of these larger days! Call here thy congress of the great, the wise,

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The hearing ears, the seeing eyes, – Enrich us out of every farthest clime, – Yea, make all ages native to our time, Till thou the freedom of the city grant To each most antique habitant Of Fame, – Bring Shakespeare back, a man and not a name, – Let every player that shall mimic us In audience see old godlike Aeschylus, – Bring Homer, Dante, Plato, Socrates, – Bring Virgil from the visionary seas Of old romance, { bring Milton, no more blind, – Bring large Lucretius, with unmaniac mind, – Bring all gold hearts and high resolved wills To be with us about these happy hills, – Bring old Renown To walk familiar citizen of the town, – Bring Tolerance, that can kiss and disagree, – Bring Virtue, Honor, Truth, and Loyalty, – Bring Faith that sees with undissembling eyes, – Bring all large Loves and heavenly Charities, – Till man seem less a riddle unto man And fair Utopia less Utopian, And many peoples call from shore to shore, `The world has bloomed again, at Baltimore!'

February, 23 1560 - Day of death of Gaspar Lax, Spanish mathematician (b. 1487). 1583 - Birthdate of Jean-Baptiste Morin, French mathematician, astrologer, and astronomer (d. 1656). 1603 - Day of death of François Viète, French mathematician (b. 1540). 1826 - Nikolai Lobachevsky first announced his principles of nonEuclidean geometry in a talk at the University of Kazan. 1844 - Day of death of Duncan Farquharson Gregory, Scottish mathematician (b. 1813). 1855 - Day of death of Carl Friedrich Gauss, German mathematician, astronomer, and physicist (b. 1777). 1861 - Birthdate of George Ballard Mathews, English mathematician (d. 1922). 1905 - Birthdate of Derrick Lehmer, American mathematician (d. 1991).

February

57

1912 - Richard Courant gives his inaugural lecture, "On Existence Proofs in Mathematics," at Göttingen. 1917 - Day of death of Jean-Gaston Darboux, French mathematician (b. 1842). 1922 - Birthdate of Anneli Cahn Lax, American mathematician (d. 1999). 1947 - Birthdate of Rufus Bowen, American mathematician (d. 1978). 1951 - Birthdate of Shigefumi Mori, Japanese mathematician. 1955 - Germany issued a postage stamp for the centenary of the death of Gauss.

1961 - Day of death of Mary Ann Elizabeth Stephansen, Norwegian mathematician (b. 1872). 1963 - Day of death of Antonio Signorini, Italian mathematical physicist and civil engineer (b. 1888). 1955 - Germany issued a stamp commemorating the centenary of the death of Gauss. 2012 - Day of death of David Sayre, American physicist and mathematician (b. 1924).

February, 24 1616 - Inquisition authorities denied the teaching of the Heliocentric view. 1728 - Day of death of Charles Rene Reyneau, French mathematician (b. 1656). 1772 - Lagrange, in a letter to d'Alembert, criticized higher mathematics as being "decadent" [57]. 1812 - Day of death of Etienne-Louis Malus, French physicist, and mathematician (b. 1775). 1842 - J.J. Sylvester resigned his position at the University of Virginia after a dispute with a student who was reading a newspaper in class. 1844 - Day of death of Antoine-Andre-Louis Reynaud, French mathematician (b. 1771).

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1856 - Day of death of Nikolai Lobachevsky, Russian mathematician (b. 1792). 1871 - Day of death of Julius Ludwig Weisbach, German mathematician, and engineer (b. 1806). 1878 - Birthdate of Felix Bernstein, Jewish German-American mathematician (d. 1956). 1881 - Cambridge University in England allowed women to officially take university examinations and to have their names posted along with those of male students. 1931 - The Fields Medal was established to recognize outstanding contributions to mathematics. 1933 - Day of death of Eugenio Bertini, Italian mathematician (b. 1846). 1946 - Birthdate of Grigory Margulis, Soviet mathematician. 2001 - Day of death of Claude Shannon, American mathematician, cryptographer, and engineer (b. 1916). 2020 - Day of death of Katherine Johnson, American physicist, and mathematician (b. 1918).

February, 25 1670 - Birthdate of Maria Margarethe Kirch, German astronomer, and mathematician, and the first woman to discover a comet (d. 1720). 1672 - John Wallis sends his work on tangents in a letter to Oldenburg for publication in the Philosophical Transactions [9]. 1775 - Day of death of William Small, British mathematician (b. 1734). 1786 - Day of death of Thomas Wright, English astronomer, mathematician, instrument maker, architect, and garden designer (b. 1711). 1827 - Birthdate of Henry William Watson, English mathematician (d. 1903). 1870 - Hermann Amandus Schwarz wrote Georg Cantor a letter containing the first rigorous proof of the theorem that if the derivative of a function vanishes, then the function is constant. 1902 - Birthdate of Kenjiro Shoda, Japanese mathematician (d. 1977). 1922 - Birthdate of Ernst Gabor Straus, German-American mathematician (d. 1983). 1926 - Day of death of Masatoshi Gunduz Ikeda, Japanese-Turkish mathematician (d. 2003). 1972 - Day of death of Wladyslaw Hugo Dionizy Steinhaus, Polish mathematician, and educator (b. 1887). 1976 - Romania issued a stamp picturing the mathematician Anton Davidoglu (1876-1958).

February

59

1988 - Day of death of Kurt Mahler, German-Australian mathematician (b. 1903).

February, 26 1616 - Galileo was ordered to abandon Copernicanism by the Roman Inquisition. 1638 - Day of death of Claude Gaspard Bachet de Meziriac, French mathematician, and linguist (b. 1581). 1664 - Birthdate of Nicolas Fatio de Duillier, Swiss mathematician (d. 1753). 1693 - Day of death of Charles Scarborough, English physician, and mathematician (b. 1615). 1786 - Day of death of Francois Arago, French mathematician, and politician, 25th Prime Minister of France (d. 1853). 1843 - Birthdate of Karl Friedrich Geiser, Swiss mathematician, organizer of the first International Congress of Mathematicians (d. 1934). 1885 - The Burroughs Company introduced the first adding machine. 1894 - Heaviside, in a letter to FitzGerald: “It is impossible to think in quaternions; you can only pretend to do it" [121]. 1912 - Birthdate of Istvan Vincze, Hungarian mathematician (d. 1999). 1985 - Day of death of Tjalling Koopmans, Dutch-American economist, and mathematician, Nobel Prize laureate (b. 1910). 1976 - Birthdate of Nalini Anantharaman, French mathematician. 2017 - Day of death of Ludvig Dmitrievich Faddeev, Russian mathematician (b. 1934).

February, 27 1477 - Founding of the University of Uppsala, the oldest university in Sweden and Northern Europe. 1547 - Birthdate of Baha' ad-Din al-Amili, Lebanese-born mathematician (d. 1621). 1735 - Day of death of John Arbuthnot, Scottish physician, and satirist, who first used the word "probability" (b. 1667). 1881 - Birthdate of Luitzen Egbertus Jan Brouwer, Dutch mathematician, philosopher (d. 1966). 1890 - Dedekind, in the letter to Keferstein, presents and develops his ideas on the notion of the natural number [73]. 1903 - Birthdate of Hans Rohrbach, German mathematician (d. 1993). 1910 - Birthdate of Joseph Doob, American mathematician (d. 2004).

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1915 - Day of death of Nikolay Yakovlevich Sonin, Russian mathematician (b. 1849). 1927 - Birthdate of Peter Whittle, English-New Zealand mathematician. 1983 - Grothendieck started on a new text, called Reflections on homotopical algebra.

February, 28 1412 - The University of St Andrews was founded by Bishop Henry Wardlaw. 1552 - Birthdate of Jost Burgi, Swiss mathematician, and clockmaker (d. 1632). 1691 - Day of death of Joseph Moxon, English printer of mathematical books and maps, a maker of globes and mathematical instruments, and a mathematical lexicographer (b. 1627). 1695 - Leibniz writes to Johann Bernoulli encouraging him to use the term "calculus summatorius," which Leibniz used for integration. 1735 - Birthdate of Alexandre-Théophile Vandermonde, French musician, and mathematician (d. 1796). 1742 - Day of death of Willem 's Gravesande, Dutch mathematician (b. 1688). 1825 - Cauchy presented a paper to the Académie on integrals of complexvalued functions where the limits of integration were allowed to be complex. Previously, he had done much work on such integrals when the limits were real [59]. 1859 - Birthdate of Florian Cajori, Swiss-American historian of mathematics, and mathematics educator (d. 1930). 1863 - Day of death of Jakob Philipp Kulik, Austrian mathematician (b. 1793). 1878 - Birthdate of Pierre Fatou, French mathematician, and astronomer (d. 1929). 1915 - Friedman explains how to use Runge's integration method to compute the solution of a system of nonlinear differential equations [7]. 1925 - Birthdate of Louis Nirenberg, Canadian-born American mathematician (d. 2020). 1945 - Birthdate of Linda Preiss Rothschild, American mathematician. 1952 - Birthdate of Simon Phillips Norton, British mathematician (d. 2019). 1954 - Birthdate of Jean Bourgain, Belgian mathematician. 1956 - Day of death of Frigyes Riesz, Hungarian mathematician (b. 1880).

February

61

2014 - Day of death of Lee Lorch, American mathematician, and activist (b. 1915). 2020 - Day of death of Freeman Dyson, English-American physicist, and mathematician (b. 1923).

February, 29 1924 - The first Josiah Willard Gibbs lecture was delivered by Professor M. I. Pupin of Columbia University at an AMS meeting. 1928 - Birthdate of Seymour Papert, South African mathematician, and computer scientist, co-created the Logo programming language (d. 2016). 1932 - Birthdate of Gene H. Golub, American mathematician (d. 2007). 1932 - Day of death of Giuseppe Vitali, Italian mathematician (b. 1875). 1960 - Day of death of Teiji Takagi, Japanese mathematician (b. 1875).

CHAPTER THREE MARCH

March, 1 1597 - Birthdate of Jean-Charles della Faille, Flemish priest, and mathematician (d. 1652). 1611 - Birthdate of John Pell, English mathematician, and linguist (d. 1685). 1847 - G. Lamé presented a proof of Fermat's Last Theorem to the French Academy. His error was later pointed out by Liouville and by Kummer. 1849 - Cauchy was reinstated at the Faculté de Sciences as a professor of mathematical astronomy. 1862 - Day of death of Peter Barlow, English mathematician, and engineer (b. 1776). 1879 - Birthdate of Robert Daniel Carmichael, American mathematician (d. 1967). 1884 - Day of death of Isaac Todhunter, English mathematician (b. 1820). 1908 - Day of death of Heinrich Maschke, German mathematician (b. 1853). 1913 - Day of death of Mario Pieri, Italian mathematician (b. 1860). 1978 - Day of death of Kiyoshi Oka, Japanese mathematician (b. 1901). 1980 - Benoit B. Mandelbrot first saw an image of the set that would eventually bear his name. 2015 - Day of death of Georg Kreisel, Austrian-born mathematical logician (b. 1923).

March, 2 1836 - Birthdate of Julius Weingartnen, German mathematician (d. 1910). 1862 - Birthdate of Robert Edgar Allardice, Scottish mathematician (d. 1928). 1885 - Day of death of Joseph Alfred Serret, French mathematician (b. 1819).

March

63

1901 - Birthdate of Grete Hermann, German mathematician, and philosopher (d. 1984). 1906 - Birthdate of Boris Pavlovich Demidovich, Soviet mathematician (d. 1977). 1912 - Birthdate of Clifford Hugh Dowker, Canadian-British mathematician (d. 1982). 1962 - Day of death of Charles Jean de la Vallée-Poussin, Belgian mathematician (b. 1866). 1978 - Day of death of Edward Begle, American mathematician, and educator (b. 1914). 2009 - Day of death of Jacob Theodore (Jack) Schwartz, American mathematician, and computer scientist (b. 1930).

March, 3 1703 - Day of death of Robert Hooke, English natural philosopher, architect, and polymath (b. 1635). 1837 - Birthdate of Aleksandr Nikolayevich Korkin, Russian mathematician (d. 1908). 1845 - Birthdate of Georg Cantor, German mathematician, and philosopher (d. 1918). 1879 - Day of death of William Kingdon Clifford, English mathematician (b. 1845). 1898 - Birthdate of Emil Artin, Austrian-German mathematician (d. 1962). 1901 - Birthdate of Otto Schreier, German mathematician (d. 1929). 1912 - Birthdate of Andrew Paul Guinand, Canadian mathematician (d. 1987). 1916 - Birthdate of Paul Halmos, Hungarian-American mathematician (d. 2006). 1931 - The managing editor of the Zentralblatt, Otto Neugebauer from Göttingen, announced, in a letter to Courant, "new plans for the foundation of an American abstract journal." But, in the same letter, Neugebauer expressed his confidence in his ability to convince the Americans of the Zentralblatt's qualities and their willingness to collaborate: “Veblen is going to come to Germany and will try to reach an agreement with us. Personally, I am very much in favor of the idea of an American branch of the Zentralblatt." [158] 1954 - Day of death of Hendrik de Vries (b. 1867). 1977 - Birthdate of Kenjiro Shoda, Japanese mathematician (b. 1902). 1991 - Day of death of William Penney, Baron Penney, Gibraltar-born English mathematician, physicist (b. 1909).

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March, 4 1711 - Leibniz, in a letter to Hans Sloane, complained: “Nobody knew better than Newton that this charge is false, for certainly, I never heard of the name of the Calculus of Fluxions, nor saw with these eyes the characters which Newton used." [22] 1816 - Day of death of Jose de Mendoza y Rios, Spanish mathematician (b. 1761). 1822 - Birthdate of Jules Antoine Lissajous, French mathematician (d. 1880). 1833 - Birthdate of John Monroe Van Vleck, American mathematician, and astronomer (d. 1912). 1862 - Birthdate of Robert Emden, Swiss astrophysicist, and mathematician (d. 1940). 1866 - Birthdate of Eugene Cosserat, French mathematician, and astronomer (d. 1931). 1871 - Birthdate of Boris Galerkin, Soviet mathematician, and engineer (d. 1945). 1889 - Birthdate of Oscar Chisini, Italian mathematician, and statistician (d. 1967). 1891 - David Hilbert submits an article on his space-filling curve "Ueber die stetige Abbildung einer Line auf ein Flächenstück" to the journal Mathematische Annalen. 2005 - The first “Pythagorean Day" of the 21st Century (the second was on June 8, 2010, and the third was on May 12, 2013).

March, 5 1512 - Birthdate of Gerardus Mercator, Flemish mathematician, cartographer, and philosopher (d. 1594). 1575 - Birthdate of William Oughtred, English minister, and mathematician, inventor of the slide rule (d. 1660). 1624 - Birthdate of John Collins, English mathematician (d. 1683). 1639 - Florimond De Beaune wrote to Marin Mersenne: “I do not think that one could acquire any solid knowledge of nature in physics without geometry, and the best of geometry consists of analysis, of such kind that without the latter it is quite imperfect." 1750 - Euler read his "Recherches sur la Precession" at the Berlin Academy. 1779 - Birthdate of Benjamin Gompertz, English mathematician, and statistician (d. 1865).

March

65

1794 - Birthdate of Jacques Babinet, French physicist, mathematician, and astronomer (d. 1872). 1815 - Birthdate of Angelo Genocchi, Italian mathematician (d. 1889). 1827 - Day of death of Pierre-Simon Laplace, French mathematician, and astronomer (b. 1749). 1875 - Day of death of Claude-Louis Mathieu, French astronomer, and mathematician (b. 1783). 1876 - J.J. Sylvester appointed professor of mathematics at Johns Hopkins University. This marked the beginning of graduate mathematics education in the United States. 1880 - Birthdate of Sergei Natanovich Bernstein, Soviet mathematician (d. 1968). 1885 - Birthdate of Pauline Sperry, American mathematician (d. 1967). 1885 - Day of death of John Radford Young, English mathematician (b. 1799). 1915 - Birthdate of Laurent-Moise Schwartz, French mathematician (d. 2002). 1925 - Day of death of Johan Jensen, Danish mathematician, and engineer (b. 1859). 1927 - Day of death of Franz Mertens, Polish-Austrian mathematician (b. 1840). 1931 - Vera S. Pless, American mathematician. 1954 - Day of death of Julian Lowell Coolidge, American mathematician, and educator (b. 1873).

March, 6 1661 - The Royal Society, London, England, elected Sir Robert Moray as its first president. 1741 - Euler writes to Goldbach that he has proved "a theorem of Fermat's" according to which primes p = 4n + 3 cannot divide a sum of two squares a2 + b2 except when both a and b are divisible by p. 1766 - D'Alembert writes to Lagrange to inform him that Euler is leaving the Berlin Academy for St. Petersburg. 1805 - Adrien-Marie Legendre introduced the method of least squares (which was known 10 years before by Gauss, who didn't publish his work) in "Sur la Methode des moindres quarres" [On the method of least squares], the title of an appendix to "Nouvelles methodes pour la determination des orbites des cometes." 1832 - Gauss replied to Farkas Bolyai about Janos Bolyai's work "The Absolutely True Science of Space," stating "if I praised your son's

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work, I would praise myself." The letter deeply afflicted and upset Janos Bolyai, although it reflects appreciation as well: "... I am very glad that it is my old friend's son who so splendidly preceded me." [91] 1866 - Birthdate of Ettore Bortolotti, Italian mathematician, and historian of mathematics (d. 1947). 1901 - Birthdate of Naum Ilyich Akhiezer, Soviet mathematician (d. 1980). 1939 - Day of death of Ferdinand von Lindemann, German mathematician (b. 1852). 1944 - Day of death of Aleksandr Petrovich Kotelnikov, Soviet mathematician (b. 1865).

March, 7 1737 - Euler presents his seminal paper, "De fractionibus continuis dissertatio" ("Essay on Continued Fractions"), to the St Petersburg Academy of Sciences. 1750 - Euler wrote to d'Alembert, describing his efforts to derive the precession and inspiring d'Alembert to attempt to solve it [79, V. 35]. 1792 - Birthdate of John Herschel, English mathematician, and astronomer (d. 1871). 1824 - Birthdate of Delfino Codazzi, Italian mathematician (d. 1873). 1870 - Birthdate of Ernst Leonard Lindelöf, Finnish mathematician (d. 1946). 1886 - Birthdate of Geoffrey Ingram Taylor, English mathematician, and physicist (d. 1975). 1889 - Day of death of Angelo Genocchi, Italian mathematician (b. 1817). 1893 - Birthdate of Anna Margaret Mullikin, American mathematician (d. 1975). 1918 - Jan àukasiewicz, in his "Farewell Lecture" as Rector of Warsaw University, announced his work on three-valued logic. 1905 - Birthdate of John Macnaghten Whittaker I, British mathematician (d. 1984). 1922 - Birthdate of Olga Ladyzhenskaya, Soviet mathematician (d. 2004). 1922 - Day of death of Axel Thue, Norwegian mathematician (b. 1863). 1957 - Teenager John H Conway, in his first year at Cambridge, writes to H. S. M. Coxeter to ask a question about the 5,3,3 polytope in four dimensions [144]. 1964 - Day of death of Samuel Stanley Wilks, American mathematician (b. 1906). 1966 - Day of death of Georg Faber, German mathematician (b. 1877).

March

1971 - Day of death of Richard Montague, American mathematician, philosopher (b. 1930). 1982 - Day of death of Ida Barney, American astronomer, mathematician (b. 1886). 1988 - Day of death of George McVittie, British mathematician, cosmologist (b. 1904). 2008 - Day of death of David Gale, American mathematician, economist (b. 1921).

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and and and and

March, 8 1688 - Day of death of Honoré Fabri, French-Italian Jesuit, mathematician, physicist, and astronomer (b. 1608). 1671 - Hooke demonstrates vibrations due to sound. 1777 - Laplace read his memoir "Recherches sur le milieu qu'il faut choisir entre les résultats de plusieurs observations" to the Académie des Sciences [55]. 1788 - Birthdate of William Stirling Hamilton, Scottish mathematician (d. 1856). 1822 - Birthdate of Jules Antoine Lissajous, French mathematician (d. 1880). 1851 - Birthdate of George Chrystal, Scottish mathematician (d. 1911). 1865 - Birthdate of Ernest Vessiot, French mathematician (d. 1952). 1895 - Birthdate of Wilhelm Suess, German mathematician (d. 1958). 1920 - Birthdate of George Keith Batchelor, Australian applied mathematician, and fluid dynamicist (d. 2000). 1945 - Birthdate of Sylvia Wiegand, American mathematician. 1974 - Day of death of Olive Clio Hazlett, American mathematician, and cryptographer (b. 1890).

March, 9 1497 - Nicolaus Copernicus made his first recorded astronomical observation of the moon eclipsing a star. 1736 - Carl Leonhard Gottlieb Ehler, the mayor of Danzig in Prussia (now GdaĔsk in Poland), sent a letter to Euler challenging him to solve the Königsberg Bridge Problem [84].

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1818 - Birthdate of Ferdinand Joachimsthal, German mathematician (d. 1861). 1832 - Wolfgang Bolyai was made a corresponding member of the mathematics section of the Magyar Academy (Hungarian Academy of Sciences, Budapest). 1833 - Day of death of Jacques Frédéric Français, French mathematician (b. 1775). 1852 - Birthdate of Constantin Marie Le Paige, Belgian mathematician (d. 1929). 1866 - Day of death of Edmond Bour, French mathematician (b. 1832). 1900 - Birthdate of Howard Hathaway Aiken, American mathematician (d. 1973). 1917 - Day of death of Agnes Sime Baxter, Canadian mathematician (b. 1870). 1931 - Day of death of Ivan Vladislavovich Sleszynski, Ukrainian-Polish mathematician (b. 1854). 1942 - Day of death of Mykhailo Pilipovich Krawtchouk, Ukrainian Soviet mathematician (b. 1892). 1948 - Birthdate of László Lovász, Hungarian mathematician. 1993 - Day of death of Max August Zorn, German mathematician (b. 1906). 2020 - Day of death of Richard Kenneth Guy, British mathematician (b. 1916).

March, 10 1615 - Henry Briggs wrote, “Neper, lord of Markinston, hath set my head and hands to work with his new and admirable logarithms. I hope to see him this summer, if it pleases God, for I never saw a book which pleased me better and made me wonder more."

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1622 - Birthdate of Johann Heinrich Rahn, Swiss mathematician (d. 1676). 1748 - Birthdate of John Playfair, Scottish mathematician (d. 1819). 1773 - Laplace introduces inverse probability. 1797 - Caspar Wessel presented to the Danish Academy of Science his paper on the geometric representation of complex numbers. 1812 - Jean Jacques Bret became docteur des sciences, having previously been a professor of transcendental mathematics at the lycée in Grenoble. 1818 - Birthdate of Joel E. Hendricks, American mathematician (d. 1893). 1825 - Day of death of Karl Brandan Mollweide, German mathematician (b. 1774). 1864 - Birthdate of William Fogg Osgood, American mathematician (d. 1943). 1869 - Birthdate of Benjamin Fedorovich Kagan, Soviet mathematician (d. 1953). 1872 - Birthdate of Mary Ann Elizabeth Stephansen, Norwegian mathematician (d. 1961). 1912 - Birthdate of Frank Smithies, British mathematician (d. 2002). 1914 - In a letter to Geheeb written by Mario Jona, who interviewed H. Muntz for a position at a boarding school called the Odenwaldschule, there is the following passage: “He [Muntz] is perfectly aware of what he is worth and shows it, which, face to face, is not so unpleasant as in writing. As it was, I imagined him from his letter to be much more terrible. He is short, pleasant, and with a very serious appearance and sometimes a little clumsy in politeness. ... For him, the most important thing is his scientific work. He is in a period of important scientific activity but would also like to work in a school like ours if he also has time to work for himself." [129] 1921 - Day of death of Francis Robbins Upton, American mathematician, and physicist (b. 1852). 1948 - Day of death of Evgeny Evgenievich Slutsky, Soviet mathematician, and economist (b. 1880). 1981 - Day of death of Yaroslav Borisovich Lopatynsky (b. 1906). 1981 - Czechoslovakia issued a stamp picturing the philosopher and mathematician Bernhard Bolzano (1781-1848).

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March, 11 1672 - Robert Hooke began writing his "Memoranda," as he called his daily entries. 1711 - Robert Simson, who had no formal training in mathematics, was elected to the chair of mathematics at the University of Glasgow on the condition that "he gives satisfactory proof of his skill in mathematics previous to his admission." 1780 - Birthdate of August Leopold Crelle, German mathematician, and engineer (d. 1855). 1782 - Euler accepted membership in the American Academy of Arts and Sciences. 1794 - Ecole Polytechnique was founded. 1811 - Birthdate of Urbain Le Verrier, French mathematician, and astronomer (d. 1877). 1822 - Birthdate of Joseph Louis François Bertrand, French mathematician, economist (d. 1900). 1832 - Birthdate of Mary Everest Boole, self-taught British mathematician, wife of fellow mathematician George Boole (d. 1916). 1849 - Day of death of Louis Paul Emile Richard (d. 1849). 1853 - Birthdate of Salvatore Pincherle, Italian mathematician (d. 1936). 1870 - Birthdate of Louis Bachelier, French mathematician (d. 1946). 1887 - Birthdate of Walther Mayer, Austrian mathematician (d. 1948). 1888 - Birthdate of William Edward Hodgson Berwick, British mathematician (d. 1944). 1895 - Day of death of Daniel Friedrich Ernst Meissel, German mathematician (b. 1826). 1920 - Day of death of Julio Garavito Armero, Colombian astronomer, mathematician, and engineer (b. 1865). 1921 - Birthdate of Frank Harary, American mathematician (d. 2005). 1924 - Day of death of Helge von Koch, Swedish mathematician (b. 1870).

March, 12 1685 - Birthdate of George Berkeley, English mathematician (d. 1753). 1774 - Birthdate of Johann Caspar Horner, Swiss physicist, mathematician, and astronomer (d. 1834). 1834 - Day of death of Karl Wilhelm Feuerbach, German mathematician (b. 1800).

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1835 - Birthdate of Simon Newcomb, Canadian-American astronomer, and mathematician (d. 1909). 1859 - Birthdate of Ernesto Cesàro, Italian mathematician (d. 1906). 1883 - Professor George Chrystal gave an address on "Present Fields of Mathematical Research" at the first regular meeting of the Edinburgh Mathematical Society. 1891 - Nature published an unsolicited letter from a German hausfrau, Miss Agnes Pockels, to John William Strutt (Lord Rayleigh), describing many of the results of Strutt's own experiments, and conjectures even beyond his, all done in her own kitchen. 1898 - Day of death of Johann Jakob Balmer, Swiss mathematician, and physicist (b. 1825). 1904 - Birthdate of Lyudmila Keldysh, Soviet mathematician (d. 1976). 1905 - Day of death of William Allen Whitworth, English mathematician, and priest (b. 1840). 1915 - Birthdate of László Fejes Tóth, Hungarian mathematician (d. 2005). 1915 - Day of death of Arthur Edwin Haynes (b. 1849). 1920 - Birthdate of Roland Fraïssé, French mathematical logician (d. 2008). 1926 - John von Neumann received his doctorate summa cum laude in mathematics, with minors in experimental physics and chemistry, from the University of Budapest. 1929 - Birthdate of Louis Norberg Howard (d. 2015). 1942 - Day of death of William Henry Bragg, English physicist, chemist, and mathematician, Nobel Prize laureate (b. 1862). 1945 - Birthdate of Vijay Kumar Patodi, Indian mathematician (d. 1976). 1946 - Day of death of Leonida Tonelli, Italian mathematician (b. 1885). 1959 - Birthdate of Kenji Fukaya, Japanese mathematician. 1972 - Day of death of Louis Joel Mordell, British mathematician (b. 1888). 2016 - Day of death of Lloyd Shapley, American mathematician, and economist, Nobel Prize laureate (b. 1923).

March, 13 1641 - Vincenzo Renieri wrote to Galileo describing certain experiments on falling bodies and casting doubt on Vincenzo Viviani's account of Galileo's legendary experiments involving dropping different weights from the top of the Leaning Tower of Pisa. 1781 - Sir William Herschel discovered Uranus.

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1833 - Day of death of Daniel Friedrich Hecht, German mathematician (b. 1777). 1842 - Birthdate of Joseph Valentin Boussinesq, French mathematician, and physicist (d. 1929). 1855 - Birthdate of Percival Lowell, American astronomer, and mathematician (d. 1916). 1879 - Day of death of Adolf Anderssen, German mathematician, and chess player (b. 1818). 1884 - Day of death of Siegfried Heinrich Aronhold, German mathematician (b. 1819). 1899 - Birthdate of John Hasbrouck Van Vleck, American physicist, and mathematician, Nobel Prize laureate (d. 1980). 1925 - Birthdate of John Tate, American mathematician. 1928 - Birthdate of Paulo Ribenboim, Brazilian-Canadian mathematician. 1945 - Birthdate of Anatoly Fomenko, Russian mathematician. 1965 - Day of death of Corrado Gini, Italian statistician (b. 1884). 1987 - Day of death of Peter Karl Henrici, Swiss mathematician (b. 1923). 2016 - Day of death of Hilary Putnam, American philosopher, mathematician, and computer scientist (b. 1926).

March, 14 The day of ʌ, the World Maths Day* 1664 - Isaac Barrow delivered his “Prefatory Oration" as the first Lucasian Professor at Cambridge. 1692 - Birthdate of Pieter van Musschenbroek, Dutch mathematician, and physicist (d. 1761). 1838 - Birthdate of Rev U Jessee Kniseley, American mathematician (d. 1881). 1864 - Birthdate of Jozsef Kurschak, Hungarian mathematician (d. 1933). 1879 - Birthdate of Albert Einstein (d. 1955). 1882 - Birthdate of Wacáaw SierpiĔski, Polish mathematician (d. 1969). 1889 - Birthdate of Oscar Chisini, Italian mathematician (d. 1967). 1951 - Kurt Gödel shared the first Einstein Award with Julian Schwinger. 1962 - Norway issued a pair of stamps commemorating the centenary of the birth of Vilhelm Bjerknes (1862-1951), physicist, meteorologist, and mathematician. 1973 - Day of death of Howard Hathaway Aiken, American mathematician (b. 1900). 1995 - Speaking at the string theory conference at the University of Southern California, Edward Witten made a suggestion that the five

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existing string theories were, in fact, not distinct theories but different limits of a single theory which he called M-theory. 2005 - Ireland issued a stamp to commemorate the World Year of Physics and his 200th birthday.

2007 - The New York Times published a crossword in which to solve the puzzle, one had first to note that the clue for 28 down was “March 14, to Mathematicians," to which the answer is ʌ-day. [17] The puzzle is reproduced in [18]. 2016 - Sphere packing for eight dimensions is solved by Maryna Viazovska. 2018 - Day of death of Stephen W. Hawking, English theoretical physicist (b. 1942). *

PI, by Wisáawa Szymborska (translated by Stanislaw Baranczak and Clare Cavanagh) The admirable number pi: three point one four one. All the following digits are also initial, five nine two because it never ends. It can't be comprehended six five three fiveat a glance, eight nine by calculation, seven nine or imagination, not even three two three eight by wit, that is, by comparison four six to anything else two six four three in the world. The longest snake on earth calls it quits at about forty feet. Likewise, snakes of myth and legend, though they may hold out a bit longer. The pageant of digits comprising the number pi doesn't stop at the page's edge. It goes on across the table, through the air, over a wall, a leaf, a bird's nest, clouds, straight into the sky, through all the bottomless, bloated heavens.

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Oh how brief a mouse tail, a pigtail is the tail of a comet! How feeble the star's ray, bent by bumping up against space! While here we have two three fifteen three hundred nineteen my phone number your shirt size the year nineteen hundred and seventy-three the sixth floor the number of inhabitants sixty-five cents hip measurement two fingers a charade, a code, in which we find hail to thee, blithe spirit, bird thou never wert alongside ladies and gentlemen, no cause for alarm, as well as heaven and earth shall pass away, but not the number pi, oh no, nothing doing, it keeps right on with its rather remarkable five, its uncommonly fine eight, its far from final seven, nudging, always nudging a sluggish eternity to continue.

March, 15 1570 - Andrea Argoli, Italian jurist, mathematician, astronomer, and medical writer (d. 1657). 1790 - Birthdate of Ludwig Immanuel Magnus, German mathematician (d. 1861). 1868 - Birthdate of Grace Chisholm Young, English mathematician (d. 1944). 1871 - James Clerk Maxwell, in a letter to C. J. Monro, comments on the fourth dimension, “The peculiarity of our space is that of its three dimensions, none is before or after another. As x is, so is y, and so is z... I am quite sure that the kind of continuity which has four dimensions all co-equal is not to be discovered by merely generalizing Cartesian space equations." [16] 1890 - Birthdate of Boris Delaunay, Soviet mathematician, and mountaineer (d. 1980). 1897 - Day of death of James Joseph Sylvester, English mathematician (b. 1814). 1900 - Day of death of Elwin Bruno Christoffel, German mathematician, and physicist (b. 1829). 1915 - The Paris Academy of Science, at a secret meeting, voted to exclude foreign correspondents and associates who had signed the manifesto “Aufruf an die Kulturwelt!" [7].

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1939 - In his letter, Hasse claimed there was a “state of war between the Germans and the Jews" and considered the separation of both parties in mathematical reviewing a “truly impartial and hence genuinely international course." In reaction to this letter, Veblen insisted “that there is a war by the Germans against civilization." [158]. 1960 - Day of death of Eduard ýech, Czech mathematician (b. 1893). 1992 - Day of death of Deane Montgomery, American mathematician (b. 1909). 2004 - Day of death of John A. Pople, British mathematician, and chemist (b. 1925). 2006 - Day of death of George Whitelaw Mackey, American mathematician (b. 1916).

March, 16 1789 - Birthdate of Georg Ohm, German physicist, and mathematician (d. 1854). 1821 - Birthdate of Eduard Heine, German mathematician (d. 1881). 1838 - Day of death of Nathaniel Bowditch, American captain, and mathematician (b. 1773). 1846 - Birthdate of Gösta Mittag-Lefler, Swedish mathematician (d. 1927). 1866 - Friedrich Heinrich Albert Wangerin completed his doctorate from Königsberg University. 1915 - Birthdate of Kunihiko Kodaira, Japanese mathematician (d. 1997). 1916 - On his seventieth birthday in 1916, Mittag-Lefler and his wife signed their last will and testament. They gave their entire fortune to found a Mathematical Institute which now bears their names. 1922 - Day of death of George Bruce Halsted, American mathematician (b. 1853). 1933 - Day of death of Alfred Haar, Hungarian mathematician (b. 1885). 1940 - Day of death of Thomas Little Heath, British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer (b. 1861). 1941 - Day of death of Edward Lindsay Ince, British mathematician (b. 1891). 1980 - Day of death of William Prager, German-born American mathematician (b. 1903). 1986 - The Manchester Guardian Weekly announces that Colin Rourke of Warwick and his student Eduardo Rego of Oporto University in

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Portugal have solved the Poincaré conjecture. (It appeared that the proof contained a gap.) 1992 - Day of death of Yves-André Rocard, French mathematician, and physicist (b. 1903). 2016 - Day of death of Alexander Esenin-Volpin, Russian-American mathematician, and poet (b. 1924).

March, 17 1652 - Day of death of Benjamin Bramer, German architect, and mathematician (b. 1588). 1694 - Guillaume L'Hospital hired his former tutor Johann Bernoulli to “work on what I shall ask you ... and also to communicate to me your discoveries, with the request not to mention them to others." As a result of this cooperation, a calculus text containing the famous “L'Hôpital's rule" (founded by Bernoulli) appeared in 1696. 1733 - Birthdate of Carsten Niebuhr, German mathematician, cartographer, and explorer in the service of Denmark (d. 1815). 1771 - Day of death of Chester Moor Hall, English jurist, and mathematician (b. 1703). 1782 - Day of death of Daniel Bernoulli, Dutch-Swiss mathematician, and physicist (b. 1700). 1808 - Day of death of Carl Friedrich Hindenburg, German mathematician (b. 1741). 1846 - Day of death of Friedrich Bessel, German astronomer, mathematician, and physicist (b. 1784). 1876 - Birthdate of Ernest Benjamin Esclangon, French astronomer, and mathematician (d. 1954). 1853 - Day of death of Christian Doppler, Austrian physicist, and mathematician (b. 1803). 1897 - Birthdate of Charles Fox, British-Canadian mathematician (d. 1977). 1905 - Albert Einstein submits his paper “On a Heuristic Point of View Concerning the Production and Transformation of Light" to the Annalen der Physik. 1914 - Ramanujan departed from Madras aboard a ship. 1915 - Birthdate of Wolfgang Döblin, German-French mathematician (d. 1940). 1922 - Day of death of Heinrich Suter, Swiss historian of mathematics (b. 1848).

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1956 - Day of death of Henry Frederick Baker, English mathematician (b. 1866). 1955 - Day of death of Georges Jean Marie Valiron, French mathematician (b. 1884). 1962 - Day of death of Wilhelm Blaschke, German mathematician (b. 1885). 2007 - Day of death of John Backus, American mathematician, and computer scientist, designed Fortran (b. 1924). 2020 - Day of death of Pantelis Damianou, Cypriot mathematician (b. 1953).

March, 18 1602 - Birthdate of Jacques de Billy, French Jesuit, theologian, and mathematician (d. 1679). 1640 - Birthdate of Philippe de La Hire, French mathematician, and astronomer (d. 1719). 1690 - Birthdate of Christian Goldbach, Russian mathematician (d. 1764). 1796 - Birthdate of Jakob Steiner, Swiss mathematician (d. 1863). 1839 - Birthdate of Joseph-Emile Barbier, French astronomer, and mathematician (d. 1889). 1870 - Day of death of Agnes Sime Baxter, Canadian mathematician (d. 1917). 1871 - Day of death of Augustus De Morgan, Indian-English mathematician (b. 1806). 1876 - Birthdate of Ernest Benjamin Esclangon, French astronomer, and mathematician (d. 1954). 1905 - About six weeks before he submitted his doctoral thesis at the University of Zurich, Einstein submitted the paper “Uber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt" (“On a Heuristic Viewpoint Concerning the Production and Transformation of Light", the paper that earned Einstein the Nobel Prize) to Annalen der Physik. [172] 1911 - Birthdate of Walter Ledermann, German-British mathematician (d. 2009). 1928 - Birthdate of Lennart Axel Edvard Carleson, Swedish mathematician. 1930 - Birthdate of James J. Andrews, American mathematician (d. 1998). 1935 - Birthdate of Ole Barndorff-Nielsen, Danish mathematician, and statistician. 1964 - Day of death of Norbert Wiener, American mathematician (b. 1894).

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1989 - Day of death of Harold Jeffreys, English astronomer, geophysicist, and mathematician (b. 1891). 2010 - It had been announced that Grigori Yakovlevich Perelman had met the criteria to receive the first Clay Millennium Prize for the resolution of the Poincaré conjecture, but on July 1, Perelman would refuse to take it. 2013 - Day of death of Mary Ellen Rudin, American mathematician (b. 1924). 2016 - France issued a stamp for Sophie Germain.

March, 19 1685 - Day of death of René-François Walter de Sluse, Walloon mathematician, and churchman (b. 1622). 1791 - The metric system, including the decimal subdivision of the circle, was advocated in a report made to the Paris Academy of Sciences. The committee consisted of J. C. Borda, J. Lagrange, P. S. Laplace, G. Monge, and de Condorcet. 1797 - Gauss noted in his scientific diary that he had discovered the double periodicity of certain elliptic functions. 1862 - Birthdate of Adolf Kneser, German mathematician (d. 1930). 1914 - Birthdate of Leonidas Alaoglu, Canadian-American mathematician (d. 1981). 1922 - Day of death of George Ballard Mathews, English mathematician (b. 1861). 1937 - John von Neumann gave a popular lecture at Princeton on the game of poker. 1978 - Day of death of Gaston Maurice Julia, Algerian-French mathematician (b. 1893). 1984 - Day of death of Richard Ernest Bellman, American applied mathematician (b. 1920). 2011 - Day of death of James Laurie Snell, American mathematician (b. 1925).

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2019 - It was announced that Karen Uhlenbeck had won the Abel Prize, becoming the first woman to earn this award.

March, 20 1546 - Birthdate of BahƗ‫ ގ‬al-DƯn Muতammad ibn ণusayn al-‫ޏ‬ƖmilƯ, Syrian-Iranian theologian, mathematician, and astronomer (d. 1622). 1617 - Day of death of François d'Aguilon, Belgian Jesuit mathematician, physicist, and architect (b. 1567). 1665 - Robert Hooke becomes the Gresham Professor of Mathematics. 1834 - Birthdate of Charles William Eliot, American mathematician (d. 1926). 1840 - Birthdate of Franz Mertens, Polish-Austrian mathematician (d. 1927). 1884 - Birthdate of Philipp Frank, Austrian-American physicist, mathematician, and philosopher (d. 1966). 1862 - Birthdate of Adolf Kneser, German mathematician (d. 1930). 1884 - Birthdate of Philipp Frank, Austrian-American physicist, and mathematician (d. 1966). 1895 - Day of death of Ludwig Schläfli, Swiss mathematician (b. 1814). 1920 - Birthdate of Douglas George Chapman, Canadian-born American mathematical statistician (d. 1996). 1921 - Birthdate of Alfréd Rényi, Hungarian mathematician (d. 1970). 1938 - Birthdate of Sergei Novikov, Soviet-Russian mathematician. 1983 - Day of death of Ivan Matveyevich Vinogradov, Soviet mathematician (b. 1891).

March, 21 1543 - Copernicus' "De Revolutionibus" was published. 1699 - Day of death of Erhard Weigel, German mathematician, astronomer, and philosopher (b. 1625). 1768 - Birthdate of Joseph Fourier, French mathematician, and physicist (d. 1830). 1797 - Gauss makes an entry in his diary that the perimeter of the lemniscate can be divided into five equal parts by ruler and compass. 1822 - Day of death of D'Amondans Charles de Tinseau, French mathematician (b. 1748). 1884 - Birthdate of George David Birkhoff, American mathematician (d. 1944).

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1896 - Birthdate of Friedrich Waismann, Austrian mathematician, physicist, and philosopher from the Vienna Circle (d. 1959). 1920 - Birthdate of John Hammersley, British mathematician (d. 2004). 1925 - Wolfgang Pauli published his "exclusion principle." 1933 - Day of death of Enrico D'Ovidio, Italian mathematician (b. 1842). 1934 - Day of death of Thomas Muir, British mathematician (b. 1844). 1951 - Birthdate of David Nualart, Spanish mathematician. 1960 - Day of death of Sheila Scott Macintyre, Scottish mathematician (b. 1910). 1980 - Day of death of Peter Stoner, American mathematician, and astronomer (b. 1888). 2016 - France issues a stamp honoring Sophie Germain. 2016 - Sphere packing problem for 24 dimensions is solved by Maryna Viazovska.

March, 22 1394 - Birthdate of Ulugh Beg, Persian astronomer, and mathematician (d. 1449). 1638 - In a letter to Descartes, Mersenne reports that Fermat can prove that no number of the form 4n - 1 is a sum of two integral or rational squares [104]. 1784 - Birthdate of Samuel Hunter Christie, British mathematician (d. 1865). 1840 - Day of death of Étienne Bobillier, French mathematician (b. 1798). 1857 - Birthdate of Paul Doumer, French mathematician, journalist, and politician, 14th President of France (d. 1932). 1917 - Birthdate of Irving Kaplansky, Canadian-American mathematician (d. 2006). 1926 - Day of death of Joseph Jean Baptiste Neuberg, Belgian mathematician (b. 1840). 1945 - The first female Fellows were elected to the Royal Society. 1946 - Birthdate of Rudy Rucker, American mathematician, computer scientist. 1953 - Day of death of Gustav Herglotz, German mathematician (b. 1881). 1987 - Day of death of Andrew Paul Guinand, Canadian mathematician (b. 1912).

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March, 23 1749 - Birthdate of Pierre-Simon Laplace, French mathematician, and astronomer (d. 1827). 1754 - Birthdate of Jurij Vega, Slovene mathematician, physicist, and artillery officer (d. 1802). 1795 - Birthdate of Bernt Michael Holmboe, Norwegian mathematician (d. 1850). 1842 - Birthdate of Susan Jane Cunningham, American mathematician (d. 1921). 1862 - Birthdate of Eduard Study, German mathematician (d. 1930). 1882 - Birthdate of Emmy Noether, Jewish German-American mathematician, and physicist (d. 1935). 1897 - Birthdate of John Lighton Synge, Irish mathematician (d. 1995). 1907 - Birthdate of Hassler Whitney, American mathematician (d. 1989). 1934 - Birthdate of Ludvig Faddeev, Russian mathematician, and physicist (d. 2017). 1934 - Birthdate of Dmytro Petryna, Soviet-Ukrainian mathematician (d. 2006). 1963 - Day of death of Thoralf Skolem, Norwegian mathematician, and logician (b. 1887). 1979 - Day of death of Ivo Lah, Slovenian mathematician, and actuary (b. 1896). 2007 - Day of death of Paul Cohen, American mathematician (b. 1934). 2013 - Day of death of Boris Berezovsky, Soviet-British mathematician, and businessman (b. 1946).

March, 24 1653 - Birthdate of Joseph Sauveur, French mathematician, and physicist (d. 1716). 1789 - T. Jefferson wrote about the latest work by Lagrange to Joseph Willard: “A very remarkable work is the 'Mécanique Analytique' of La Grange in 4to. He is allowed to be the greatest mathematician now living, and his personal worth is equal to his science. The object of his work is to reduce all the principles of Mechanics to the single one of Equilibrium, and to give a simple formula applicable to them all. The subject is treated in the Algebraic method, without diagrams to assist the conception. My present occupation not permitting me to read anything that requires a long and undisturbed attention, I am not able

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to give you the character of this work from my examination. It has been received with great approbation in Europe." [45] 1809 - Birthdate of Joseph Liouville, French mathematician (d. 1882). 1835 - Birthdate of Joseph Stefan, Austrian physicist, mathematician, and poet (d. 1893). 1848 - Birthdate of Jules Tannery, French mathematician (d. 1910). 1880 - Day of death of Alfred Enneper, German mathematician (b. 1830). 1892 - Birthdate of Marston Morse, American mathematician (d. 1977). 1899 - René Louis Baire defended his doctoral thesis on the theory of functions of a real variable. 1915 - Day of death of Karol Olszewski, Polish chemist, mathematician, and physicist (b. 1846). 1948 - Birthdate of Alice Chang, Chinese American mathematician. 1956 - Day of death of Christine Mary Hamill, English mathematician (b. 1923). 1956 - Day of death of Edmund Taylor Whittaker, English mathematician (b. 1873). 1966 - Day of death of Anna Johnson Pell Wheeler, American mathematician (b. 1883). 1976 - Day of death of Francis Dominic Murnaghan, Irish mathematician (b. 1893). 2013 - Day of death of Yury Marchuk, Russian physicist, mathematician (b. 1925). 2019 - Day of death of Andrew Browder, American mathematician (b. 1931).

March, 25 1538 - Birthdate of Christopher Clavius, German mathematician, and astronomer (d. 1612). 1539 - Tartaglia tells Cardano about his method of solving cubic equations, and Cardano signs an oath to keep the method secret, according to Tartaglia [171]. 1656 - Christiaan Huygens discovered Saturn's moon Titan. 1792 - D'Alembert wrote: “I would like to see our friend Condorcet, who assuredly has great talent and wisdom, express himself in another manner." 1798 - Birthdate of Christoph Gudermann, German mathematician (d. 1852). 1818 - Day of death of Caspar Wessel, Norwegian-Danish mathematician, and cartographer (b. 1745).

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1822 - Gauss, in a letter to Heinrich Olbers, reveals plans to contact aliens: “With 100 separate mirrors, each of 16 square feet, used conjointly, one would be able to send good heliotropelight to the moon... This would be a discovery even greater than that of America if we could get in touch with our neighbors on the moon." 1859 - Birthdate of Samuil Shatunovsky, Russian mathematician (d. 1929). 1871 - Sophus Lie informed the faculty that he wanted to defend a doctorate [164]. 1931 - Kurt Gödel's “On Formally Undecidable Propositions of Principia Mathematica and Related Systems" was published. 1939 - Birthdate of Richard Alfred Tapia, renowned American mathematician. 1952 - Day of death of Antanas Mockus, Colombian mathematician, philosopher, and politician. 1995 - Day of death of Lee Albert Rubel, American mathematician (b. 1928).

March, 26 1535 - Day of death of Georg Tannstetter, Austrian mathematician, astronomer, and cartographer (b. 1482). 1609 - Day of death of John Dee, English astrologist, astronomer, and mathematician (b. 1527). 1619 - René Descartes reported (to Isaac Beeckman) his first results of “an entirely new science," known now as analytic geometry and which he would publish in 1637. 1656 - Birthdate of Nicolaas Hartsoeker, Dutch mathematician, and physicist (d. 1725). 1773 - Birthdate of Nathaniel Bowditch, American mathematician, and navigator (d. 1838). 1803 - Birthdate of John William Lubbock, English astronomer, and mathematician (d. 1865). 1848 - Birthdate of Konstantin Alekseevich Andreev, Russian mathematician (d. 1921). 1859 - Birthdate of Adolf Hurwitz, Jewish German-Swiss mathematician (d. 1919). 1902 - Birthdate of Marion Gray, British mathematician (d. 1979). 1903 - Birthdate of Patrick du Val, British mathematician (d. 1987). 1908 - Birthdate of Theodore Samuel Motzkin, Israeli-American mathematician (d. 1970).

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1912 - Einstein told Michele Besso that while developing the static gravitational field theory, the most interesting discovery was the following: He found that the principle of equivalence of acceleration and gravitation holds only for infinitely small systems. [179] 1913 - Birthdate of Paul ErdĘs, Hungarian-Polish mathematician (d. 1996). 1914 - Birthdate of Toru Kumon, Japanese mathematician (d. 1995). 1914 - Day of death of John S. Mackay, Scottish mathematician (b. 1843). 1922 - Birthdate of Guido Stampacchia, Italian mathematician (d. 1978). 1933 - Day of death of József Kurschák, Hungarian mathematician (b. 1864). 2015 - Day of death of Friedrich L. Bauer, German mathematician, computer scientist (b. 1924).

March, 27 1857 - Birthdate of Karl Pearson, English mathematician, eugenicist (d. 1936). 1888 - Day of death of Francesco Faà di Bruno, Italian mathematician, and priest (b. 1825). 1897 - Birthdate of Douglas Hartree, English mathematician, and physicist (d. 1958). 1905 - Birthdate of László Kalmár, Hungarian mathematician, and computer scientist (d. 1976). 1924 - Birthdate of Margaret K. Butler, American mathematician, and computer programmer (d. 2013). 1925 - Day of death of Carl Neumann, German mathematician (b. 1832). 1929 - Day of death of Samuil Shatunovsky, Russian mathematician (b. 1859). 1972 - Day of death of Maurits Escher, the famous Dutch mathematical artist (b. 1898).

March, 28 1678 - Day of death of Claude François Milliet Dechales, French mathematician (b. 1621). 1794 - Day of death of Marquis de Condorcet, French mathematician, and philosopher (b. 1743). 1809 - Gauss finished work on his Theoria Motus, which explained his methods of computing planetary orbits using least squares.

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1840 - Day of death of Simon Antoine Jean Lhuilier, Swiss mathematician (b. 1750). 1847 - Birthdate of Gyula Farkas, Hungarian mathematician, and physicist (d. 1930). 1850 - Day of death of Bernt Michael Holmboe, Norwegian mathematician (b. 1795). 1874 - Day of death of Peter Andreas Hansen, Danish-German astronomer, and mathematician (b. 1795). 1923 - Birthdate of Israel Nathan Herstein, Polish-American mathematician (d. 1988). 1928 - Birthdate of Alexander Grothendieck, German-French mathematician (d. 2014). 1950 - Day of death of Ernst David Hellinger, Jewish German-American mathematician (b. 1883).

March, 29 1749 - Day of death of Marie Jean Antoine Nicolas de Caritat Condorcet, French mathematician, and philosopher of mathematics (b. 1743). 1806 - Day of death of John Thomas Graves, Irish jurist, and mathematician (b. 1806). 1825 - Birthdate of Francesco Faa di Bruno, Italian mathematician, and priest (d. 1888). 1858 - A pencil with an attached eraser patented. 1865 - Engels, in a letter to A. Lange, wrote: “I cannot pass over without a comment on old Hegel, who they say had no profound mathematical scientific education. Hegel knew so much about mathematics that none of his pupils were in a position to publish the numerous mathematical manuscripts among his papers. The only man to my knowledge to understand enough about mathematics and philosophy to be able to do that is Mane" [113]. 1873 - Birthdate of Tullio Levi-Civita, Jewish-Italian mathematician (d. 1941). 1896 - Birthdate of Wilhelm Ackermann, German mathematician (d. 1962). 1912 - Birthdate of Martin Eichler, German mathematician (d. 1992). 1912 - Birthdate of Caius Jacob, Romanian mathematician (d. 1992). 1918 - Birthdate of Le Van Thiem, Vietnamese mathematician (d. 1991). 1923 - Birthdate of Israel Nathan Herstein, Polish-American mathematician (d. 1988). 1933 - Italy issued the world's first postage stamp portraying Galileo.

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1944 - Day of death of Grace Chisholm Young, English mathematician (b. 1868). 1969 - Birthdate of Shinichi Mochizuki, Japanese mathematician. 1999 - Day of death of Boris A. Kordemsky, Soviet mathematician, and educator (b. 1907).

March, 30 1559 - Day of death of Adam Ries, German mathematician (b. 1492). 1606 - Birthdate of Vincentio Reinieri, Italian mathematician, and astronomer (d. 1647). 1796 - The eighteen-year-old Gauss began his scientific diary. The first entry states, “Principia quibus innititur sectio circuli, ac divisibilitas eiusdem geometrica in septemdecim partes etc.," which records Gauss's discovery of the construction of a heptadecagon by ruler and compass.

1862 - Birthdate of Leonard James Rogers, British mathematician (d. 1933). 1882 - Poincaré in a letter to Klein about Riemann: “He was one of those geniuses who refresh so well the face of science that they imprint their character, not only on the works of their immediate students but on those of all successors for many years. Riemann created a new theory of functions, and it will always be possible to find there the germ of everything that has been done and that will be done after him in mathematical analysis." [90] 1886 - Birthdate of Stanisáaw LeĞniewski, Polish mathematician, philosopher, and logician (d. 1939).

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1892 - Birthdate of Stefan Banach, Polish mathematician (d. 1945). 1910 - Birthdate of Jozef Marcinkiewicz, Polish mathematician (d. 1940). 1919 - Day of death of Robin M. Williams, New Zealand mathematician (d. 2013). 1921 - The friendship and collaboration of Alexandrov and Uryson began [58]. 1929 - Birthdate of Ilya Piatetski-Shapiro, Soviet-Jewish mathematician (d. 2009). 1953 - Albert Einstein announced his revised unified field theory. 1995 - Day of death of John Lighton Synge, Irish mathematician (b. 1897). 2000 - Day of death of George Keith Batchelor, Australian applied mathematician, and fluid dynamicist (b. 1920). 2008 - Day of death of Roland Fraïssé, French mathematical logician (b. 1920). 2010 - Day of death of Jaime Alfonso Escalante Gutiérrez, Bolivian educator, and mathematician (b. 1930).

March, 31 1596 - Birthdate of René Descartes, French mathematician, and philosopher (d. 1650). 1624 - Day of death of João Baptista Lavanha, Portuguese mathematician (b. 1550). 1727 - Day of death of Isaac Newton (b. 1643). 1730 - Birthdate of Étienne Bézout, French mathematician (d. 1783). 1776 - Day of death of John Bird, English mathematical instrument maker (b. 1709). 1795 - Birthdate of Louis Paul Émile Richard (d. 1849). 1806 - Birthdate of Thomas Kirkman, English self-educated mathematician (d. 1895). 1841 - Day of death of George Green, English mathematician (b. 1793). 1847 - Birthdate of Yegor Ivanovich Zolotarev, Russian mathematician (d. 1878). 1848 - Birthdate of Diederik Korteweg, Dutch mathematician (d. 1941). 1854 - The University of Königsberg awarded Karl Weierstrass an honorary doctorate. Previously, he was a Gymnasium teacher without a university degree. 1877 - Day of death of Antoine Augustin Cournot, French mathematician, and philosopher (b. 1801). 1917 - Birthdate of Beno Eckmann, Swiss mathematician (d. 2008).

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1920 - Day of death of Paul Gustav Heinrich Bachmann, German mathematician (b. 1837). 1928 - Day of death of Hermann Felix Müller, German mathematician, and historian of mathematics (b. 1843). 1947 - Birthdate of Augustin Banyaga, Rwandan-American mathematician. 1959 - Sof'ja Janovskaja became the first chairperson of the newly created department of mathematical logic at Moscow State University. 1993 - The birth of spamming. A bug in a program written by Richard Depew sends an article to 200 newsgroups simultaneously. The term "spamming" is coined by Joel Furr (a writer and software trainer) to describe the incident. 2001 - Day of death of Geoffrey Walker, British mathematician (b. 1909). 2003 - Day of death of Harold Scott MacDonald Coxeter, EnglishCanadian mathematician (b. 1907).

CHAPTER FOUR APRIL

April, 1 1617 - Birthdate of Seth Ward, English mathematician, astronomer, and bishop (d. 1689). 1640 - Birthdate of Georg Mohr, Danish mathematician (d. 1697). 1737 - Euler reads his paper "De fractionibus continuis dissertatio" (Essay on continued fractions) to the St. Petersburg Academy of Sciences. 1776 - Birthdate of Sophie Germain, French mathematician, physicist, and philosopher (d. 1831). 1801 - Birthdate of Henry Perigal Jr., British stockbroker, and amateur mathematician (d. 1898). 1801 - Gauss records in his diary that he extended his "purely analytical formula" for Easter to the Passover date. 1820 - Day of death of Isaac Milner, British mathematician (b. 1750). 1863 - Day of death of Jakob Steiner, Swiss mathematician (b. 1796). 1872 - Day of death of Martin Ohm, German mathematician, the younger brother of physicist Georg Ohm (b. 1792). 1874 - Birthdate of Ernest William Barnes, English mathematician, and theologian (d. 1953). 1876 - A proof of the Pythagorean Theorem by James A. Garfield, then a member of Congress from Ohio, was published in the New England Journal of Education. 1891 - Birthdate of Harold Jeffreys, English astronomer, geophysicist, and mathematician (d. 1989). 1895 - Birthdate of Alexander Craig Aitken, New Zealand's mathematician (d. 1967). 1898 - Birthdate of William James Sidis, Ukrainian-Russian Jewish American mathematician, anthropologist, and historian (d. 1944). 1916 - Birthdate of Sheila May Edmonds, British mathematician (d. 2002). 1921 - Day of death of Carl Johannes Thomae, German mathematician (b. 1840). 1947 - Birthdate of Alain Connes, French mathematician.

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1975 - Martin Gardner announced that in November 1974, William McGregor, a graph theorist from Wappingers Falls, N.Y., discovered a counterexample to the four-color conjecture. He produced a map containing 110 regions that requires five colors.* [50]

2009 An article entitled “The Changing Value of Pi" appeared in the New Scientist with an analysis of how the value of ʌ has been increasing over time. (See entry seven of [168]) *

The mathematics students at the University of Warwick realized that the column was an April Fool's joke, for they published a poem in Manifold, a journal of mathematical humor: Oh Mr. Gardner, What have you done? You've started up a rumour You should never have begun! A four-colour hoax can't Be undone so quick ... Oh Mr. Gardner, what A bloody silly trick!

April, 2 999 - Gerbert was elected Pope Sylvester II. 1618 - Birthdate of Francesco Maria Grimaldi, Italian mathematician, and physicist (d. 1663). 1888 - Birthdate of Antonio Signorini, Italian mathematical physicist, and civil engineer (d. 1963).

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1898 - Birthdate of Chiungtze C. Tsen, Chinese mathematician (d. 1940). 1906 - Birthdate of Shokichi Iyanaga, Japanese mathematician (d. 2006). 1923 - Birthdate of G. Spencer-Brown, English mathematician, and psychologist (d. 2016). 1931 - Gödel, in a letter to Bernays, discussed the definition of truth for a first-order system in a second-order system [110]. 1933 - Emmy Noether's right to teach at Göttingen was withdrawn because of her Jewish ancestry. 1934 - Birthdate of Paul Cohen, American mathematician (d. 2007).

April, 3 1529 - Birthdate of Michael Neander, German mathematician, and astronomer (d. 1581). 1717 - Day of death of Jacques Ozanam, French mathematician (b. 1640). 1736 - Euler replied to Ehler on the Königsberg Bridge Challenge: “... Thus you see, most noble Sir, how this type of solution bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle. Because of this, I do not know why even questions that bear so little relationship to mathematics are solved more quickly by mathematicians than by others. In the meantime, most noble Sir, you have assigned this question to the geometry of position, but I am ignorant of what this new discipline involves and as to which types of problem Leibniz and Wolff expected to see expressed in this way...” [84]. 1753 - Goldbach wrote to Euler with a conjecture that every odd number greater than 3 is the sum of an odd number and twice a square (he allowed 02). 1817 - Day of death of Friedrich Ludwig Wachter, German mathematician (b. 1792). 1835 - Birthdate of John Howard Van Amringe, American educator, and mathematician (d. 1915). 1859 - Birthdate of Karl Heun, German mathematician (d. 1929). 1892 - Birthdate of Hans Rademacher, German-American mathematician (d. 1969). 1900 - Birthdate of Albert Edward Ingham, English mathematician (d. 1967). 1900 - Day of death of Joseph-Louis-François Bertrand, French mathematician, and educator (b. 1822).

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1907 - Birthdate of Mark Grigorievich Krein, Soviet Jewish mathematician (d. 1989). 1998 - Day of death of Mary Cartwright, English mathematician (b. 1900). 1909 - Birthdate of Stanislaw Ulam, Polish-American mathematician, and physicist (d. 1984). 1983 - Taiwan issued a pair of stamps to celebrate the 400th anniversary of the arrival of Father Matteo Ricci (1552-1610) in China.

April, 4 1597 - Galileo writes to Kepler, “Like you, I accepted the Copernican position several years ago and discovered from thence the causes of many natural effects which are doubtless inexplicable by the current theories. I have written up many of my reasons and refutations on the subject, but I have not dared until now to bring them into the open, being warned by the fortunes of Copernicus himself, our master, who procured immortal fame among a few but stepped down among the great crowd (for the foolish are numerous), only to be derided and dishonored. I would dare to publish my thoughts if there were many like you; but, since there are not, I shall forebear." [152] 1617 - Day of death of John Napier, Scottish mathematician, physicist, and astronomer (b. 1550). 1692 - "Acta Eruditorum" contained, under a pseudonym, Vincenzo Viviani's problem of constructing, in a hemispherical cupola, four equal-sized windows such that the remaining area of the cupola is quadrable. The problem was solved by Leibniz, Guido Grandi, and Viviani himself. 1803 - Gauss in his letter on this day to Niklaus Fuss, the permanent secretary of the St. Petersburg Academy of Sciences, says that he cannot accept the employment offered there. 1809 - Birthdate of Benjamin Peirce, American astronomer, mathematician, and educator (d. 1880). 1842 - Birthdate of Edouard Lucas, French mathematician (d. 1891).

April

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1868 - Birthdate of Philippa Fawcett, English mathematician, and educator (d. 1948). 1870 - Benjamin Peirce wrote in the introduction of his Linear Associative Algebra, “This work has been the pleasantest mathematical effort of my life. In no other have I seemed to myself to have received so full a reward for my mental labor in the novelty and breadth of the results." 1884 - Birthdate of Thomas Murray MacRobert, Scottish mathematician (d. 1962). 1902 - Birthdate of Eberhard Frederich Ferdinand Hopf, Austrian mathematician (d. 1983). 1923 - Day of death of John Venn, English mathematician, and philosopher (b. 1834). 1925 - Day of death of Walter William Rouse Ball, British mathematician, and lawyer (b. 1850). 1949 - Birthdate of Shing-Tung Yau, Chinese-American mathematician. 1961 - Day of death of Simion Stoilow, Romanian mathematician (b. 1873). 1981 - Day of death of Carl Ludwig Siegel, German mathematician (b. 1896). 2020 - Day of death of Volodymyr Semenovych Korolyuk, SovietUkrainian mathematician (b. 1925).

April, 5 1588 - Birthdate of Thomas Hobbes, English scholar, and amateur mathematician (d. 1679). 1622 - Birthdate of Vincenzo Viviani, Italian mathematician, astronomer, and physicist (d. 1703). 1632 - In a letter to Mersenne, Descartes wrote that it took five or six weeks for him to discover a solution to the problem Golius had posed (problem of locus stated at Pappus's Collection to mathematicians) [153]. 1678 - Day of death of Claude Hardy, French lawyer, and amateur mathematician (b. 1598). 1684 - Day of death of William Brouncker, English mathematician (b. 1620). 1711 - As a continuation of an argument with Leibniz about the priority of the creation of Calculus, Newton gave, from the chair of the Royal Society, “a short account of his invention, with the particular time of his first mentioning or discovering it" [22].

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1727 - Ten days before his 20th birthday, Leonard Euler left Basel to join his friend Daniel Bernoulli at the Academy of Sciences in St. Petersburg [151]. 1861 - Day of death of Ferdinand Joachimsthal, German mathematician (b. 1818). 1869 - Birthdate of Sergey Chaplygin, Soviet physicist, mathematician, and engineer (d. 1942). 1877 - Birthdate of Georg Faber, German mathematician (d. 1966). 1900 - Day of death of Joseph Bertrand, French mathematician, economist (b. 1822). 1901 - Birthdate of Subbayya Sivasankaranarayana Pillai, Indian mathematician (d. 1950). 1908 - Minkowski's talk was published in Gottinger Nachrichten as a technical paper, “Die Grundgleichungen fur die elektromagnetischen Vorgange in bewegten Korpern" (“The Basic Equations for Electromagnetic Processes in Moving Bodies"). This was Minkowski's only publication on the topic of electrodynamics and relativity to appear before his death. [179]. 1911 - Birthdate of Walter Warwick Sawyer, mathematician, mathematics educator, and author, who taught on several continents (d. 2008). 1913 - Niels Bohr completed his groundbreaking paper concerning the quantum theory of the hydrogen atom, “On the constitution of atoms and molecules." 1933 - Day of death of Hjalmar Mellin, Finnish mathematician (b. 1854). 1937 - Birthdate of Andrzej Schinzel, Polish mathematician. 1955 - Nobel laureate Bertrand Russell sent a letter to Albert Einstein along with a rough draft of what would soon be known as the RussellEinstein Manifesto – a written warning to the world's population on the dangers of nuclear weapons, and a plea for all leaders to avoid war when faced with conflict – and asked him to be both a signatory and supporter. 2004 - Day of death of Heiner Zieschang, German mathematician (b. 1936). 2009 - Day of death of Irving John Good, British mathematician (b. 1916).

April, 6 1528 - Day of death of Albrecht Durer, German painter, engraver, and mathematician (b. 1471).

April

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1741 - Euler's first paper on partitions (replying to September 4, 1740, Philip Naude's question) is read at the weekly meeting of the St. Petersburg Academy [150]. 1748 - Goldbach observes that if 2n + 1 is a sum of three squares, then 2n + 3, 4n + 3, 4n + 6, and 6n + 3 are sums of four squares [104]. 1749 - Birthdate of Samuel Vince, English clergyman, mathematician, and astronomer (d. 1821). 1829 - Day of death of Niels Henrik Abel, Norwegian mathematician (b. 1802). 1841 - William Thompson, the future Lord Kelvin, formally entered at St. Peter's, Cambridge as a student. 1922 - Emmy Noether named “unofficial associate professor" at Gottingen. 1929 - Norway issued a set of stamps in honor of Neils Henrik Abel. This is the first set of stamps honoring a mathematician in Philatelic history.

1947 - Birthdate of Mike Worboys, English mathematician, and computer scientist. 1972 - Cray Research founded by Seymour Cray. 1993 - Day of death of John Charles Burkill, English mathematician (b. 1900). 1995 - Stephen Hawking, in response to a request for a “time travel equation" from the editors of THE FACE magazine, sent the following fax: “Thank you for your recent fax. I do not have any equations for time travel. If I had, I would win the National Lottery every week."

April, 7 1348 - Charles University founded in Prague by King Charles of Bohemia. 1646 - Torricelli sends “The Geometry of Indivisibles" to Michelangelo Ricci. 1696 - John Bernoulli, in a letter to Leibniz, becomes the first to use the term “integral" [27]. 1761 - Day of death of Thomas Bayes, English minister, and mathematician (b. 1701).

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1768 - Birthdate of François Joseph Francais, French mathematician (d. 1810). 1811 - Birthdate of Hasan Tahsini, Albanian astronomer, mathematician, and philosopher (d. 1881). 1823 - Birthdate of Guillaume-Jules Houël, French mathematician (d. 1886). 1823 - Day of death of Jacques Charles, French physicist, and mathematician (b. 1746). 1866 - Birthdate of Erik Ivar Fredholm, Swedish mathematician (d. 1927). 1889 - Day of death of Paul David Gustav du Bois-Reymond, German mathematician (b. 1831). 1921 - Birthdate of Feza Gürsey, Turkish mathematician, and physicist (d. 1992). 1923 - Birthdate of Peter Hilton, English-American mathematician (d. 2010). 1933 - Day of death of Raymond Edward Alan Christopher Paley, English mathematician (b. 1907). 1934 - Day of death of Ernst Paul Heinz Prüfer, German mathematician (b. 1896). 1940 - André Weil wrote to his wife Eveline from jail in Rouen: “My mathematics work is proceeding beyond my wildest hopes, and I am even a bit worried – if it is only in prison that I work so well, will I have to arrange to spend two or three months locked up every year?" [76]. 1955 - Birthdate of Tim Cochran, American mathematician (d. 2014). 1970 - The Netherlands issued a set of five stamps with a geometrical motive designed with the aid of a computer.

1986 - Day of death of Leonid Kantorovich, Russian mathematician, and economist (b. 1912). 1997 - Day of death of Wilhelm Fushchych, Soviet-Ukrainian mathematical physicist (b. 1936).

April

97

2009 - Day of death of Leonard E. Gillman, American mathematician (b. 1917). 2014 - Day of death of James Alexander Green, American-English mathematician (b. 1926).

April, 8 1461 - Day of death of Georg von Peuerbach, German mathematician, and astronomer (b. 1423). 1608 - Birthdate of Honoré Fabri, French Jesuit, mathematician, physicist, astronomer, and theologian (d. 1688). 1732 - Birthdate of David Rittenhouse, American astronomer, and mathematician (d. 1796). 1796 - Gauss wrote in his diary that he completed his first of six proofs of quadratic reciprocity.

1799 - Gauss made a still uninterpreted cryptic entry “REV. GALEN" in his scientific diary. 1829 - A letter arrived at Abel's home (2 days after his death) informing him of his appointment to a professorship at the University of Berlin. 1859 - Birthdate of Edmund Husserl, German Jewish-Austrian mathematician, and philosopher (d. 1938). 1903 - Birthdate of Aurel Wintner, Hungarian-American mathematician (d. 1958). 1903 - Birthdate of Marshall Harvey Stone, American mathematician (d. 1989). 1913 - Day of death of Julius König, Hungarian mathematician (b. 1849). 1917 - Birthdate of Winifred Asprey, American mathematician, and computer scientist (d. 2007). 1938 - Birthdate of Mary W. Gray, American mathematician, statistician, and lawyer. 1943 - The Rockefeller Foundation review announced that the “differential analyzer" at MIT was built at a cost of $130,500. 1944 - Birthdate of Michael George Aschbacher, American mathematician. 2005 - Day of death of Douglas Geoffrey Northcott, British mathematician (b. 1916).

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2008 - Day of death of Graham Higman, English mathematician (b. 1917). 2018 - Amateur mathematician Aubrey de Grey found a 1581-vertex, non4-colorable unit distance graph, thus narrowing down the HadwigerNelson problem (finding the minimum number of colors required to color the plane so that no two points at distance 1 from each other have the same color) to either 5, 6, or 7 colors.

April, 9 1643 - Day of death of Benedetto Castelli, Italian mathematician (b. 1578). 1673 - Leibniz elected Fellow of the Royal Society of London. 1716 - In a letter to Conti, Leibniz again reminded Newton of the admission he had made in the scholium, which he was now desirous of disavowing; Leibniz also states that he always believed Newton, but that, seeing him connive at accusations he must have known to be false, it was natural that he (Leibniz) should begin to doubt. [27] 1752 - A letter from James Short informing about a paper by Euler on "Correcting the Aberrations in the Object-Glasses of Refracting Telescopes" is read to the Royal Society. 1754 - Day of death of Christian Freiherr von Wolff, German philosopher, and mathematician (b. 1679). 1791 - Birthdate of George Peacock, English mathematician (d. 1858). 1810 - Pierre-Simon Laplace announced his Central Limit Theorem. 1813 - Birthdate of Robert R Anstice, English mathematician (d. 1853). 1813 - Birthdate of Duncan Farquharson Gregory, Scottish mathematician (d. 1844). 1816 - Birthdate of Charles-Eugene Delaunay, French mathematician, and astronomer (d. 1872). 1834 - Birthdate of Edmond N. Laguerre, French mathematician (d. 1886). 1852 - Dirichlet asked the Minister of Culture to grant him the guardianship of Jacobi's seven children [116]. 1865 - Birthdate of Charles Proteus Steinmetz, Polish-American mathematician, and engineer (d. 1923). 1869 - Birthdate of Elie Cartan, French mathematician (d. 1951). 1878 - Birthdate of Marcel Grossmann, Swiss mathematician (d. 1936). 1900 - Birthdate of Hendrik Douwe Kloosterman, Dutch mathematician (d. 1968). 1921 - Birthdate of Mary Jackson, African American mathematician, and aerospace engineer (d. 2005). 1928 - Birthdate of Tom Lehrer, American singer-songwriter, pianist, and mathematician.

April

99

1931 - Birthdate of Heisuke Hironaka, Japanese mathematician. 1983 - Day of death of Yozo Matsushima, Japanese mathematician (b. 1921). 2002 - Day of death of Leopold Vietoris, Austrian mathematician (b. 1891). 2019 - Day of death of Elwyn Ralph Berlekamp, American mathematician (b. 1940).

April, 10 1651 - Birthdate of Ehrenfried Walther von Tschirnhaus, German mathematician, physicist, and physician (d. 1708). 1662 - Robert Hooke read his first publication, a pamphlet on capillary action, to the Society for the Promoting of Physico-Mathematical Experimental Learning. 1751 - Euler writes to Clairaut after receiving a paper from Clairaut that explained his error in a theory of the motion of the moon. 1752 - Day of death of Joseph Louis Lagrange, Italian mathematician (b. 1736). 1755 - Thomas Simpson introduced error distributions. 1756 - Birthdate of John West, Scottish mathematician (d. 1817). 1766 - Birthdate of John Leslie, Scottish physicist, and mathematician (d. 1832). 1793 - Gaspard Monge was permitted to resign from the Ministry of the Navy and the Colonies of France to undertake the urgent task of supplying the French army with gunpowder. 1813 - Day of death of Joseph-Louis Lagrange, Italian mathematician, and astronomer (b. 1736). 1920 - Day of death of Moritz Cantor, German mathematician, and historian (b. 1829). 1930 - Day of death of William Edward Story, American mathematician (b. 1850). 1954 - Day of death of Arnold Dresden, Dutch-American mathematician (b. 1882). 1967 - Day of death of Oscar Chisini, Italian mathematician (b. 1889). 2015 - "Cheryl's Birthday" question was first posted on Facebook by Singapore television presenter Kenneth Kong and quickly went viral. Kong posted the puzzle following a debate with his wife, and he incorrectly thought it to be part of a mathematics question for a primary school examination, aimed at 10- to 11-year-old students. However, it was actually part of the 2015 Singapore and Asian Schools

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Math Olympiad meant for 14-year-old students, a fact later acknowledged by Kong. The competition was held on 8 April 2015, with 28,000 participants from Singapore, Thailand, Vietnam, China, and the UK. According to SASMO's organizers, the quiz was aimed at the top 40 percent of the contestants and aimed to "sift out the better students." SASMO's executive director told the BBC that "there was a place for some kind of logical and analytical thinking in the workplace and in our daily lives."

April, 11 1594 - The twenty-two-year-old Kepler arrived in southern Austria to take up his duties as a teacher and as a provincial mathematician. 1626 - Day of death of Marino Ghetaldi, Croatian mathematician, and physicist (b. 1568). 1734 - Day of death of Thomas Fantet de Lagny, French mathematician (b. 1660). 1816 - Gauss responded to Gerling (who had written to Gauss in March about Legendre's theory of parallels) that Legendre's argument does not carry the weight of proof for him, and then comments on what happens if Euclidean geometry is not correct [26]: "It is easy to show that if Euclid's geometry is not the true one, then there are no similar figures: the angles in an equilateral triangle depend on the size of the edges, in which I do not find anything absurd. Then the angle is a function of the side, and the side is a function of the angle, naturally in such a way that a linear constant appears. It seems somewhat paradoxical that a linear constant can be a priori possible, but I don't find anything contradictory in this. It would be even desirable that Euclid's geometry is not true, for then we would have a general measure a priori. For example, one could assume as the unit of space the side of the equilateral triangle whose angle = 59°59'59".99999…." 1894 - Birthdate of Paul Finsler, German, and Swiss mathematician (d. 1970). 1904 - Birthdate of Phillip Hall, British mathematician (d. 1982). 1907 - Day of death of Christian Gustav Adolph Mayer, German mathematician (b. 1839). 1908 - Birthdate of Brian Kuttner, British mathematician (d. 1992). 1914 - Birthdate of Dorothy Lewis Bernstein, American mathematician (d. 1988). 1921 - Birthdate of Leo Moser, Austrian-Canadian mathematician (d. 1970).

April

101

1953 - Birthdate of Andrew Wiles, English mathematician. 1969 - Day of death of Werner Schmeidler, German mathematician (b. 1890). 1974 - Day of death of Abraham Robinson, Jewish mathematician (d. 1974). 1989 - Day of death of Emil Grosswald, Romanian-American mathematician (b. 1912). 2020 - Day of death of John Horton Conway, English mathematician, known for Conway's Game of Life (b. 1937).

April, 12 1734 - Day of death of Thomas Fantet de Lagny, French mathematician (b. 1660). 1749 - Euler closes the gap in his proof of the Two-Squares Theorem. He can prove the Four-Squares Theorem except for the lemma: If ab and b are sums of four squares, then so is a. [104] 1794 - Birthdate of Germinal Pierre Dandelin, Belgian mathematician, and engineer (d. 1847). 1804 - Gauss became a fellow of the Royal Society of London. 1852 - Birthdate of Ferdinand von Lindemann, German mathematician (d. 1939). 1874 - Birthdate of William Charles Brenke, American mathematician (d. 1964). 1919 - Day of death of Friedrich Otto Rudolf Sturm, German mathematician (b. 1841). 1961 - In Syracuse, Italy, the scientific festivities began to celebrate the memory of Archimedes who was born in the city in 287 BC and was killed there in 212 BC by a Roman soldier. His last words, according to Livy, were “Nolitangere circulos meos" (Don't touch my circles). 1971 - Day of death of Wolfgang Krull, German mathematician (b. 1899). 1977 - Fiji issued a stamp showing a world map in a sinusoidal projection.

1983 - In his autobiography "Adventures of a Mathematician," Stanislaw M. Ulam (1976, pp. 196-200) wrote that the Monte Carlo method came to him while playing solitaire during an illness in 1946. Ulam

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described the method to John von Neumann, and they "developed the mathematics together." In an unpublished manuscript titled "The Origin of the Monte-Carlo Method," dated Apr. 12, 1983, Ulam adds that what seems to be the first written account of the method was given by von Neumann in a letter to Robert Richtmyer of Los Alamos in early 1947. [118] 2000 - Day of death of David George Crighton, British mathematician, and physicist (b. 1942). 2003 - National Public Radio reported that novelty automatic teller machine withdrawal slips, showing a balance of $314,159.26, were hot in New York City. [17]

April, 13 953 - Birthdate of Abu Bekr ibn Muhammad ibn al-Husayn Al-Karaji, Arab mathematician (b. 1029). 1668 - Lord Brouncker, President of the Royal Society, publishes "the first mathematical result to be published in a mathematical journal" in the Philosophical Transactions of the Royal Society. His demonstration of the method of quadrature of the rectangular hyperbola, y = x - 1, extended the work of Wallis in Arithmetica infinitorium. [161] 1728 - Birthdate of Paolo Frisi, Italian mathematician, astronomer, and physicist (d. 1784). 1743 - Birthdate of Thomas Jefferson, American President, and mathematical enthusiast (d. 1826). 1791 - Adrien-Marie Legendre was named one of the French Academy's three commissioners for the astronomical operations and triangulations necessary for determining the standard meter. The others were Mechain and Cassini IV. 1813 - Birthdate of Duncan Farquharson Gregory, Scottish mathematician (d. 1844). 1869 - Birthdate of Ada Isabel Maddison, British mathematician (d. 1950). 1879 - Birthdate of Francesco Severi, Italian mathematician (d. 1961). 1894 - Day of death of Baldassarre Boncompagni, Italian historian of mathematics (b. 1821). 1909 - Birthdate of Stanislaw Ulam, Polish-American mathematician (d. 1984). 1949 - Birthdate of Len Cook, New Zealand-English mathematician, and statistician. 1992 - Day of death of Feza Gursey, Turkish mathematician, and physicist (b. 1921).

April

103

2004 - Day of death of David Herbert Fowler, historian of Greek mathematics (b. 1937).

April, 14 1572 - Birthdate of Adam Tanner, Austrian mathematician, philosopher (d. 1632). 1611 - Galileo visited Rome at the height of his fame and was made the sixth member of the Accademia dei Lincei (Lynx Society). 1629 - Birthdate of Christiaan Huygens, Dutch mathematician, astronomer, and physicist (d. 1695). 1822 - In a letter to Gauss, Bessell recommends his student, Heinrich Ferdinand Scherk. Gauss considered Scherk one of the best students he ever had [175]. 1822 - Birthdate of Achille Sannia, Italian mathematician, and politician (d. 1892). 1828 - Having read Dirichlet's article "Recherches sur les diviseurs premiers d'une classe de formules du quatrième degré," F.W. Bessel enthusiastically wrote to A. von Humboldt: "... who could have imagined that this genius would succeed in reducing something appearing so difficult to such simple considerations. The name Lagrange could stand at the top of the memoir, and nobody would realize the incorrectness." [43] 1860 - A printed article on the Four-Color theorem (perhaps only the second public statement about it, see June 10, 1854, entry) was printed in the form of an Athanaeum book review of "The Philosophy of Discovery" by William Whewell. (Unsigned, but almost surely written by De Morgan, the review launched into a discussion of the Four-Color problem.) 1914 - Ramanujan first disembarked in London. 1917 - Birthdate of Nathan Saul Mendelsohn, American-born Canadian mathematician (d. 2006). 1927 - Birthdate of Marcel Berger, French mathematician (d. 2016). 1931 - The first issue of the review journal "Zentralblatt für Mathematik" published by Springer. 1935 - Day of death of Emmy Noether, German-American mathematician (b. 1882). 1964 - Day of death of Tatyana Afanasyeva, Russian-Dutch mathematician (b. 1876). 1977 - The German Democratic Republic issued a stamp commemorating the 200th anniversary of Gauss's birth, 30 April 1777.

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1983 - Day of death of Errett Albert Bishop, American mathematician (b. 1928). 2005 - Day of death of Saunders MacLane, American mathematician (b. 1909).

April, 15 1446 - Day of death of Filippo Brunelleschi, Italian mathematician (b. 1377). 1452 - Birthdate of Leonardo da Vinci (d. 1519). 1548 - Birthdate of Pietro Cataldi, Italian mathematician and astronomer (d. 1626). 1608 - Birthdate of Honoré Fabri, French Jesuit theologian, mathematician, physicist, and controversialist (d. 1688). 1630 - Descartes wrote to Mersenne, who had requested him to propose some appropriate mathematical problems to the Parisian mathematicians, that he was no longer able to solve mathematical problems himself [153]. 1704 - Day of death of Johan van Waveren Hudde, Dutch mathematician, and statesman (b. 1628). 1707 - Birthdate of Leonhard Euler, Swiss-Russian mathematician, and physicist (d. 1783). 1726 - Writer William Stukeley held a conversation with Isaac Newton in Kensington during which Newton recalled “when formerly, the notion of gravitation came into his mind" (see May 16, 1667 entry). Later, Stukeley, writing in his Memoirs of Sir Isaac Newton's Life, recorded that Newton said, “It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the earth's center." 1747 - Goldbach is skeptical about some of Fermat's claims, i.e., that every number is a sum of three triangular numbers, or that every integer 8n + 3 is the sum of three squares. [104]

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1747 - Euler, writing in response to a now-lost letter from D'Alembert, opposes the suggestion that logarithms of negative numbers could exist and, in particular, that ex could have both a positive and a negative value. He adds that as soon as the value of e, in y = ex is defined, then the logarithm of all values are also assigned. In the same letter, he continues his argument by giving a new definition, now popular, of ex as ex = 1 + x + x²/2 + … and hence the idea of a negative logarithm is impossible. [28] 1754 - Day of death of Jacopo Riccati, Italian mathematician (b. 1676). 1764 - Day of death of Peder Horrebow, Danish astronomer, and mathematician (b. 1679). 1793 - Day of death of Ignacije Szentmartony, Croatian priest, mathematician, and astronomer (b. 1718). 1809 - Birthdate of Hermann Grassmann, German linguist, and mathematician (d. 1877). 1831 - Gauss introduces the term “complex" for a + bi [118]. 1904 - The term “discrete mathematics" was introduced in the Twelfth Annual Report of the Ohio State Academy of Science [118]. 1912 - The fourth dimension was spoken of by Albert Einstein as time. 1929 - Birthdate of Thomas Brooke Benjamin, English mathematical physicist, and mathematician (d. 1995). 1934 - Birthdate of James Wiegold, Welsh mathematician (d. 2009). 1990 - Day of death of Karl Heinrich Weise, German mathematician (b. 1909).

April, 16 1178 BC - Homer records the events of a solar eclipse. This may have marked the return of Odysseus, the legendary King of Ithaca, to his kingdom after the Trojan War. The date is surmised from a passage in Homer's Odyssey, which reads, "The Sun has been obliterated from the sky, and an unlucky darkness invades the world." 1495 - Birthdate of Petrus Apianus, German mathematician, and astronomer (d. 1557). 1673 - G. Leibniz wrote to Oldenburg about series: “I conjecture that Mr. Collins himself does not speak of these summations of infinite series because he brings forward the example of the series 1/2, 1/3, 1/4, 1/5, 1/6, ...which if it is continued to infinity cannot be summed because the sum is not infinite, like the sum of the triangular numbers, but infinite. But now I am cramped by the space of my paper." 1682 - Birthdate of John Hadley, English mathematician (d. 1744).

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1705 - Isaac Newton was knighted by Queen Anne at Trinity College. 1788 - Day of death of Georges-Louis Leclerc, Comte de Buffon, French mathematician, and cosmologist (b. 1707). 1816 - Gauss writes to his friend H. C. Schumacker that he had independently discovered the Arithmetic-Geometric mean as a youth of 14 in 1791 [4]. 1820 - Birthdate of Victor Alexandre Puiseux, French mathematician, and astronomer (d. 1883). 1823 - Birthdate of Gotthold Eisenstein, German mathematician (d. 1852). 1866 - At the meeting of the London Mathematical Society, Prof. Cayley called attention to the theorem that the difference between two consecutive prime numbers may exceed any given number N - 1, whatever. For if a, b, c, …, k are the prime numbers not greater than N, then abc…k + 1, and abc…k + 1 + N may be one or both of them prime, but all the intermediate numbers are composite; that is, the difference of the two successive primes is • N at least. 1894 - Birthdate of Jerzy Neyman, Russian-American mathematician (d. 1981). 1898 - Birthdate of Helmuth Kneser, Baltic German mathematician (d. 1973). 1914 - Day of death of George William Hill, American astronomer, and mathematician (b. 1838). 1931 - Heinrich Scholz wrote to Rudolf Carnap about Gödel's work: “What is going on with Mr. Gödel? I hear all kinds of exciting things but I cannot make out what is all about" [110]. 1932 - Birthdate of Myhailo Yosypovych Yadrenko, Soviet-Ukrainian mathematician (d. 2017). 1998 - Day of death of Alberto Calderón, Argentinian-American mathematician (b. 1920). 2008 - Day of death of Edward Norton Lorenz, American mathematician, and meteorologist (b. 1917). 2019 - Day of death of Vladimir Boltyansky, Soviet-Russian mathematician, educator (b. 1925).

April, 17 485 - Day of death of Proclus Diadochus, Greek mathematician, and philosopher (b. 412). 1761 - Day of death of Thomas Bayes, English mathematician, and minister (b. 1702). 1766 - Birthdate of John Leslie, Scottish mathematician (d. 1832).

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1787 - Day of death of Wenceslaus Johann Gustav Karsten, German mathematician (b. 1732). 1798 - Birthdate of Etienne Bobillier, French mathematician (d. 1840). 1847 - Day of death of Francois-Joseph Servois, French mathematician (b. 1768). 1853 - Birthdate of Arthur Moritz Schönies, German mathematician (d. 1928). 1863 - Birthdate of Augustus Edward Hough Love, English mathematician (d. 1940). 1878 - Birthdate of Matteo Bottasso, Italian mathematician (d. 1918). 1902 - Day of death of Eberhard Frederich Ferdinand Hopf, German mathematician (d. 1983). 1956 - Day of death of Herman Muntz, German mathematician (b. 1884). 1977 - Day of death of Richard Dagobert Brauer, German-American mathematician (b. 1901). 1996 - Day of death of Piet Hein, Danish poet, and mathematician (b. 1905). 2013 - Zhang announced a proof that states there are infinitely many pairs of prime numbers that differ by 70 million or less. This result implies the existence of an infinitely repeatable prime 2-tuple, thus establishing a theorem akin to the twin prime conjecture.

April, 18 1557 - Maurolico completed the first volume of his Arithmetic.

1796 - Professor E.A.W. Zimmerman sent a short notice of Gauss's work on the constructibility of regular polygons to the Jenenser Intelligenzblatt. He added, “It is worthy of notice that Herr Gauss is now in his 18th year and has devoted himself here in Brunswick to philosophy and classical literature with just as great success as to higher mathematics."

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1803 - Day of death of Louis Francois Antoine Arbogast, French mathematician (b. 1759). 1810 - Gauss was elected as a member of the Berlin Academy of Sciences. 1831 - The University of the City of New York was founded. 1892 - Birthdate of Dmitrii Evgenevich Menshov, Soviet mathematician (d. 1988). 1904 - Birthdate of Stefan E Warschawski, American mathematician (d. 1991). 1907 - Birthdate of Lars Valerian Ahlfors, Finnish mathematician (d. 1996). 1916 - Birthdate of Ellis Robert Kolchin, American mathematician (d. 1991). 1918 - Birthdate of Hsien Chung Wang, Chinese-American mathematician (d. 1978). 1923 - Day of death of Pieter Hendrik Schoute, Dutch mathematician (b. 1846). 1928 - Birthdate of Mikio Sato, Japanese mathematician. 1943 - Day of death of William Henry Metzler, Canadian mathematician (b. 1863). 1945 - Birthdate of Joseph Bernstein, Soviet-Israeli mathematician. 1949 - Birthdate of Charles Louis Fefferman, American mathematician. 1955 - Day of death of Albert Einstein (b. 1879). 1999 - Day of death of Gian-Carlo Rota, Italian-American mathematician (b. 1932). 1999 - Day of death of Istvan Vincze, Hungarian mathematician (b. 1912). 2000 - Day of death of Mary Cannell, British historian of mathematics (b. 1913).

April, 19 1567 - Day of death of Michael Stifel, German monk, and mathematician (b. 1487). 1610 - Upon receiving an advance copy of Galileo's "Starry Messenger," Johannes Kepler composed a fan letter. "I may perhaps seem rash in accepting your claims so readily with no support of my own experience," Kepler wrote to Galileo, "But should I not believe a most learned mathematician, whose very style attests the soundness of his judgment?" [127]. 1739 - Day of death of Nicholas Saunderson, English mathematician (b. 1682).

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1748 - Birthdate of D'Amondans Charles de Tinseau, French mathematician (d. 1822). 1760 - Euler writes the first of many "Letters to a German Princess." 1831 - Day of death of Johann Gottlieb Friedrich von Bohnenberger, German astronomer, and mathematician (b. 1765). 1880 - Birthdate of Evgeny Evgenievich Slutsky, Soviet mathematician, and economist (d. 1948). 1881 - Day of death of Karl Peterson, Latvian-Russian mathematician (b. 1828). 1883 - Birthdate of Richard von Mises, Austrian-American mathematician, and physicist (d. 1953). 1885 - Birthdate of Leonida Tonelli, Italian mathematician (d. 1946). 1901 - Birthdate of Kiyoshi Oka, Japanese mathematician (d. 1978). 1905 - Birthdate of Charles Ehresmann, French mathematician (d. 1979). 1914 - Day of death of Charles Sanders Peirce, American mathematician, and philosopher (b. 1839). 1933 - Day of death of Ernest William Hobson, English mathematician (b. 1856). 1957 - First FORTRAN program run. 1958 - France issued a stamp to honor Jean Cavaillès (1903-1944).

1974 - Day of death of Alexander Dinghas, Turkish mathematician (b. 1908). 2013 - Day of death of Kenneth Ira Appel, American mathematician (b. 1932).

April, 20 1344 - Day of death of Levi ben Gerson, Jewish French astronomer and mathematician (b. 1288). 1543 - Copernicus' De Revolutionibus published.

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1543 edition held by University of Edinburgh Library

1644 - Birthdate of Heinrich Meissner, German mathematician (d. 1716). 1829 - Simeon Denis Poisson read his Memoir on the Mean Results of Observations before the Academy of Sciences. This paper contains his observations on the function f(x) = 1/ʌ(1+x2), which is often credited to Cauchy, whose interest in the function begins around 20 years later [96]. 1833 - Jakob Steiner received an honorary degree from the University of Königsberg. 1839 - Birthdate of Francesco Siacci, an Italian mathematician, ballistician, and officer in the Italian army (d. 1907). 1928 - Birthdate of Gerald Stanley Hawkins, English astronomer and mathematician (d. 2003). 1932 - Day of death of Giuseppe Peano, Italian mathematician and philosopher (b. 1858). 1942 - Day of death of Ludwig Berwald, Czech mathematician (b. 1883). 1945 - Day of death of Georg Feigl, German mathematician (b. 1890). 1957 - Day of death of Konrad Knopp, German mathematician (b. 1882). 1995 - Day of death of Paul Allen Catlin, American mathematician (b. 1948). 2006 - Day of death of Paul Moritz Cohn, German-British mathematician (b. 1924).

April, 21 1557(2) - Day of death of Petrus Apianus, German mathematician, and astronomer (b. 1495). 1642 - Birthdate of Simon de la Loubère, French mathematician, poet, and diplomat (d. 1729). 1652 - Birthdate of Michel Rolle, French mathematician (d. 1719).

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1692 - David Gregory delivered his inaugural lecture as Savilian professor of astronomy at Oxford. He received his post on the recommendation of Newton. 1719 - Day of death of Philippe de La Hire, French mathematician, and astronomer (b. 1640). 1774 - Birthdate of Jean-Baptiste Biot, French physicist, astronomer, and mathematician (d. 1862). 1825 - Day of death of Johann Friedrich Pfaff, German mathematician (b. 1765). 1875 - Birthdate of Teiji Takagi, Japanese mathematician (d. 1960). 1882 - Birthdate of Maurice Kraitchik, Belgian mathematician, and game designer (d. 1957). 1909 - Birthdate of Eduard L. Stiefel, Swiss mathematician (d. 1978). 1911 - Birthdate of Felix Adalbert Behrend, Jewish German-Australian mathematician (d. 1962). 1922 - Day of death of Alfred Bray Kempe, British mathematician (b. 1849). 1951 - Birthdate of Michael Freedman, American mathematician. 1954 - Day of death of Emil Leon Post, Polish-American mathematician (b. 1897). 2005 - Day of death of William H. Kruskal, American mathematician, and statistician (b. 1919). 2006 - Day of death of Paul Moritz Cohn, German-British mathematician (b. 1924). 2010 - Day of death of Herbert Federer, American mathematician (b. 1920). 2013 - Day of death of Shakuntala Devi, Indian mathematician, and astrologer (b. 1929).

April, 22 1592 - Birthdate of Wilhelm Schickard, German astronomer, and mathematician (d. 1635). 1724 - Birthdate of Immanuel Kant, German philosopher, who was trained as a mathematician and physicist (d. 1804). 1811 - Birthdate of Otto Hesse, German mathematician (d. 1874). 1830 - Birthdate of Thomas Archer Hirst, English mathematician (d. 1892). 1884 - Birthdate of David Enskog, Swedish mathematical physicist (d. 1947). 1887 - Birthdate of Harald August Bohr, Danish mathematician (d. 1951).

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1891 - Birthdate of Harold Jeffreys, English mathematician, geophysicist, and astronomer (d. 1989). 1903 - Birthdate of Taro Morishima, Japanese mathematician (d. 1989). 1903 - Birthdate of John Francis Riordan, American mathematician (d. 1988). 1910 - Birthdate of Norman Steenrod, American mathematician (d. 1971). 1916 - Birthdate of Hanfried Lenz, German mathematician (d. 2013). 1923 - Emmy Noether received a contract at Göttingen for teaching algebra, including lectures and exercises [38]. 1927 - Sugiura left Copenhagen for Göttingen. 1929 - Birthdate of Michael Atiyah, English-Lebanese mathematician (d. 2019). 1935 - Birthdate of Bhama Srinivasan, Indian-American mathematician. 1940 - André Weil wrote to his wife Eveline from jail in Rouen: “My mathematical fevers have abated... before I can go any further, it is incumbent upon me to work out the details of my proofs" [76]. 1945 - Day of death of Wilhelm Cauer, German mathematician (b. 1900). 1948 - Day of death of Herbert Richmond, British mathematician (b. 1863). 2008 - Day of death of Derek Thomas Whiteside, British historian of mathematics (b. 1932).

April, 23 1628 - Birthdate of Johannes Hudde, Dutch mathematician, and politician (d. 1704). 1827 - William Rowan Hamilton presented a paper on optics, titled “Theory of systems of rays," to the Royal Irish Academy while still an undergraduate. 1839 - Day of death of James Wood, British mathematician (b. 1760). 1858 - Birthdate of Max Planck, German physicist (d. 1947). 1910 - Birthdate of Sheila Scott Macintyre, Scottish mathematician (d. 1960). 1911 - Birthdate of Felix Adalbert Behrend, German-Australian mathematician (d. 1962). 1914 - Birthdate of Georgii Nikolaevich Polozii, Soviet mathematician (d. 1968). 1933 - Birthdate of Annie Easley, American computer scientist, mathematician, and engineer (d. 2011). 1973 - The USA issued a commemorative stamp honoring the 500th year of the publication of Copernicus' De Revolutionibus.

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1977 - Day of death of Boris Pavlovich Demidovich, Soviet mathematician (b. 1906). 2013 - Day of death of Frank W. J. Olver, English-American mathematician (b. 1924).

April, 24 1562 - Birthdate of Xu Guang-qi, Chinese mathematician (d. 1633). 1656 - Day of death of Thomas Fincke, Danish mathematician and physicist (b. 1561). 1750 - Birthdate of Simon Antoine Jean Lhuilier, Swiss mathematician (d. 1840). 1800 - The Library of Congress was established in Washington. 1863 - Birthdate of Giovanni Vailati, Italian philosopher, historian of science, and mathematician (d. 1909). 1897 - The first American Mathematical Society sectional meeting was held. 1899 - Birthdate of Oscar Zariski, Russian-American mathematician (d. 1986). 1919 - Birthdate of David Blackwell, American mathematician (d. 2010). 1924 - Birthdate of Isadore Manuel Singer. 1947 - Birthdate of Ovide Arino, French mathematician (d. 2003). 1949 - Columbia issued a stamp honoring the mathematician Julio Garavito Armero (1865-1920).

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April, 25 1744 - Day of death of Anders Celsius, Swedish astronomer, physicist, and mathematician (b. 1701). 1840 - Day of death of Simeon Denis Poisson, French mathematician and physicist (b. 1781). 1849 - Birthdate of Felix Klein, German mathematician (d. 1925). 1879 - Birthdate of Edwill Bidwell Wilson, American physicist and mathematician (d. 1964). 1810 - Wilhelm von Humboldt sent Gauss an offer of 1500 Thalers a year to serve as ordentliches Mitglied of the Academy with the assurance that, "... you are only requested to lend your name as a full professor to the new university and, as much as your leisure and health allow, to teach a course from time to time." 1898 - Bjornson wrote to his friend: "Sophus Lie has been here with his whole family. He is someone you ought to get to know! It is a fundamental and life-affirming experience. What a fellow!" 1903 - Birthdate of Andrey Kolmogorov, Soviet mathematician (d. 1987). 1912 - Birthdate of Donald Clayton Spencer, American mathematician (d. 2001). 1931 - Birthdate of Felix Berezin, Soviet mathematician and physicist (d. 1980). 1999 - Day of death of William Hunter McCrea, English astronomer, and mathematician (b. 1904). 2000 - Day of death of Lucien Le Cam, French mathematician, and statistician (b. 1924).

April, 26 1572 - Day of death of Petrus Ramus, French mathematician, and logician (b. 1515). 1636 - Fermat wrote to Mersenne about errors he believed Galileo had made in his description of free fall. He also told Mersenne about his work on spirals and his restoration of Apollonius's Plane loci. His work on spirals had been motivated by considering the path of free-falling bodies, and he had used methods generalized from Archimedes' work on spirals to compute areas under the spirals. In addition, Fermat wrote: "I have also found many sorts of analyses for diverse problems, numerical as well as geometrical, for the solution of which Viète's analysis could not have sufficed. I will share all of this with you

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whenever you wish and do so without any ambition, from which I am more exempt and more distant than any man in the world."

1760 - Euler was asked to tutor the niece of Frederick the Great, the Princess of Anhalt-Dessau. 1766 - D'Alembert, after writing to Frederick II in praise of Lagrange, wrote to Lagrange about an offer to move to Berlin: “My dear and illustrious friend, the king of Prussia has charged me to write you that if you would like to come to Berlin to occupy a place in the Academy, he would give you a pension of 1,500 crowns, which are 6,000 French pounds. Mr. Euler, unhappy for reasons of which I do not know the details, but in which I see that everyone thinks him wrong, requests permission to leave and wants to go to St. Petersburg. The king, who was not too anxious to grant it, would definitely give it to him if you accept the proposition that he has made." 1815 - Day of death of Carsten Niebuhr, German mathematician, cartographer, and explorer in the service of Denmark (b. 1733). 1832 - Birthdate of Robert Tucker, English mathematician (d. 1905). 1874 - Birthdate of Edward Huntington, American mathematician (d. 1952). 1876 - Day of death of Osip Ivanovich Somov, Russian mathematician (b. 1815). 1892 - Hermite to Stieltjes: “You state this result and then try to mortify me by saying that it is easy to prove. Since I can’t succeed in doing it, I appeal to your good nature to help me out of this difficulty." 1902 - Day of death of Lazarus Immanuel Fuchs, Jewish-German mathematician (b. 1833). 1903 - In a letter to Volterra, Levi-Civita wrote: “Before leaving [for the Easter holiday] I started and now go on studying wave theory […] – it is the subject I shall develop in my course of higher mechanics. I met, however, a preliminary difficulty […] concerning the lack of a definition of a wave, both general and rigorous" [21]. 1920 - Day of death of Srinivasa Ramanujan, Indian mathematician (b. 1887).

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1922 - Birthdate of Asger Hartvig Aaboe, American historian of the exact sciences and mathematician (d. 2007). 1925 - Birthdate of Vladimir Boltyansky, Soviet mathematician, educator (d. 2019). 1976 - Day of death of Carl Benjamin Boyer, American historian of sciences, and especially mathematics (b. 1906). 2007 - Day of death of Leonid Volevich, Soviet-Russian mathematician (b. 1932). 2019 - Rob van Nobelen computed a new World Record for the Most Delayed Palindromic Number: 12,000,700,000,025,339,936,491, which takes 288 iterations to reach a 142-digit palindrome.

April, 27 1755 - Birthdate of Marc-Antoine Parseval, French mathematician (d. 1836). 1740 - The French Academie des Sciences announced that their prize on the ebb and flow of the tides would be shared between Leonhard Euler, Daniel Bernoulli, Antoine Cavalleri, and Colin Maclaurin [66]. 1837 - Birthdate of Paul Albert Gordan, German mathematician (d. 1912). 1843 - Birthdate of Hermann Felix Muller, German mathematician and historian of mathematics (d. 1928). 1865 - King George V of Hanover visited Gottingen and ordered a commemorative plate placed in the room in which Gauss had died ten years before. 1913 - Birthdate of Irving Adler, American mathematician and writer (d. 2012). 1920 - Birthdate of Mark Krasnosel'skii, Soviet mathematician (d. 1997). 1932 - Birthdate of Gian-Carlo Rota, Italian-American mathematician and philosopher (d. 1999). 1936 - Day of death of Karl Pearson, English mathematician (b. 1857). 1938 - Day of death of Edmund Husserl, Czech mathematician, and philosopher (b. 1859). 1952 - Day of death of Guido Castelnuovo, Italian mathematician, and statistician (b. 1865). 1978 - Day of death of Guido Stampacchia, Italian mathematician (b. 1922).

April, 28 1664 - Trinity College, Cambridge awards a scholarship to Isaac Newton to study for his Master's Degree.

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1686 - The first book of Newton's Principia was completed [27]. 1693 - G. Leibniz wrote to L'Hospital, announcing his discovery of determinants fifty years before Cramer. Leibniz's work had little or no influence because it was not published until 1850 in his "Mathematische Schriften." 1714 - Leibniz, in a letter to Chamberlayne, wrote: "... that Newton produced a book to be published, which was written purposely to discredit me, and sent it to Germany, France, and Italy, as in the name of the [Royal] Society"; and he stated "that there was great room to doubt whether Newton knew his invention before he had it from him" [22]. 1765 - Birthdate of Sylvestre Francois Lacroix, French mathematician (d. 1834). 1773 - Birthdate of Robert Woodhouse, English mathematician (d. 1827). 1817 - C.F. Gauss wrote to the astronomer H. W. M. Olbers, saying, "I am becoming more and more convinced that the necessity of our (Euclidean) geometry cannot be proved, at least not by human intellect nor for the human intellect." 1831 - Birthdate of Peter Guthrie Tait, Scottish physicist, and mathematician (d. 1901). 1843 - Day of death of William Wallace, Scottish mathematician (b. 1768). 1854 - Birthdate of Hertha Marks Ayrton, Polish-British engineer, mathematician, and physicist (d. 1923). 1868 - Birthdate of Georgy Voronoy, Ukrainian mathematician (d. 1908). 1897 - In a letter to Fuchs, Dedekind expressed skepticism of a tale about Gauss attempting to light his pipe with a copy of his Disquisitiones Arithmeticiae [115]. 1906 - Birthdate of Kurt Gödel, Czech-American mathematician, philosopher (d. 1978). 1906 - Birthdate of Richard Rado, Jewish German mathematician (d. 1989). 1912 - Day of death of Wilhelm Cauer, German mathematician (b. 1900). 1923 - Birthdate of Fritz Joseph Ursell, British mathematician (d. 2012). 1937 - Birthdate of David Herbert Fowler, historian of Greek mathematics (d. 2004). 1946 - Day of death of Louis Bachelier, French mathematician (b. 1870). 1975 - Day of death of Hans Arnold Heilbronn, German-Jewish mathematician (b. 1908). 1983 - Greece issued a stamp portraying Archimedes and his Hydrostatic Principle.

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1986 - Day of death of R.H. Bing, American mathematician (b. 1914). 2004 - A paper was submitted electronically to the American Mathematical Monthly, which purports to be the shortest journal entry ever, essentially two words, "n² + 2 can." After some correspondence back and forth (the journal suggested, "a line or two of explanation might help"), the paper was accepted as a "filler" in the January 2005 issue.

April, 29 1667 - Birthdate of John Arbuthnot, Scottish physicist, and mathematician (d. 1735). 1699 - The French Academy of Sciences held its first public meeting in the Louvre.

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1756 - Benjamin Franklin was elected a Fellow of the Royal Society. 1831 - Weber was offered the position of a full professor of Physics at Gottingen to fill the position of Tobias Mayer, partially on the recommendation of Gauss. 1832 - Galois was released from prison. 1850 - Birthdate of William Edward Story, American mathematician (d. 1930). 1854 - Birthdate of Henri Poincaré, French mathematician, physicist, and engineer (d. 1912). 1864 - Day of death of Charles-Julien Brianchon, French mathematician (b. 1783). 1872 - Day of death of Jean-Marie-Constant Duhamel, French mathematician, and physicist (b. 1797). 1894 - Day of death of Giuseppe Battaglini, Italian mathematician (b. 1826). 1906 - Birthdate of Eugene Ehrhart, French mathematician (d. 2000). 1916 - Day of death of Jorgen Pedersen Gram, Danish mathematician (b. 1850). 1926 - Birthdate of Vera Nikolaevna Maslennikova, Soviet mathematician (d. 2000). 1930 - Birthdate of Yuan Wang, Chinese mathematician. 1936 - Birthdate of Volker Strassen, German mathematician. 1970 - Day of death of Paul Finsler, German-Swiss mathematician (b. 1894). 2005 - Day of death of Leonid Genrikhovich Khachiyan, Soviet mathematician (b. 1952). 2013 - Day of death of Ernest Michael, American mathematician (b. 1925).

April, 30 1633 - Galileo was forced to recant his scientific findings related to the Copernican Theory as "abjured, cursed, and detested" by the Inquisition. 1695 - Bernoulli explains to Leibniz his reasons for the use of the term "integral calculus" for Leibniz's new calculus. 1777 - Birthdate of Carl Friedrich Gauss, German mathematician, and physicist (d. 1855). 1807 - Gauss replies to S. Germain's letter (February 20, 1807) informing him that she is the person who had written to him using the name M. LeBlanc, that this will not change their correspondence [25]: "The

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scientific notes with which your letters are so richly filled have given me a thousand pleasures. I have studied them with attention, and I admire the ease with which you penetrate all branches of arithmetic, and the wisdom with which you generalize and perfect." 1861 - Birthdate of John Clark, Scottish mathematician (d. 1947). 1891 - Nature magazine publishes Peter Guthrie Tait's "The Role of Quaternions in the Algebra of Vectors." 1895 - Georg Cantor, in a letter to Felix Klein, explains the choice of aleph for the cardinality of sets [68]. 1904 - Birthdate of George Robert Stibitz, American mathematician (d. 1995). 1905 - Birthdate of Sergey Nikolsky, Russian mathematician (d. 2012). 1905 - Einstein completed his Doctoral thesis, with Alfred Kleiner, Professor of Experimental Physics, serving as a pro-forma advisor. 1907 - Day of death of Charles Howard Hinton, British mathematician (b. 1853). 1916 - Birthdate of Claude Shannon, American mathematician, and engineer (d. 2001). 1977 - Day of death of Charles Fox, British-Canadian mathematician (b. 1897). 1980 - Day of death of Stanislaw Golab, Polish mathematician (b. 1902). 1989 - Day of death of Gottfried Maria Hugo Kothe, German mathematician (b. 1905). 1993 - CERN announces World Wide Web protocols will be free. 2011 - Day of death of Daniel Gray Quillen, American mathematician (b. 1940).

CHAPTER FIVE MAY

May, 1 1514 - The catalogue of a Cracow professor's books included “a manuscript of six leaves expounding the theory of an author who asserts that the earth moves while the sun stands still. The professor was unable to identify the author, as Copernicus withheld his name from his Commentariolus. 1527 - Birthdate of Johannes Stadius, German astronomer, astrologer, mathematician (d. 1579). 1631 - Fermat received the degree of Bachelor of Civil Laws from the University of Orleans. 1791 - Birthdate of Jakob Philipp Kulik, Austrian mathematician (d. 1863). 1804 - George Baron publishes the first copy of the Mathematical Correspondent, the first mathematics journal published in the USA, and the first specialized science journal of any kind in the USA. 1825 - Birthdate of Johann Jakob Balmer, Swiss mathematician and physicist (d. 1898). 1870 - Day of death of Gabriel Lamé, French mathematician (b. 1795). 1891 - Birthdate of Louis Melville Milne-Thomson, English applied mathematician (d. 1974). 1908 - Birthdate of Morris Kline, American mathematician (d. 1992). 1908 - Birthdate of Hans Herbert Schubert, German mathematician (d. 1987). 1924 - Birthdate of Evelyn Boyd Granville, American mathematician, and computer scientist. 1926 - Birthdate of Peter Lax, Hungarian-American mathematician. 1930 - The name for Pluto (proposed by Venetia Burney, an eleven-yearold schoolgirl in Oxford, England) is announced to the world. 1935 - Albert Einstein wrote about Emmy Noether in his New York Times obituary: “In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant creative

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mathematical genius thus far produced since the higher education of women began." 1949 - Gerard Kuiper discovered Nereid, the second satellite of Neptune. 1964 - John Kemeny and John Kurtz ran the first BASIC program at Dartmouth.

May, 2 1519 - Day of death of Leonardo da Vinci (b. 1452). 1588 - Birthdate of Étienne Pascal, French tax assessor, lawyer, and mathematician, father of Blaise Pascal (d. 1651). 1683 - Day of death of Stjepan Gradic, Croatian philosopher, and mathematician (b. 1613). 1860 - Birthdate of D'Arcy Wentworth Thompson, Scottish biologist, and mathematician (d. 1948). 1901 - Birthdate of Édouard Zeckendorf, Belgian doctor, army officer, and mathematician (d. 1983). 1928 - Birthdate of Jacques-Louis Lions, French mathematician (d. 2001). 1967 - Day of death of Robert Daniel Carmichael, American mathematician (b. 1879). 1983 - Microsoft introduces the two-button mouse.

1982 - Day of death of Salomon Bochner, Galician-born American mathematician and educator (b. 1899). 2002 - Day of death of W. T. Tutte, English-Canadian mathematician (b. 1917). 2004 - Day of death of John Hammersley, British mathematician (b. 1920).

May, 3 1375 BC - The oldest recorded eclipse occurred. 1779 - Day of death of John Winthrop, American mathematician, physicist, and astronomer (b. 1714).

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1841 - L. G. J. Jacobi wrote, "It is worth noting that it is impossible today to choke down a single line of d'Alembert's mathematics, while most of Euler's works can be read with delight, and they died in the same year [1783]. D'Alembert seems to have been entirely absorbed in belles-lettres." 1842 - Birthdate of Otto Stolz, Austrian mathematician (d. 1905). 1849 - Arthur Cayley called to the Bar. He abandoned his fellowship at Cambridge and took up law as he didn't want to take Holy Orders. 1860 - Birthdate of Vito Volterra, Italian mathematician, and physicist (d. 1940). 1885 - Day of death of Ernst Ferdinand Adolf Minding, Russian mathematician (b. 1806). 1902 - The San Francisco Section of the AMS was founded. 1905 - Birthdate of Werner Fenchel, German-Danish mathematician (d. 1988). 1924 - Birthdate of Isadore Manuel Singer, American mathematician. 1928 - Birthdate of Jacques-Louis Lions, French mathematician (d. 2001). 1934 - Henri-Leon Lebesgue elected a foreign member of the Royal Society. 1940 - A. Weil was sentenced to 5 years in prison, which was immediately commuted if he agreed to serve in combat. 1948 - Birthdate of Vitaly Bondarenko, Ukrainian mathematician. 1977 - Birthdate of Maryam Mirzakhani, Iranian mathematician, the first female Fields medal winner (d. 2017). 1988 - Day of death of Lev Pontryagin, Russian mathematician (b. 1908). 1988 - Day of death of Abraham Seidenberg, American mathematician (b. 1916). 1997 - Garry Kasparov beat IBM's Deep Blue in the first match of what many considered a test of artificial intelligence. 2016 - The largest mathematical proof (taking 200 terabytes of space) of the "Boolean Pythagorean Triples" problem was submitted to Arxiv.org.

May, 4 1612 - Galileo wrote to Mark Welser, "The spots seen at sunset are observed to change place from one evening to the next, descending from the part of the sun then uppermost, and the morning spots ascend from the part then below." 1615 - Day of death of Adriaan van Roomen, Flemish priest, and mathematician (b. 1561).

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1677 - Day of death of Isaac Barrow, English mathematician, and theologian (b. 1630). 1694 - David Gregory and Newton disagreed on "kissing numbers" during Gregory's visit to Newton in Cambridge. Newton asserted that 12 was the maximum number of spheres that could be placed touching around a central sphere. Gregory held out that a 13th was possible. Kepler had shown a completely rigid arrangement of 12 spheres around one in his Six-cornered Snow. His method is called a hexagonal packing. But Newton and Gregory both knew that placing the surrounding 12 spheres at the vertices of an icosahedron around the central sphere, there was enough space to move the balls around. In fact, any two balls could be moved around and interchanged while all twelve balls were still in contact with the central one. The maximum "kissing number" is known for the first four dimensions, but beyond that only the eighth (240) and twenty-fourth (196,560) are exactly known. 1733 - Birthdate of Jean-Charles de Borda, French mathematician, physicist, and sailor (d. 1799). 1748 - Euler stated the product formula for sums of four squares. He also suggested proving theorems such as the Four-Squares Theorem using generating functions. 1756 - A letter from John Elliot to his father: "There is no News here worth troubling you with, only the discovery of the longitude by a Hanovarien, it is perform'd by an Observation of the Moon & any fix'd Star by knowing there distance at a given place & observing there difference at Sea given the difference of time. The observation is simple & easy but the Calculation is extremely perplexed. I had this from a Man that is making the Instrument." 1780 - American Academy of Arts and Sciences founded. 1820 - Birthdate of John Casey, Irish mathematician (d. 1891). 1845 - Birthdate of William Kingdon Clifford, English mathematician (d. 1879). 1859 - Day of death of Joseph Diaz Gergonne, French mathematician, and philosopher (b. 1771). 1876 - Birthdate of Heinrich Jung, German mathematician (d. 1953). 1916 - Birthdate of Elliott Waters Montroll, American mathematician (d. 1983). 1922 - Birthdate of Wooster Woodruff Beman, American mathematician, philologist, and historian of mathematics (d. 1922). 1935 - Albert Einstein, in a letter to the New York Times, wrote, “In the judgment of the most competent living mathematicians, Fraulein

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Noether was the most significant creative mathematical genius thus far produced since the higher education of women began." 1936 - Day of death of Alfred Cardew Dixon, English mathematician (b. 1865). 1961 - Day of death of Herbert Westren Turnbull, English mathematician (b. 1885). 1974 - Day of death of Otton Marcin Nikodym, Polish-American mathematician (b. 1887).

May, 5 1580 - Birthdate of Johann Faulhaber, German mathematician (d. 1635). 1777 - Euler addressed the paper "De Formulis Differentialibus Angularibus maxime irrationalibus quas tamen per logarithmos et arcus circulares integrare licet" to the 'Academiae,' where the symbol "i" for the imaginary constant was used for the first time. According to Cajori, the next appearance of "i" in print is by Gauss in 1801 in the Disquisitiones Arithmeticae. 1833 - Birthdate of Lazarus Immanuel Fuchs, Jewish-German mathematician (d. 1902). 1859 - Day of death of Peter Gustav Lejeune Dirichlet, German mathematician (b. 1805). 1877 - Birthdate of Alexander Brown, South African mathematician (d. 1947). 1883 - George Cantor wrote to Mitag-Lefler that Kronecker had called his work on transfinite set theory "Humbug" in a letter to Hermite. Kronecker reserved his attacks for personal correspondence and student lectures but said little or nothing publicly against Cantor. 1883 - Birthdate of Anna Johnson Pell Wheeler, American mathematician (d. 1966). 1889 - Birthdate of Rene Eugene Gateaux, French mathematician (d. 1914). 1895 - Birthdate of Stefan Bergman, Polish-born American mathematician (d. 1977). 1897 - Birthdate of Francesco Giacomo Tricomi, Italian mathematician (d. 1978). 1925 - Birthdate of Yuri Berezansky, Ukrainian mathematician (d. 2019). 1957 - Day of death of Leopold Löwenheim, German mathematician, and logician (b. 1878). 1980 - Greece issued a stamp honoring the 2300th anniversary of Aristarchus of Samos, the discoverer of the heliocentric theory.

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1981 - The German Democratic Republic issued a stamp honoring Richard Dedekind. 1989 - Day of death of Stefan E. Warschawski, American mathematician (b. 1904). 2002 - Day of death of Barry Edward Johnson, British mathematician (b. 1937). 2020 - Day of death of Yuri Kozachenko, Soviet-Ukrainian mathematician (b. 1940).

May, 6 1643 - Day of death of Pierre Herigone, French mathematician (b. 1580). 1667 - Birthdate of Abraham De Moivre, French mathematician (d. 1754). 1747 - Euler proves the Two-Squares Theorem except for the following lemma: There exist integers a, b such that an - bn is not divisible by the prime 4n + 1 [104]. 1769 - Birthdate of Jean Nicolas Pierre Hachette, French mathematician (d. 1834). 1792 - Birthdate of Martin Ohm, German mathematician, younger brother of physicist Georg Ohm (d. 1872). 1807 - Bessel wrote to Gauss, “I saw with pleasure that you have calculated the orbit of Vesta; also the name chosen by you is splendid, and therefore certainly also pleasant to all your friends because it shows them to which goddess you sacrifice." [175]. 1856 - Day of death of William Stirling Hamilton, Scottish mathematician (b. 1788). 1862 - Day of death of Olry Terquem, French mathematician (b. 1782). 1872 - Birthdate of Willem de Sitter, Dutch mathematician, physicist, and astronomer (d. 1934). 1895 - Birthdate of Julio Cesar de Mello e Souza, Brazilian mathematician and writer (d. 1974). 1906 - Birthdate of Andre Weil, French mathematician (d. 1998). 1916 - Day of death of Agoston Scholtz, Hungarian mathematician (b. 1844).

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1928 - Day of death of Robert Edgar Allardice, Scottish mathematician (b. 1862). 1951 - Day of death of Elie Joseph Cartan, French mathematician (b. 1869). 1968 - Day of death of Hendrik Douwe Kloosterman, Dutch mathematician (b. 1900). 1983 - Day of death of Yudell Leo Luke, American mathematician (b. 1918). 1993 - The new episode of The Simpsons has the character Apu boast “I can recite ʌ to 40,000 places. The last digit is one." [17]. 2009 - Chuan-Chih Hsiung, Chinese-American mathematician (b. 1915).

May, 7 1713 - Birthdate of Alexis Claude Clairaut, French astronomer, mathematician, and geophysicist (d. 1765). 1772 - Rev. Samuel Horsley's study “The Sieve of Eratosthenes. Being an Account of His Method of Finding All the First Numbers" was presented to the Royal Society of London. [85]. 1832 - Birthdate of Carl Gottfried Neumann, German mathematician (d. 1925). 1854 - Birthdate of Giuseppe Veronese, Italian mathematician (d. 1917). 1880 - Birthdate of Oskar Perron, German mathematician (d. 1975). 1881 - Birthdate of Ebenezer Cunningham, British mathematician (d. 1977). 1895 - Otto Steiger was issued a patent for his Millionaire calculating machine. For the next 40 years, Switzerland's Hans Egli manufactured 4,700 machines. The Millionaire was notable in its ability to perform direct multiplication, which meant a user could multiply a number by a single digit with a single rotation of the handle. 1900 - Day of death of Ernst Reinhold Eduard Hoppe, German mathematician (b. 1816). 1911 - Birthdate of Raymond Arthur Lyttleton, English mathematician, and theoretical astronomer (d. 1995). 1914 - Birthdate of Johannes de Groot, Dutch mathematician (d. 1972). 1927 - Birthdate of Allen Shields, American mathematician (d. 1989). 1934 - Day of death of Karl Friedrich Geiser, Swiss mathematician, organizer of the first International Congress of Mathematicians (b. 1843). 1980 - Day of death of Federico Cafiero, Italian mathematician (b. 1914).

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2007 - Day of death of Emma Markovna Lehmer, Russian-American mathematician (b. 1906).

May, 8 1654 - Otto von Guericke demonstrates the Magdenburg hemispheres.

Gaspar Schott's sketch of Otto von Guericke's Magdeburg hemispheres experiment.

1790 - The Assembly (French) ordered the Academie des Sciences to standardize weights and measures. 1859 - Birthdate of Johan Jensen, Danish mathematician, and engineer (d. 1925). 1900 - Day of death of Thomas Craig, American mathematician (b. 1855). 1905 - Birthdate of Karol Borsuk, Polish mathematician (d. 1982). 1951 - Day of death of Gilbert Ames Bliss, American mathematician (b. 1876). 1953 - Day of death of Benjamin Fedorovich Kagan, Soviet mathematician (b. 1869). 1959 - Day of death of Renato Caccioppoli, Italian mathematician (b. 1904). 1960 - Day of death of J. H. C. Whitehead, Indian-English mathematician (b. 1904). 1977 - Birthdate of Kathrin Bringmann, German mathematician. 2000 - Day of death Glen Eugene Bredon, American mathematician (b. 1932).

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May, 9 1694 - Johann Bernoulli wrote to Leibniz, introducing the method of "separation of variables" or "separation of indeterminates." 1746 - Birthdate of Gaspard Monge, French mathematician, and engineer (d. 1818). 1809 - A long correspondence between Legendre and Gauss on priority on least squares started. 1831 - Galois was arrested for proposing a toast to King Louis Philippe with a dagger above his cup, which was interpreted as a threat against the king's life. 1876 - Birthdate of Gilbert Ames Bliss, American mathematician (d. 1951). 1898 - Birthdate of Arend Heyting, Dutch mathematician (d. 1980). 1904 - Day of death of George Johnston Allman, Irish mathematician, and historian of ancient Greek mathematics (b. 1824). 1912 - Birthdate of Geza Ottlik, Hungarian mathematician (d. 1990). 1936 - Birthdate of Alexandre Aleksandrovich Kirillov, Soviet and Russian mathematician. 1948 - Birthdate of Hans Georg Bock, German mathematician, and computer scientist. 1950 - Day of death of Esteban Terradas i Illa, Spanish mathematician, and engineer (b. 1883).

May, 10 1482 - Day of death of Paolo dal Pozzo Toscanelli, Italian mathematician, and astronomer (b. 1397). 1741 - D'Alembert is accepted as an adjunct associate astronomer to the French Academy of Sciences. 1760 - Euler writes the tenth of his Letters (on the "compression of the air") to a German Princess. 1810 - Wilhelm Bessel became Professor of Astronomy at the University at Königsberg and director of the new observatory at Königsberg. 1821 - Birthdate of Baldassarre Boncompagni, Italian historian of mathematics (d. 1894). 1822 - Day of death of Paolo Ruffini, Italian mathematician, and physicist (b. 1765). 1829 - Day of death of Thomas Young, English polymath (b. 1773). 1847 - Birthdate of Wilhelm Killing, German mathematician (d. 1923). 1899 - Birthdate of Otakar Boruvka, Czech mathematician (d. 1995).

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1899 - F.A. Schossow patented a game called Katzenjammer Puzzle. In 1967, the Parker Brothers company released a similar game called Instant Insanity that caused a frenzy and was the ancestor of the Rubik's Cube. 1904 - Birthdate of Edward James McShane, American mathematician (d. 1989). 1924 - Day of death of August Gutzmer, German mathematician (b. 1860). 1933 - Kurt Schutte, the last of Hilbert's 75 doctoral students, defended his dissertation on logic. 1941 - Day of death of Diederik Korteweg, Dutch mathematician (b. 1848). 1989 - Day of death of Hassler Whitney, American mathematician (b. 1907). 1992 - Day of death of K. G. Ramanathan, Indian mathematician (b. 1920).

May, 11 1610 - Day of death of Matteo Ricci, Italian priest, and mathematician (b. 1552). 1702 - Birthdate of Isaac Greenwood, American mathematician (d. 1745). 1871 - Day of death of John Herschel, English mathematician, astronomer, and chemist (b. 1792). 1881 - Birthdate of Theodore von Karman, Hungarian-American mathematician, physicist, and engineer (d. 1963). 1887 - Birthdate of Griffith Conrad Evans, American mathematician (d. 1973). 1892 - Edgeworth's first Newmarch lecture in Oxford entitled "On the Uses and Methods of Statistics." 1902 - Birthdate of Edna Ernestine Kramer Lassar, American mathematician (d. 1984). 1905 - Albert Einstein's paper, "On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat" (Brownian motion paper), is received by Annalen der Physik. 1918 - Birthdate of Richard Phillips Feynman, American theoretical physicist (d. 1988). 1920 - Oxford admitted women to degree programs. 1924 - Birthdate of Eugene Dynkin, Soviet-American mathematician (d. 2014). 1940 - The Nimatron, an electro-mechanical machine that played Nim, was first exhibited by the Westinghouse Electric Corporation at the

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1939-1940 New York World's Fair to entertain fair-goers. Nim is a purely mathematical game with a winning strategy derived from the use of a binary number system. In the six weeks it was at the fair, it played 100,000 games with fair visitors and won 90% of them. The winners received a commemorative coin (Nim Champ).

Drawing of the Nimatron from patent application

1951 – Jay Forrester patented computer core memory. 1955 – Day of death of Nikolai Mitrofanovich Krylov, Russian and Soviet mathematician (b. 1879). 1957 – Day of death of Theophile Ernest de Donder, Belgian mathematician, and physicist (b. 1872). 1959 – Eugene P. Wigner delivered a penetrating Courant Lecture at NYU on “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” See the text of the lecture at [181]. 1997 – Garry Kasparov loses in the rematch with IBM’s Deep Blue in the first match of what many considered a test of artificial intelligence. 2012 – Day of death of Fritz Joseph Ursell, British mathematician (b. 1923).

May, 12 International Day of Women in Mathematics is celebrated on Maryam Mirzakhani's birthday. 1003 - Day of death of Gerbert d'Aurillac (Pope Sylvester II), French priest, and mathematician (b. 946). 1364 - Uniwersytet Jagiellonski (where N. Copernicus studied) was founded.

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1682 - Day of death of Michelangelo Ricci, Italian mathematician (b. 1619). 1732 - Laura Maria Caterina Bassi awarded a Doctorate of Science from the University of Bologna. 1753 - Day of death of Nicolas Fatio de Duillier, Swiss mathematician (b. 1664). 1796 - A paper on "Newton's Binomial Theorem Legally Demonstrated by Algebra" was read to the Royal Society by the Rev. William Sewell. 1819 - Sophie Germain wrote a letter to Carl Friedrich Gauss about her Grand plan to prove Fermat's Last Theorem. This letter contained the first substantial progress toward a proof in 200 years. 1820 - Birthdate of Florence Nightingale, English nurse, and pioneering statistician (d. 1910). 1845 - Birthdate of Pierre Rene Jean Baptiste Henri Brocard, French mathematician (d. 1922). 1851 - Birthdate of Samuel Dickstein, Polish mathematician (d. 1939). 1856 - Day of death of Jacques Philippe Marie Binet, French mathematician, physicist, and astronomer (b. 1786). 1857 - Birthdate of Oskar Bolza, German-American mathematician (d. 1942). 1865 - Birthdate of Thomas Scott Fiske, American mathematician (d. 1944). 1902 - Birthdate of Frank Yates, British statistician (d. 1994). 1919 - Birthdate of Wu Wenjun or Wu Wen-Tsun, Chinese mathematician. 1924 - Birthdate of Alexander Esenin-Volpin, Russian-American mathematician, and poet (d. 2016). 1967 - Birthdate of Mireille Bousquet-Melou, French mathematician. 1977 - Birthdate of Maryam Mirzakhani, Iranian mathematician (d. 2017). 1984 - The Hindu newspaper from Madras, India, reported the unveiling of a statue of Srinivasa Ramanujan. 2010 - Christian Mauduit and Joel Rivat prove Gelfond's 1968 conjecture that "on average, there are as many prime numbers for which the sum of decimal digits is even as prime numbers for which it is odd," according to a press release from CNRS. 2013 - The third "Pythagorean Day" of the 21st Century (the first was on March 4, 2005 (3/4/05) and the second on June 8, 2010). 2017 - A. Shchebetov's sequence of 261-step delay palindromes was extended to 108864 terms in total and included the first 108864 delayed palindromes with 261-step delay. The extended sequence ended with 1,999,291,987,030,606,810 – its largest and its final term.

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2020 - Day of death of Ernest Vingerg, Soviet-Russian mathematician (b. 1937).

May, 13 1713 - Birthdate of Alexis Clairaut, French mathematician, astronomer, and geophysicist (d. 1765). 1750 - Birthdate of Lorenzo Mascheroni, Italian mathematician (d. 1800). 1753 - Birthdate of Lazare Carnot, French general, mathematician, and politician, French Minister of the Interior (d. 1823). 1769 - Britain's Board of Longitude awarded 10 Pounds to Israel Lyons, Mathematician for, “Reward for his solution to a problem proposed by the late Dr. Halley which the Commissioners of Longitude think will be useful to Navigation." The problem seemed to be related to “traverse sailing." 1826 - Day of death of Christian Kramp, French mathematician (b. 1760). 1829 - Charles-Francois Sturm presented his theorem for finding the number of real roots of a polynomial equation to the French Academy. 1857 - Birthdate of Ronald Ross, Indian-English physician and mathematician, Nobel Prize laureate (d. 1932). 1866 - Day of death of Nikolai Brashman, Czech-Russian mathematician (b. 1796). 1914 - Birthdate of Antonia Ferrin Moreiras, Spanish mathematician and astronomer (d. 2009). 1931 - Birthdate of Andras Hajnal, Hungarian mathematician. 1939 - Day of death of Stanislaw Lesniewski, Polish mathematician, philosopher, and logician (b. 1886). 1944 - Day of death of William Edward Hodgson Berwick, British mathematician (b. 1888). 1957 - Day of death of Michael Fekete, Hungarian-Israeli mathematician (b. 1886). 1984 - Day of death of Stanislaw Marcin Ulam (b. 1909), Polish-American mathematician. 1995 - Day of death of Hao Wang, Chinese-American logician, philosopher, and mathematician (b. 1921). 2005 - Day of death of George Dantzig, American mathematician (b. 1914). 2013 - Peruvian mathematician Harald Andres Helfgott releases the first pre-print claiming a completed proof of the weak Goldbach Conjecture [74]. As of 2018, the proof is widely accepted in the mathematics community, but it has not yet been published in a peer-reviewed journal.

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May, 14 1631 - Pierre de Fermat installed at Toulouse, at age 31, as commissioner of requests. 1679 - Birthdate of Peder Horrebow, Danish astronomer and mathematician (d. 1764). 1701 - Birthdate of William Emerson, English mathematician (d. 1782). 1743 - In a letter to Nikolaus Bernoulli, Euler writes 1 + x + x2 + ... + xn. Previously, it was mostly represented as "etc." or "&c." 1755 - Joseph Louis Vincens de Mauleon, governor of the principality of Orange, published his "proof" that the circle could be squared. He claimed this proof enabled him to explain the mysteries of original sin and the Holy Trinity. Although he offered a prize of 300,000 francs to anyone who could show his proof fallacious, it is pure nonsense. 1761 - Day of death of Thomas Simpson, English mathematician (b. 1710). 1797 - Day of death of Giovanni Francesco Fagnano dei Toschi, Italian mathematician (b. 1715). 1832 - Birthdate of Rudolf Lipschitz, German mathematician (d. 1903). 1863 - Birthdate of John Charles Fields, Canadian mathematician, founder of the Fields Medal (d. 1932). 1888 - Birthdate of Archie Alexander, African-American mathematician and engineer (d. 1958). 1893 - Day of death of Ernst Kummer, German mathematician (b. 1810). 1917 - Birthdate of William Thomas Tutte, British-Canadian codebreaker, and mathematician (d. 2002).

May, 15 1615 - Birthdate of Frans van Schooten, Dutch mathematician (d. 1660). 1618 - Johannes Kepler discovered his third law of planetary motion. 1637 - Birthdate of Valentin Heins, German arithmetician (d. 1704). 1817 - John Herschel, in a letter to Charles Babbage, sent a mysterious doodle that still seems to be much of a mystery. Herschel said: "Interpret this hieroglyphic; it contains a great discovery." The figure at the center is described as "Dionysius the God of Functions, alias the genius of numerical magnitude." The God of Functions is suspected to refer to Dionysius Lardner, who taught Mathematics at Trinity College at that time. Many of the symbols seem to have no relevance to mathematics of the period. They may have been ideas tossed around

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between the two men in their attempts to modernize British Mathematics. 1833 - Day of death of Bewick Bridge, English vicar, and mathematical author (b. 1767). 1835 - Birthdate of Emile Mathieu, French mathematician (d. 1890). 1857 - Birthdate of Hermann Ludwig Gustav Wiener, German mathematician (d. 1939). 1900 - Birthdate of Ida Rhodes, American mathematician, pioneer in computer programming (d. 1986). 1903 - Birthdate of Maria Reiche, German-born Peruvian mathematician, and archaeologist (d. 1998). 1935 - Albert Einstein was awarded the Benjamin Franklin Medal for his outstanding fundamental contributions to theoretical physics, especially his relativity theory. 1939 - Birthdate of Brian Hartley, British mathematician (d. 1994). 1951 - Birthdate of Frank Wilczek, American mathematician, and physicist, Nobel Prize laureate. 1964 - Birthdate of Sijue Wu, Chinese-American mathematician. 1971 - Nicaragua issued a series of stamps showing "mathematical equations which changed the world." They range from 1 + 1 = 2 (Egyptians counting on their fingers) to Napier's law of logarithms and the Pythagorean Theorem. On the back of each stamp is a descriptive paragraph.

1975 - Day of death of Taira Honda, Japanese mathematician (b. 1932). 1985 - Benoit Mandelbrot received the Barnard Medal for Meritorious Service to Science. 1991 - Day of death of Andreas Floer, German mathematician (b. 1956). 2004 - Josh Findley discovered the 41st Mersenne prime, 224,036,583 - 1.

May, 16 1667 - In the course of attempting to conceive the physical laws explaining the Moon's revolution around the Earth, Newton happened to be sitting

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near the apple tree in the garden at Woolsthorpe when he saw an apple drop to the ground. At that moment, he realized that the same central pull of the Earth applied to both objects [23]. 1695 - Leibniz, in a letter to Johann Bernoulli, tells of his discovery of the multinomial theorem, "a wonderful rule for the coefficients of powers not only of the binomial x + y but also of the trinomial x + y + z, in fact, of any polynomial" [159]. 1718 - Birthdate of Maria Gaetana Agnesi, Italian mathematician, and philosopher (d. 1799). 1800 - Gauss records in his diary, "On about these days, we most elegantly resolved the problem of the chronology of the Easter Feast." 1821 - Birthdate of Pafnuty Chebyshev, Russian mathematician, and statistician (d. 1894). 1830 - Day of death of Joseph Fourier, French mathematician, and physicist (b. 1768). 1911 - Birthdate of John (Jack) Todd, Northern Irish mathematician (d. 2007). 1931 - Einstein visited Oxford University to give the Rhodes Lectures and receive a degree. During his talks, one of his blackboards was preserved and is now stored in the Museum of the History of Science in Oxford. The calculations are related to what is now called the Friedman-Einstein model of the universe. 1934 - Birthdate of Roy Patrick Kerr, New Zealander mathematician. 1983 - Day of death of Edouard Zeckendorf, Belgian doctor, army officer, and mathematician (b. 1901). 1995 - Day of death of Raymond Arthur Lyttleton, English mathematician, and theoretical astronomer (b. 1911). 2018 - Day of death of Sergiy Kolyada, Ukrainian mathematician (b. 1957).

May, 17 1702 - Richard Sault, English mathematician, editor, and translator, was buried. His exact date of birth and death are unknown. 1749 - Clairaut made an announcement in which he claimed that Newton's theory of gravity was right. In 1747, at a public session in the French Academy of Sciences, he had stated that Newton was wrong. Euler and d'Alembert had simultaneously come to the same conclusion as all had been working on the motion of the moon as a special case of the threebody problem. Clairaut suggested that the strength of gravity was proportional not only to 1/r2 but also to 1/r2 + c/r4 for some constant c.

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Over large distances, the c/r4 term would effectively disappear, accounting for the utility of the inverse square law over large distances. He continued to pursue this idea until May 17, 1749. 1765 - Day of death of Alexis Clairaut, French mathematician, astronomer, and geophysicist (b. 1713). 1818 - Birthdate of Ezra Otis Kendall, American astronomer, and mathematician (d. 1899). 1860 - Birthdate of Charlotte Barnum, American mathematician, and social activist (d. 1934). 1913 - Day of death of Heinrich Martin Georg Friedrich Weber, German mathematician (b. 1882). 1916 - Day of death of Mary Everest Boole, self-taught British mathematician, and wife of fellow mathematician George Boole (b. 1832). 1928 - Birthdate of Eric Charles Milner, British mathematician (d. 1997). 2001 - Day of death of Jacques-Louis Lions, French mathematician (b. 1928).

May, 18 1048 - Birthdate of Omar Khayyam, Persian mathematician, astronomer, and poet (d. 1131). 1711 - Birthdate of Roger Joseph Boscovich, Ragusan physicist, astronomer, and mathematician (d. 1787). 1772 Euler shows that in a paper to the St. Petersburg Academy. 1850 - Birthdate of Oliver Heaviside, English engineer, mathematician, and physicist (d. 1925). 1872 - Birthdate of Bertrand Russell, British mathematician, historian, and philosopher, Nobel Prize laureate (d. 1970). 1901 - Charles Sanders Peirce wrote to George Arthur Plimpton, a famous collector of rare mathematical books, describing what the contents of a newly acquired book must be were it indeed the Liber abaci of Fibonacci. 1914 - Birthdate of Stefan Schwarz, Slovakian mathematician (d. 1996). 1971 - Day of death of Aleksandr Gennadievich Kurosh, Soviet mathematician (b. 1908).

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May, 19 804 - Day of death of Alcuin of York, French mathematician, and educator (b. 735). 1682 - Birthdate of Mei Juecheng, Chinese writer, and mathematician (d. 1763). 1803 - Nicholas Fuss, Secretary of the St. Petersburg Academy of Sciences, writes to Carl Gauss to offer Gauss a position with a salary of 2400 rubles plus free lodgings and heat. 1832 - Birthdate of Edmond Bour, French mathematician (d. 1866). 1862 - Birthdate of Gino Benedetto Loria, Italian historian of mathematics (d. 1954). 1881 - Day of death of Rev. U Jessee Kniseley, American mathematician (b. 1838). 1919 - Birthdate of Georgii Dmitrievic Suvorov, Soviet mathematician (d. 1984). 1927 - Birthdate of Serge Lang, French-American mathematician (d. 2005). 1979 - Day of death of Ralph Duncan James, English-Canadian mathematician (b. 1909).

May, 20 1663 - Robert Hooke was one of 98 persons who were declared members at a meeting of the Royal Society. 1665 - Isaac Newton first used 'pricked letters' or dots to indicate derivatives, according to Florian Cajori's Mathematical Notations. 1716 - In a letter written to Leibniz, John Bernoulli discussed the equation d2y/dx2 = 2y/x2. 1861 - Birthdate of Henry White, founder of the American Mathematical Society's Colloquium Lectures (d. 1943). 1782 - Day of death of William Emerson, English mathematician (b. 1701). 1798 - Day of death of Erland Bring, Swedish mathematician (b. 1736). 1874 - Birthdate of Friedrich Moritz Hartogs, Jewish-German mathematician (d. 1943). 1875 - The International Bureau of Weights and Measures was established by the International Metric Convention in Sevres, France. 1901 - Birthdate of Max Euwe, Dutch chess player, mathematician, and author (d. 1981).

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1921 - Birthdate of Hao Wang, Chinese-American logician, philosopher, and mathematician (d. 1995). 1930 - The Institute for Advanced Study was established in Princeton, New Jersey. 1943 - Day of death of Henry White, founder of the American Mathematical Society's Colloquium Lectures (b. 1861). 1975 - Sweden issued a stamp picturing a metric tape measure to honor the centenary of the International Meter Convention in Paris.

May, 21 429 BC - Birthdate of Plato. 348 BC - Day of death of Plato. 1471 - Birthdate of Albrecht Durer, German painter, engraver, and mathematician (d. 1528). 1728 - The term "mathematical expectation," "l'esperance mathematique," with its modern meaning, is found in a letter by Gabriel Cramer to Nicholas Bernoulli. 1792 - Birthdate of Gaspard-Gustave de Coriolis, French mathematician, and engineer (d. 1843). 1847 - Birthdate of Antonio Favaro, Italian mathematician (d. 1922). 1848 - Day of death of Pierre Laurent Wantzel, French mathematician (b. 1814). 1858 - Birthdate of Edouard-Jean-Baptiste Goursat, French mathematician (d. 1936). 1919 - Day of death of Evgraf Fedorov, Russian mathematician, crystallographer, and mineralogist (b. 1853). 1923 - Birthdate of Armand Borel, Swiss-American mathematician (d. 2003). 1937 - Day of death of Herbert Ellsworth Slaught, American mathematician (b. 1861). 1953 - Day of death of Ernst Zermelo, German mathematician (b. 1871). 1957 - Day of death of Aleksandr Ivanovich Nekrasov, Soviet mathematician (b. 1883).

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1958 - Birthdate of Curtis Tracy McMullen, American mathematician. 1958 - Day of death of Wilhelm Suss, German mathematician (b. 1895). 1973 - Day of death of Grigore Constantin Moisil, Romanian mathematician, and computer pioneer (b. 1906).

May, 22 1649 - Blaise Pascal obtained, by royal decree, a monopoly for his computing machine. 1865 - Birthdate of Alfred Cardew Dixon, English mathematician (d. 1936). 1866 - Hermann von Helmholtz published "On the facts that underlie the foundations of geometry," containing an account of elliptic geometry. 1666 - Day of death of Gaspar Schott, German physicist, and mathematician (b. 1608). 1730 - Goldbach explains how to compute with remainders. 1868 - Day of death of Julius Plucker, German mathematician, and physicist (b. 1801). 1881 - Birthdate of William P. Milne, Scottish mathematician (d. 1967). 1903 - Birthdate of Yves-Andre Rocard, French mathematician, and physicist (d. 1992). 1916 - Birthdate of Albrecht Frohlich, German mathematician (d. 2001). 1933 - Birthdate of Chen Jingrun, Chinese mathematician (d. 1996). 1942 - Birthdate of Ted Kaczynski, American mathematician turned anarchist, and serial murderer (Unabomber). 1974 - Day of death of Irmgard Flogge-Lotz, German-American mathematician, and aerospace engineer (b. 1903). 1991 - Day of death of Derrick Lehmer, American mathematician (b. 1905). 2009 - Day of death of Walter Ledermann, German-British mathematician (b. 1911). 2010 - Day of death of Martin Gardner, American mathematician, cryptographer, and writer (b. 1914).

May, 23 1576 - Tycho Brahe was given the use of the island of Hven for his astronomical observatory. 1606 - Birthdate of Juan Caramuel y Lobkowitz, Spanish mathematician, and philosopher (d. 1682). 1849 - Birthdate of Arthur Edwin Haynes (d. 1915).

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1884 - Birthdate of Corrado Gini, Italian statistician (d. 1965). 1885 - Day of death of Thomas Clausen, Danish mathematician, and astronomer (b. 1801). 1887 - Birthdate of Thoralf Skolem, Norwegian mathematician (d. 1963). 1889 - Day of death of George Henri Halphen, French mathematician (b. 1844). 1895 - Day of death of Franz Ernst Neumann, German mineralogist, physicist, and mathematician (b. 1798). 1903 - Birthdate of William Prager, German-born American mathematician (d. 1980). 1907 - Birthdate of Boris A. Kordemsky, Soviet mathematician, and educator (d. 1999). 1917 - Birthdate of Edward Norton Lorenz, American mathematician, and meteorologist (d. 2008). 1940 - Birthdate of Cora Sadosky, Argentinian mathematician (d. 2010). 1953 - Day of death of Ernest Friedrich Ferdinand Zermelo, German mathematician (b. 1871). 1963 - Birthdate of Viviane Baladi, Swiss mathematician. 2015 - Day of death of John Forbes Nash, Jr., American mathematician, and Nobel Prize laureate (b. 1928).

May, 24 997 - Al-Biruni in Kath and Abu'l-Wafa in Baghdad simultaneously watched a lunar eclipse. The time obtained by this prearranged cooperation allowed them to determine the difference in longitude between the cities. 1543 - Day of death of Nicolaus Copernicus, Polish mathematician, and astronomer (b. 1473). On the same day, an advance copy of his work De revolutionibus orbium coelestium was presented to him. 1547 - Ferrari replied to Tartaglia's letter of 21 April 1547 by sending 31 challenge problems of his own. Tartaglia solved all but the five dealing with cubic equations. 1632 - Day of death of Robert Hues, English mathematician, and geographer (b. 1553). 1727 - Euler arrived in St. Petersburg for the first time. 1843 - Day of death of Sylvestre Francois Lacroix, French mathematician (b. 1765). 1903 - Birthdate of Wladyslaw Roman Orlicz, Polish mathematician (d. 1990).

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1909 - Birthdate of Karl Heinrich Weise, German mathematician (d. 1990). 1914 - Birthdate of Federico Cafiero, Italian mathematician (d. 1980). 1942 - Birthdate of Olexandr Stepanets, Soviet-Ukrainian mathematician (d. 2007). 1976 - Day of death of Cecil John Alvin Evelyn, English mathematician (b. 1904).

May, 25 1555 - Day of death of Gemma Frisius, Dutch physician, mathematician, and cartographer (b. 1508). 1632 - Day of death of Adam Tanner, Austrian mathematician, and philosopher (b. 1572). 1676 - Day of death of Johann Heinrich Rahn, Swiss mathematician (b. 1622). 1694 - Isaac Newton wrote to Nathaniel Hawes: “A Vulgar Mechanick can practice what he has been taught or seen done, but if he is in an error he knows not how to find it out and correct it, and if you put him out of his road, he is at a stand; Whereas he that is able to reason nimbly and judiciously about figure, force and motion, is never at rest till he gets over every rub." 1794 - Birthdate of William Whewell, English crystallographer, and mathematician (d. 1866). 1828 - Birthdate of Karl Peterson, Latvian-Russian mathematician (d. 1881). 1832 - E. Galois writes to his friend, Auguste Chevalier, about his broken romance for Stephanie Dumotel. 1901 - Giuseppe Peano (1858-1932) ended his service at the Royal Military Academy in Turin, where he had taught for more than fifteen years. In fact, he was fired. The problem was his teaching. In the early years of his career as a professor, he was excellent, but over the years, he devoted himself to mathematical research with an emphasis mainly on mathematical logic where he introduced new symbolism. He spent too much time on what the students called “symbols," and the result was his removal. 1914 - The Pi Mu Epsilon Fraternity was incorporated. 1919 - Birthdate of Raymond Merrill Smullyan, American mathematician, concert pianist, logician, Taoist philosopher. 1944 - Birthdate of Robert MacPherson, American mathematician.

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1946 - The Soviet Union issued two stamps to celebrate the 125th anniversary of Pafnuti Lvovich Chebyshev.

1954 - Birthdate of Clyde P. Kruskal, American computer scientist, and mathematician. 1956 - Day of death of Johann Radon, Austrian mathematician (b. 1887). 1973 - French mathematicians Jean Guilloud and Martine Bouyer computed ʌ on a CDC 7600 computer to one million decimal places, the greatest accuracy to date.

May, 26 1667 - Birthdate of Abraham de Moivre, French-English mathematician (d. 1754). 1796 - Gauss wrote to his counselor, Zimmerman, discussing his studies on the construction of the 17-gon and the quadratic reciprocity law. He expresses his preference for writing it in German before translating it to Latin. 1899 - Birthdate of Otto Neugebauer, German-American historian of mathematics (d. 1990). 1901 - Giuseppe Peano terminates his services at the Royal Military Academy in Turin. 1926 - Day of death of Frank Nelson Cole, American mathematician (b. 1861). 1941 - Birthdate of Constantine Michael Dafermos, Greek-American mathematician. 2002 - The minor planet 28242 was named after the Mongolian Mathematician Minggatu (Sharabiin Myangat) as 28242 Mingantu.

May, 27 1638 - In a letter to Fr. Marin Mersenne, René Descartes claimed to have a general rule to find a number "n" with a sum of its factors "S(n)" given only the ratio of "n/S(n) = p/q." He showed that "n/S(n) = 4/9" is solved

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for "n = 360." Fermat responded to Mersenne that 2016 has the same property. 1832 - In a letter to Legendre, Carl Gustav Jacob Jacobi stated that the solutions to the equation "x2 - ay2 = 1" can be expressed in terms of the sine and cosine of "2kʌ/a." 1849 - Pafnuty Chebyshev defended his doctoral dissertation on the theory of numbers at St. Petersburg University. 1862 - Birthdate of John Edward Campbell, Irish-English mathematician (d. 1924). 1907 - Birthdate of Herbert Seifert, German mathematician (d. 1996). 1928 - Day of death of Arthur Moritz Schönflies, German mathematician (b. 1853). 1962 - Day of death of Felix Adalbert Behrend, Jewish German-Australian mathematician (b. 1911). 1964 - Day of death of Colin Brian Haselgrove, English mathematician (b. 1926). 2012 - Day of death of Friedrich Hirzebruch, German mathematician (b. 1927).

May, 28 585 BCE - Thales of Miletus predicted the total eclipse of the sun that took place on this date in 585 BCE. 1665 - The earliest documentary proof of Isaac Newton's invention of "fluxions." 1676 - Birthdate of Jacopo Riccati, Italian mathematician (d. 1754). 1710 - Birthdate of Johann (II) Bernoulli, Swiss mathematician (d. 1790). 1765 - The Longitude Board at Greenwich awards Leonhard Euler an amount of 300 Pounds as a reward for the theorems he furnished to assist Professor Mayer in the construction of lunar tables based on the principles of gravitation laid down by Sir Isaac Newton. 1848 - Birthdate of Hermann Casar Hannibal Schubert, German mathematician (d. 1911). 1879 - Birthdate of Milutin Milankovic, Serbian mathematician, astronomer, and geophysicist (d. 1958). 1850 - Birthdate of Wooster Woodruff Beman, American mathematician and historian of mathematics (d. 1922). 1908 - Birthdate of Egbert Rudolf van Kampen, Dutch-American mathematician (d. 1942). 1912 - Birthdate of Hans Zassenhaus, German-American mathematician (d. 1991).

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1936 - Alan Turing submitted his article titled "On Computable Numbers, with an Application to the Entscheidungsproblem" to the Proceedings of the London Mathematical Society. The concept of the modern computer is based on this work.

1953 - Albert Einstein wrote to Maurice Solovine: "Moral: Unless one sins against logic, one generally gets nowhere; or, one cannot build a house or construct a bridge without using a scaffold which is really not one of its basic parts." 1959 - A committee was formed to develop COBOL (Common BusinessOriented Language), a high-level programming language used in business and administrative systems.

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1980 - Day of death of Rolf Nevanlinna, Finnish mathematician (b. 1895), known for his work in complex analysis and the Nevanlinna theory.

May, 29 1660 - Frans van Schooten, a Dutch mathematician, died at the age of 45. He is known for his work on analytical geometry and for publishing the works of René Descartes. 1675 – Birthdate of Humphry Ditton, English mathematician, and philosopher. 1733 - Leonhard Euler introduced the term "Pell Equations" and provided a method for finding multiple solutions to them. The Pell Equations are a type of Diophantine equation named after John Pell. 1832 - Évariste Galois, a French mathematician, wrote a letter predicting his own death in a duel the next day. In the letter, he expressed the hope that mathematicians like Carl Friedrich Gauss and Carl Gustav Jacob Jacobi would recognize the importance of his mathematical theorems: “Ask Jacobi or Gauss publicly to give their opinion, not as to the truth, but as to the importance of these theorems. Later there will be, I hope, some people who will find it to their advantage to decipher all this mess."

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1882 - Birthdate of Harry Bateman, an English mathematician known for his work in special functions and differential equations. He made significant contributions to the field of mathematical physics. 1893 - Birthdate of Charles Loewner, an American mathematician known for his work in complex analysis, operator theory, and mathematical physics. He made significant contributions to the theory of Loewner equations. 1898 - The heirs of Alfred Nobel, the inventor of dynamite, signed a "reconciliation agreement" to execute his will. This will eventually lead to the establishment of the Nobel Prizes, including the Nobel Prize in Physics and the Nobel Prize in Chemistry. 1906 - Birthdate of Gerrit Bol, a Dutch mathematician known for his work in topology, especially in the field of dimension theory. 1911 - Birthdate of George Szekeres, a Hungarian-born Australian mathematician known for his work in combinatorics, particularly on the ErdĘs-Szekeres theorem. 1919 - Einstein's prediction about the deflection of light in a gravitational field was confirmed during a solar eclipse. This confirmed a key prediction of his theory of general relativity, which was published in 1915-1916. 1929 - Birthdate of Peter Ware Higgs, an English theoretical physicist known for his groundbreaking work on the Higgs mechanism, which explains how particles acquire mass. The Higgs boson, a particle associated with this mechanism, was discovered in 2012. 1957 - Birthdate of Jean-Christophe Yoccoz, a French mathematician known for his work in dynamical systems and the theory of fractals. He was awarded the Fields Medal in 1994 for his contributions to mathematics. 2005 - Day of death of Urbanik Kazimierz, a Polish mathematician known for his work in probability theory and functional analysis. He made significant contributions to the study of random processes and stochastic analysis.

May, 30 1423 - Birthdate of Georg von Peuerbach, a German mathematician and astronomer known for his work on planetary motion. He was a leading figure in the European Renaissance and influenced the development of astronomy.

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1800 - Birthdate of Karl Feuerbach, a German mathematician who made contributions to geometry. Feuerbach's theorem in geometry is named after him and relates to the incircle and excircles of a triangle. 1814 - Birthdate of Eugène Charles Catalan, a Belgian-French mathematician known for his work in number theory and combinatorics. The Catalan numbers, which appear in various mathematical problems, are named after him. 1832 - Evariste Galois, the French mathematician who made pioneering contributions to abstract algebra and group theory, was mortally wounded in a duel. He died the following day at the age of 20. Galois' work laid the foundation for modern algebra. 1869 - Birthdate of Grace Andrews, an American mathematician known for her contributions to the theory of functions and functional equations. She was a pioneer in the field of functional equations. 1901 - Day of death of Victor D'Hondt, a Belgian mathematician, lawyer, and jurist. He is known for his work on electoral systems and is credited with developing the D'Hondt method for proportional representation in elections. 1926 - Day of death of Vladimir Steklov, a Russian mathematician and physicist known for his contributions to mathematical physics and potential theory. He made significant advancements in the study of harmonic functions. 1927 - Birthdate of Joan Birman, an American mathematician known for her research in low-dimensional topology and knot theory. Her work has had a significant impact on the field of mathematics. 1992 - Day of death of Antoni Zygmund, a Polish-born mathematician known for his contributions to mathematical analysis, particularly in the field of Fourier analysis. Zygmund's work has had a lasting influence on the study of functions and their properties.

May, 31 1503 - Nicolaus Copernicus received a doctoral degree in canon law from the University of Ferrara. 1683 - Birthdate of Jean-Pierre Christin, a French physicist, mathematician, and astronomer who is credited with inventing the Celsius thermometer. 1796 - Carl Friedrich Gauss recorded in his diary a prime number theorem conjecture. He conjectured that the function p(n), which counts the number of prime numbers less than or equal to n, is approximately equal to the integral of the logarithmic function for large values of n.

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This conjecture played a significant role in the development of number theory. 1813 - Louis Poinsot was elected to the mathematics section of the French Académie des Sciences, replacing the renowned mathematician Joseph-Louis Lagrange. 1823 - In a letter to a cousin, William Rowan Hamilton disclosed that he had made a "very curious discovery." This discovery is believed to be related to his development of quaternions, a significant contribution to algebra. 1832 - On this day, Evariste Galois, the French mathematician known for his groundbreaking work in group theory and abstract algebra, passed away at the age of 20. 1841 - Day of death of George Green, a British mathematical physicist known for Green's theorem in vector calculus. 1874 - Oliver Heaviside left his job as Chief Operator at Newcastle. Heaviside was a self-taught electrical engineer and mathematician known for his pioneering work in the theory of electromagnetism. He made significant contributions to the development of telegraphy and electrical engineering. 1926 - Birthdate of John Kemeny, Hungarian-American mathematician, and computer scientist. Kemeny was a co-developer of the BASIC programming language and played a key role in the development of early computer systems. 1991 - Day of death of Robert Schlapp, a Scottish mathematician known for his work in algebraic topology and homotopy theory. 1998 - Day of death of Michio Suzuki, a Japanese mathematician known for his work in group theory. 2000 - Day of death of Erich Kähler, a German mathematician known for his contributions to differential geometry.

CHAPTER SIX JUNE

June, 1 1631 - Pierre de Fermat married Louise de Long (his mother’s cousin), who gave him three sons. One of them (Samuel) edited and published his father's mathematical letters and papers in 1679. It was in these publications that Samuel revealed the marginal note in his father's copy of Diophantus's Arithmetica, which became known to the world as Fermat's Last Theorem. 1658 - Pascal posed his six questions related to the cycloid as challenge problems. For the complete list, see [19]. 1709 - The Rev. John Colson became the first headmaster of Sir Joseph Williamson's Free Mathematical School. 1815 - Birthdate of Osip Ivanovich Somov, Russian mathematician (d. 1876). 1851 - Birthdate of Edwin Bailey Elliott, British mathematician (d. 1937). 1867 - Day of death of Karl George Christian von Staudt, German mathematician (b. 1798). 1884 - Birthdate of Eduard Helly, Austrian mathematician (d. 1943). 1899 - Birthdate of Edward Charles Titchmarsh, English mathematician (d. 1963). 1904 - Day of death of Edward James McShane, American mathematician (b. 1904). 1912 - The problem of the division of coconuts with leftovers going to a monkey was first printed in English, in School Science and Mathematics by N. Anning. The problem is known to have existed back to the 8th century when Mahavira wrote the recreational math book: Ganita-sara-sangraha. 1918 - Day of death of Eduardo Torroja Caballe, Spanish mathematician (b. 1847). 1936 - The Physical Review received Einstein's submission. Tate returned the manuscript to Einstein on 23 July with a critical review and the mild request that he “would be glad to have [Einstein's] reaction to the various comments and criticisms the referee has made." Einstein wrote

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back on 27 July in high dudgeon, withdrawing the paper and dismissing out of hand the referee's comments. In the paper, it seems Einstein thought he had a proof that gravity waves, something of his own creation, could not exist. 1941 - Day of death of Kurt Hensel, German mathematician (b. 1861). 1944 - First COLOSSUS Mark II works. The Colossus machines were electronic computing devices used by British codebreakers to help read encrypted German messages during World War II. 1947 - Day of death of David Enskog, Swedish mathematical physicist (b. 1884). 2006 - Day of death of Shokichi Iyanaga, Japanese mathematician (b. 1906).

June, 2 1661 - Isaac Newton departed from his farm home at Woolsthorpe for Trinity College. 1686 - The publication of Newton's Principia was arranged in London at the Royal Society. 1785 - Day of death of Jean Paul de Gua de Malves, French mathematician, and academic (b. 1713). 1884 - Birthdate of Henry Thomas Herbert Piaggio, British mathematician (d. 1967). 1895 - Birthdate of Tibor Rado, Hungarian mathematician (d. 1965). 1916 - Birthdate of Abraham Seidenberg, American mathematician (d. 1988). 1917 - Day of death of William Henry Besant, British mathematician (b. 1828). 1923 - Birthdate of Lloyd Shapley, American mathematician, and economist, Nobel Prize laureate (d. 2016). 1924 - Birthdate of Hans-Egon Richert, German mathematician (d. 1993). 1929 - Day of death of Otto Schreier, German mathematician (b. 1901). 1932 - Birthdate of Taira Honda, Japanese mathematician (d. 1975). 1942 - Day of death of Andrew Russell Forsyth, Scottish mathematician (b. 1858). 2000 - Day of death of Gerald James Whitrow, English mathematician, cosmologist, and historian (b. 1912).

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June, 3 1659 - Birthdate of David Gregory, Scottish-English mathematician, and astronomer (d. 1708). 1663 - Robert Hooke was admitted to the Royal Society and was peculiarly exempted from all payments. 1856 - Lewis Carroll took his first photo of Alice Liddell. 1863 - Day of death of Edward Burr Van Vleck, American mathematician (b. 1818). 1903 - Day of death of Leopold Bernhard Gegenbauer, Austrian mathematician (b. 1849). 1906 - Birthdate of R. G. D. Allen, English economist, mathematician, and statistician (d. 1983). 1923 - Birthdate of Igor Shafarevich, Russian mathematician (d. 2017). 1928 - Birthdate of Karl Walter Gruenberg, British mathematician (d. 2007). 1943 - Birthdate of George Bluman, Canadian mathematician. 1954 - Birthdate of Susan Landau, American mathematician, and engineer. 1971 - Day of death of Heinz Hopf, German-Swiss mathematician (b. 1894). 1980 - Day of death of Naum Ilyich Akhiezer, Soviet mathematician (b. 1901). 1991 - Day of death of Le Van Thiem, Vietnamese mathematician, and academic (b. 1918).

June, 4 1730 - Euler observes that 2n + 1 is composite if n has an odd prime divisor. 1734 - George Berkeley's "The Analyst" is published. 1809 - Birthdate of John Henry Pratt, British clergyman, and mathematician (d. 1871). 1874 - William Kingdom Clifford is elected to the Royal Society of London. 1919 - Emmy Noether finally received the right to teach at Göttingen. 1925 - "No one shall expel us from the paradise which Cantor created for us," said David Hilbert in an address to the Westphalian Mathematical Society in Münster in honor of Karl Weierstrass. 1946 - Day of death of Ernst Leonard Lindelöf, Finnish mathematician (b. 1870). 1966 - Birthdate of Vladimir Voevodsky, Russian mathematician (d. 2017).

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1966 - To commemorate the 300th anniversary of the Académie des Sciences, France issued a stamp picturing Bernard Le Bovier de Fontenelle and the 1666 meeting room of the Académie.

1973 - Day of death of Maurice René Fréchet, French mathematician (b. 1878). 1982 - Hungary issued a stamp picturing Rubik's cube to celebrate the beginning of the First Rubik's Cube World Championship, which began in Budapest the next day.

2000 - Day of death of Albert Cyril Offord, British mathematician (b. 1906). 2008 - Day of death of Brian Griffiths, English mathematician (b. 1927). 2015 - Day of death of Leonid Plyushch, Ukrainian mathematician (b. 1938).

June, 5 1646 - Birthdate of Elena Cornaro Piscopia, Italian mathematician and philosopher (d. 1684). 1661 - Isaac Newton entered Trinity College, Cambridge, intending to earn a law degree.

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1667 - Day of death of Grégoire de Saint-Vincent, Flemish Jesuit and mathematician (b. 1584). 1716 - Day of death of Roger Cotes, English mathematician and academic (b. 1682). 1819 - Birthdate of John Couch Adams, English mathematician and astronomer (d. 1892). 1814 - Birthdate of Pierre Laurent Wantzel, French mathematician (d. 1848). 1833 - Ada Lovelace first met Charles Babbage at the home of Mary Sommerville. 1873 - The term 'radian' first appeared in print (in examination questions at Queen's College, Belfast, given by James Thomson). 1888 - Birthdate of Grigory Michailowitch Fichtenholz, Soviet mathematician (d. 1959). 1904 - Birthdate of George McVittie, British mathematician and cosmologist (d. 1988). 1930 - Birthdate of Gregory Maxwell Kelly, Australian mathematician (d. 2007). 1940 - Day of death of Augustus Edward Hough Love, British geophysicist and mathematician (b. 1863). 1965 - Day of death of Tadashi Nakayama, Japanese mathematician (b. 1912). 1977 - The first personal computer, the Apple II, went on sale.

June, 6 1436 - Birthdate of Regiomontanus, German mathematician, astronomer, and bishop (d. 1476). 1553 - Birthdate of Bernardino Baldi, Italian mathematician (d. 1617). 1857 - Birthdate of Aleksandr Lyapunov, Russian mathematician and physicist (d. 1918). 1858 - Schering qualified as a full professor at Göttingen. 1882 - Birthdate of Clement Vavasor Durell, English mathematician and writer of mathematical books (d. 1968). 1888 - Day of death of Erastus Lyman De Forest, American mathematician (b. 1834). 1898 - Day of death of Henry Perigal, Jr., British stockbroker and amateur mathematician (b. 1801). 1906 - Birthdate of Max August Zorn, German mathematician (d. 1993). 1907 - The University of Bern refused to appoint Einstein, saying “Dear Mr. Einstein, Your application for the Doctorate has not been

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successful at this time and as such you are not eligible for the position of Associate Professor. While you posed an interesting article published in “Annalen der Physik", we feel that your conclusion about the nature of light and the fundamental connection between space and time are somewhat radical. Overall, we find your assumptions to be more artistic than actual Physics. Sincerely yours, Professor Wilhelm Heinrich, Ph.D., Dean of Science". 1928 - Day of death of Luigi Bianchi, Italian mathematician. 1943 - Day of death of Guido Fubini, Italian-American mathematician (b. 1879). 1972 - Day of death of Abraham Adrian Albert, American mathematician (b. 1905). 1977 - Day of death of Stefan Bergman, Polish-born American mathematician (b. 1905). 1985 - Day of death of András P. Huhn, Hungarian mathematician (b. 1947). 2012 - Day of death of Jean-Louis Loday, French mathematician (b. 1946).

June, 7 1713 - Johan (I) Bernoulli wrote to Leibniz, informing him of the book from London accusing Leibniz of "plagiarism": "...my nephew (Nikolaus) brought from Paris a single copy of the Commercium Epistolicum... sent from London for distribution to the learned....you are at once accused by a tribunal consisting, ..., of the participants and witnesses themselves... documents against you are produced, sentence is passed; you lose the case, you are condemned." 1742 - Christian Goldbach wrote a letter to Leonhard Euler in which he proposed the following conjecture: "Every integer which can be written as the sum of two primes can also be written as the sum of as many primes as one wishes, until all terms are units." He then proposed a second conjecture in the margin of his letter: "Every integer greater than 2 can be written as the sum of three primes." 1847 - Day of death of Gustav Adolph Gopel, German mathematician (b. 1812). 1863 - Birthdate of Edward Burr Van Vleck, American mathematician (d. 1943). 1886 - Winifred Edgerton completed her thesis at Columbia, becoming the first American woman to receive her Ph.D. in mathematics and the first woman to graduate from Columbia University. 1890 - Birthdate of Werner Schmeidler, German mathematician (d. 1969). 1907 - Day of death of Edward John Routh, English mathematician (b. 1831).

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1954 - Day of death of Alan Turing, English mathematician, and computer scientist (b. 1912). 1958 - France issued a stamp with a portrait of Denis Diderot.

1967 - Day of death of Anatoly Maltsev, Soviet mathematician (b. 1909). 1990 - Day of death of Winifred Deans, British mathematician (b. 1901). 2004 - Day of death of Joseph Doob, American mathematician (b. 1910). 2019 - Day of death of Yuri Berezansky, Ukrainian mathematician (b. 1925).

June, 8 1625 - Birthdate of Giovanni Domenico Cassini, Italian-French mathematician and astronomer (d. 1712). 1637 - Printing of René Descartes' Discourse on the Method completed.

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1724 - Euler received a master’s degree in philosophy at the age of 17. 1736 - Euler wrote to James Stirling, informing him about his results on summing reciprocals of powers, including the harmonic series and Euler's constant, and other results on series: “Concerning the summation of very slowly converging series, in the past year I have lectured to our Academy on a special method of which I have given the sums of very many series sufficiently accurately and with very little effort." 1745 - Birthdate of Caspar Wessel, Norwegian-Danish mathematician and cartographer (d. 1818). 1860 - Birthdate of Alicia Boole Stott, Irish-English mathematician (d. 1940). 1870 - Birthdate of Peter Pinkerton, Scottish mathematician (d. 1930). 1887 - Herman Hollerith received a patent for his punch card calculator. 1897 - Birthdate of John G. Bennett, English mathematician, and technologist (d. 1974). 1905 - Birthdate of Edward Hubert Linfoot, English mathematician (d. 1982). 1924 - Birthdate of Samuel Karlin, American mathematician (d. 2007). 1930 - Birthdate of Robert Aumann, German-American mathematician and economist, Nobel Prize laureate. 1935 - Day of death of Alexander Wilhelm von Brill, German mathematician (b. 1842). 1947 - Day of death of Giacomo Albanese, Italian mathematician (b. 1890). 1955 - Birthdate of Tim Berners-Lee, English computer scientist who invented the World Wide Web. 1988 - Day of death of Roger Conant Lyndon, American mathematician (b. 1917). 1998 - Day of death of Maria Reiche, German mathematician, and archaeologist (b. 1903). 2010 - The second “Pythagorean Day" of the 21st Century (the first was on March 4, 2005 (3/4/05), and the third on May 14, 2013). 2012 - Day of death of Charles E. M. Pearce, New Zealand-Australian mathematician (b. 1940).

June, 9 1663 - Leibniz defended his Disputatio Metaphysica de Principio Individui (Metaphysical Disputation on the Principle of Individuation), which addressed the principle of individuation.

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1669 - Birthdate of Leonty Filippovich Magnitsky, Russian mathematician, and educator (d. 1739). 1750 - Euler lamented the fact that he could prove that every natural number is the sum of four rational squares, but not for integers. 1751 - Day of death of John Machin, English mathematician (b. 1680). 1861 - Birthdate of Pierre Duhem, French physicist, mathematician, and historian (d. 1916). 1885 - Birthdate of John Edensor Littlewood, English mathematician (d. 1977). 1893 - Day of death of Joel E. Hendricks, American mathematician (b. 1818). 1905 - Albert Einstein published his analysis of Planck's quantum theory and its application to light. 1906 - Birthdate of Albert Cyril Offord, British mathematician (d. 2000). 1969 - Day of death of Harold Davenport, English mathematician (b. 1907). 1977 - Day of death of Gustav Doetsch, German mathematician (b. 1892).

June, 10 940 - Birthdate of Abu al-Wafa' Buzjani, Persian mathematician, and astronomer (d. 998). 1827 - William Rowan Hamilton, at the age of 21, was appointed Astronomer Royal at Dunsink observatory at Trinity College, Ireland. This was a unique event as he was still an undergraduate. 1836 - Day of death of Andre-Marie Ampere, French physicist, and mathematician (b. 1775). 1854 - Riemann delivered the lecture "Uber die Hypothesen welche der Geometrie zu Grunde liegen Freudenthal" ("On the hypotheses at the foundations of geometry") to the philosophical faculty at Göttingen, in which he challenged the mathematical world to redefine the concept of infinity to be either endless or unbounded. 1854 - The first known published mention of the Four-Color Problem was printed in the Athenaeum on this date, appearing in the Miscellanea portion. The letter was signed with the initials F. G., which many supposed might have been one of the two Guthrie brothers involved in discovering the story and revealing it to DeMorgan, but others suspect it may have been Francis Galton, who had requested admission to the esteemed Athenaeum Club during this period. Certainly, many of the members would have heard the story of the four colors problem from

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De Morgan who had first circulated it to William R. Hamilton. (See also Oct. 23, 1852 entry). 1861 - Birthdate of Pierre (-Maurice-Marie) Duhem, French physicist, mathematician, and philosopher of science (d. 1916). 1885 - Birthdate of Andreas Speiser, Swiss mathematician (d. 1970). 1887 - Birthdate of Vladimir Ivanovich Smirnov, Soviet mathematician (d. 1974). 1903 - Day of death of (Antonio) Luigi (Gaudenzio Giuseppe) Cremona, Italian mathematician (d. 1830). 1904 - Birthdate of John Semple, Irish-English mathematician (d. 1985). 1924 - Birthdate of Friedrich L. Bauer, German mathematician and computer scientist (d. 2015). 1932 - Birthdate of Pierre Cartier, French mathematician. 1935 - Birthdate of Lu Jiaxi, Chinese self-taught mathematician (d. 1983). 1938 - Birthdate of Vasanti N. Bhat-Nayak, Indian mathematician (d. 2009). 1944 - Day of death of Willem Jacob van Stockum, Dutch mathematician (b. 1910). 1974 - Day of death of Jaroslav Hajek, Czech mathematician (b. 1926). 1992 - Day of death of Morris Kline, American mathematician, and popularizer of mathematical subjects (b. 1908).

June, 11 1656 - Birthdate of Charles Rene Reyneau, French mathematician (d. 1728). 1825 - Dirichlet gave his lecture "Mémoire sur l'impossibilité de quelques équations indéterminées du cinquième degré" (based on his first scientific work), and already one week later, Lacroix and Legendre gave a very favorable report on his paper. The Academy decided to have it printed in the Recueil des Mémoires des Savants étrangers. 1860 - Day of death of Baden Powell, English mathematician (b. 1796). 1862 - Birthdate of Lothar Heffter, German mathematician (d. 1962). 1881 - Birthdate of Hilda Hudson, English mathematician (d. 1965). 1895 - Day of death of Daniel Kirkwood, American mathematician, and astronomer (b. 1814). 1903 - Day of death of Nikolai Bugaev, Russian mathematician, and philosopher (b. 1837). 1909 - Birthdate of Natascha Artin Brunswick, German-American mathematician, and photographer (d. 2003). 1914 - Birthdate of Rufus Philip Isaacs, American mathematician (d. 1981).

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1915 - Birthdate of Nicholas Metropolis, American mathematician, and physicist (d. 1999). 1921 - Birthdate of Rodney Hill, English mathematician (d. 2011). 1934 - Day of death of Friedrich Wilhelm Franz Meyer, German mathematician (b. 1856). 1937 - Birthdate of David Mumford, English mathematician. 1955 - France issued a postage stamp with a portrait of Pierre Simon de Laplace (1749-1827).

1956 - Birthdate of Simon Plouffe, Canadian mathematician.

June, 12 1577 - Birthdate of Paul Guldin, Swiss astronomer, and mathematician (d. 1643). 1689 - Newton first met Christiaan Huygens at a Royal Society meeting in London. 1855 - Birthdate of Eduard Wiltheiss, German mathematician (d. 1900). 1888 - Birthdate of Zygmunt Janiszewski, Polish mathematician (d. 1920). 1900 - Day of death of Jean Frenet, French mathematician (b. 1816). 1918 - Birthdate of Christie Jayaratnam Eliezer, Sri Lankan-Australian mathematician (d. 2001). 1937 - Birthdate of Vladimir Arnold, Soviet-French mathematician (d. 2010). 1973 - Germany issued a postage stamp picturing a model of the calculator built by Wilhelm Schickard of the University of Tubingen 350 years before.

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1985 - Day of death of Hua Luogeng, Chinese mathematician (b. 1910).

June, 13 1555 - Birthdate of Giovanni Antonio Magini, Italian mathematician, cartographer, and astronomer (d. 1617). 1580 - Birthdate of Willebrord Snell, Dutch astronomer, and mathematician (d. 1626). 1676 - Newton corresponded with Leibniz, sending Henry Oldenburg the "Epistola prior" for transmission to Leibniz. It contained the first statement of the binomial theorem for negative and fractional exponents, among other things. 1676 - Modern notation for negative exponents a-n and exponents of the form an/2 appear in a letter from Newton to Oldenburg [29]. 1771 - Lagrange presented, to the Berlin Academy, the first proof of Wilson's theorem (n is prime iff n divides (n - 1)! + 1). Edward Waring published the theorem in 1770, but Leibniz knew it previously. 1773 - Birthdate of Thomas Young, English polymath (d. 1829). 1831 - Birthdate of James Clerk Maxwell, Scottish physicist, and mathematician (d. 1879). 1865 - Only three months before his death, Sir William Rowan Hamilton received a letter from the American astronomer Benjamin Gould, informing him that the newly created U.S. National Academy of Sciences had elected him first on its list of Foreign Associates, signifying that the academy considered him the greatest living scientist. 1871 - Birthdate of Ernst Steinitz, German mathematician (d. 1928). 1876 - Birthdate of William Sealy Gosset, English mathematician (d. 1937). 1878 - Arthur Cayley presented the four-color theorem to the London Mathematical Society [141]. 1884 - Birthdate of Leon Chwistek, Polish painter, philosopher, and mathematician (d. 1944). 1891 - Birthdate of Pierre Humbert, French mathematician (d. 1953). 1902 - Birthdate of Carolyn Eisele, American mathematician and historian (d. 2000). 1906 - Birthdate of Bruno de Finetti, Austrian-Italian mathematician, and statistician (d. 1985). 1916 - Day of death of Silvanus P. Thomson, English physicist, and mathematician (b. 1851).

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1920 - Birthdate of Iosif Vorovich, Russian mathematician, and engineer (d. 2001). 1928 - Birthdate of John Forbes Nash, Jr., American mathematician, Nobel Prize laureate (d. 2015). 1939 - Day of death of Hermann Ludwig Gustav Wiener, German mathematician (b. 1857). 1959 - France issued a stamp picturing Jean Le Rond d'Alembert.

1966 - Birthdate of Grigori Perelman, Russian mathematician. 1994 - Day of death of John Leslie Britton, English mathematician (b. 1927).

June, 14 1444 - Birthdate of Nilakantha Somayaji, Indian astronomer, and mathematician (d. 1544). 1649 - John Wallis appointed Savilian Professor of Geometry at Oxford University. 1746 - Day of death of Colin Maclaurin, Scottish mathematician (b. 1698). 1796 - Birthdate of Nikolai Brashman, Czech-Russian mathematician (d. 1866). 1822 - Charles Babbage read his paper "Note on the application of machinery to the computation of astronomical and mathematical tables" to the Astronomical Society of London and introduced the "Difference engine," the forerunner of modern computers. 1856 - Birthdate of Andrey Markov, Russian mathematician (d. 1922). 1886 - Day of death of Guillaume-Jules Houel, French mathematician (b. 1823). 1903 - Birthdate of Alonzo Church, American mathematician (d. 1995). 1910 - Birthdate of Fritz John, German-born American mathematician (d. 1994). 1917 - Birthdate of Atle Selberg, Norwegian-American mathematician (d. 2007). 1946 - Day of death of Federigo Enriques, Italian mathematician (b. 1871).

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2008 - Day of death of Yurii Alekseevich Mitropolskiy, Ukrainian mathematician (b. 1917).

June, 15 1640 - Birthdate of Bernard Lamy, French mathematician, and theologian (d. 1715). 1641 - In a letter to Frenicle, Fermat called the theorem that every prime of the form 4n+1 is the sum of two squares, the fundamental theorem of right triangles. 1734 - Day of death of Giovanni Ceva Italian mathematician (b. 1647). 1765 - Birthdate of Johann Gottlieb Friedrich von Bohnenberger, German astronomer, and mathematician (d. 1831). 1768 - Day of death of James Short, Scottish mathematician, and optician (b. 1710). 1865 - A. Cayley wrote to Hirst on June 15, 1865, four days before his election: "I shall really be glad to join the London Mathematical Society; it has always appeared to me that something of the kind was a desideratum; and tho' I cannot do it so much as if I had been still in London, I will certainly try to take part in the proceedings; I shall, therefore, be much obliged if you will propose me as a member." 1865 - Sylvester wrote to Hirst, expressing interest in the London Mathematical Society: "I shall be happy if you care about it to be made a member – or if you don't care about it but think it right I should do so." 1894 - Birthdate of Nikolai Chebotaryov, Soviet mathematician (d. 1947). 1906 - Birthdate of Gordon Welchman, English-American mathematician (d. 1985).

June, 16 1591 - Birthdate of Joseph Solomon Delmedigo, Greek-Italian physician, mathematician (d. 1655). 1640 - Birthdate of Jacques Ozanam, French mathematician (d. 1718, frequently cited as 1717 because of an error in "eloge de Fontenelle"). 1641 - In a letter to Fr. Marin Mersenne, Descartes states that no prime of the form 12n ± 1 will divide a number that is one more than a power of three. He adds that 12n ± 5 will always divide some 3m + 1. He gives a similar rule for five, and states he has one for all primes. [39]. 1782 - Birthdate of Olry Terquem, French mathematician (d. 1862). 1799 - Gauss received his Ph.D. at age 22 for his dissertation giving the first correct proof of the Fundamental Theorem of Algebra.

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1801 - Birthdate of Julius Plucker, German mathematician and physicist (d. 1868). 1830 - Birthdate of Alfred Enneper, German mathematician (d. 1885). 1833 - Janos Bolyai retired [91] as Captain in the cavalry for dueling with thirteen other officers. He accepted their challenge on the condition that he be allowed to play his violin between duels. 1839 - Birthdate of Julius Petersen, Danish mathematician (d. 1910). 1866 - Birthdate of James P. Pierpont, American mathematician (d. 1938). 1867 - A monument to Leonardo Bigolli (Fibonacci) was erected in Pisa. 1866 - Birthdate of James P. Pierpont, American mathematician (d. 1938). 1888 - Birthdate of Alexander Friedmann, Russian physicist and mathematician (d. 1925). 1888 - Birthdate of Peter Stoner, American mathematician and astronomer (d. 1980). 1902 - Bertrand Russell wrote to Gottlob Frege to say that in his Grundgesetze der Arithmetik, "there is just one point where I have encountered a difficulty." The difficulty was the Russell Antinomy. On June 22, 1902, Frege responded that "your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build arithmetic." 1902 - Day of death of Ernst Schröder, German mathematician (b. 1841). 1902 - Albert Einstein was formally appointed as Technical Expert at the Swiss Patent Office at Bern at a salary equivalent to about $3,000 a year. 1904 - B. Brouwer finished his studies at the University of Amsterdam. 1910 - Day of death of Julius Weingartnen, German mathematician (b. 1836). 1915 - Birthdate of John Tukey, American mathematician (d. 2000). 1947 - ENIAC patent filed. The Electronic Numerical Integrator and Computer was the first general-purpose electronic computer. 1970 - Day of death of Sydney Chapman, English mathematician and geophysicist (b. 1888). 1973 - Afghanistan issued a postage stamp commemorating the millennium of the birth of Ab'u Rayhan Muhammad ibn Ahmad Al Biruni.

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2001 - Day of death of Alessandro Faedo, Italian mathematician and politician (b. 1913). 2004 - Day of death of Herman Heine Goldstine, American mathematician, computer scientist, and scientific administrator (b. 1913).

June, 17 1713 - Leibniz replies to Johan (I) Bernoulli's letter of June 7th informing him of the book from London accusing Leibniz of “plagiary." He states, “I have not yet seen the little English book directed against me... It appears that he (Newton) no more knew our calculus than Apollonius knew the algebraic calculus of Viete and Descartes." [125]. 1870 - Benjamin Pierce, Superintendent of the U. S. Coast Survey, sends a letter of introduction for his son to August De Morgan: “I presume upon the unseen brotherhood of science to introduce to you my son Charles S. Peirce Esq., who is a devoted student of Logic. I think that he has original thoughts which you may regard as deserving your consideration. He carries with him a memoir which he has written upon one of the subjects of your own learned investigations..." 1898 - Birthdate of Maurits Escher, Dutch painter, known for his planefilling prints and his study of mathematics (d. 1972). 1903 - Birthdate of William Vallance Douglas Hodge, English mathematician (d. 1975). 1906 - Birthdate of Samuel Stanley Wilks, American mathematician (d. 1964). 2012 - Day of death of Nathan Divinsky, Canadian mathematician, and chess player (b. 1925).

June, 18 1584 - Jacob Christmann was appointed professor of Hebrew at Heidelberg. In 1595, he defended the view that the circle could only be approximately squared. 1799 - Thomas Jefferson wrote to a young man, William Greene Munford, seeking educational advice: “Dear Sir, I have to acknowledge the receipt of your favor of May 14. In which you mention that you have finished the first six books of Euclid, plane trigonometry, surveying, and algebra, and ask whether I think a further pursuit of that branch of science would be useful to you. There are some propositions in the latter books of Euclid, and some of Archimedes, which are useful, and I have no doubt you have been made acquainted with them.

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Trigonometry, so far as this, is most valuable to every man. There is scarcely a day in which he will not resort to it for some of the purposes of common life. The science of calculation also is indispensable as far as the extraction of the square and cube roots. Algebra, as far as the quadratic equation and the use of logarithms, is often of value in ordinary cases. But all beyond them is but a luxury; a delicious luxury indeed, but not to be indulged in by one who is to have a profession to follow for his subsistence. In this light, I view the conic sections, curves of the higher orders, perhaps even spherical trigonometry, algebraical operations beyond the 2nd dimension, and fluxions... I have indulged myself in these observations to you because the evidence cannot be unuseful to you of a person who has often had occasion to consider which of his acquisitions in science have been really useful to him in life, and which of them have been merely a matter of luxury." [45] 1858 - Birthdate of Andrew Forsyth, Scottish-English mathematician (d. 1942). 1864 - Lewis Carroll finally decided to write up Alice's Adventures in Wonderland. 1870 - Birthdate of Edouard Le Roy, French mathematician, and philosopher (d. 1954). 1884 - Birthdate of Charles Weatherburn, Australian mathematician (d. 1974). 1884 - Birthdate of Frieda Nugel, German mathematician (d. 1966). 1890 - Day of death of Kazimierz Kuratowski, Polish mathematician (b. 1896). 1913 - Birthdate of Oswald Teichmuller, German mathematician (d. 1943). 1915 - Birthdate of Alice T. Schafer, American mathematician (d. 2009). 1935 - Birthdate of Alexander von Brill, German mathematician (b. 1842). 1974 - Day of death of Julio Cesar de Mello e Souza, Brazilian mathematician (b. 1896). 2005 - Day of death of Manuel Sadosky, Argentine mathematician (b. 1914).

June, 19 240 B.C. - Eratosthenes estimated the circumference of the Earth. As the director of the great library of Alexandria, he read in a papyrus book that in Syene, approaching noon on the summer solstice, the longest day of the year, shadows of temple columns grew shorter. At noon,

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they were gone. The sun was directly overhead. However, a stick in Alexandria, far to the north, could cast a pronounced shadow. Thus, he realized that the surface of the Earth could not be flat. It must be curved. Not only that, but the greater the curvature, the greater the difference in the shadow lengths. By measurement on the ground and application of geometry, he calculated the circumference of the Earth. 1623 - Birthdate of Blaise Pascal, French mathematician, and physicist (d. 1662). 1771 - Birthdate of Joseph Diaz Gergonne, French mathematician, and philosopher (d. 1859). 1851 - Birthdate of Silvanus P. Thomson, English physicist, and mathematician (d. 1916). 1854 - Birthdate of Hjalmar Mellin, Finnish mathematician (d. 1933). 1865 - Keen to help the London Mathematical Society establish a high scientific reputation, Sylvester also announced a significant new result – his discovery of a demonstration of Newton's rule for finding the imaginary roots of algebraic equations. "If you can arrange for my doing so, I shall have much pleasure in bringing it before the Mathematical Society of London about which you spoke to me some time back... You will wonder, I think, at the simplicity and at the same time elegance of the method." This important result was presented on June 19, 1865, becoming the first mathematical paper to be published by the Society. 1926 - Birthdate of Erna Schneider Hoover, American mathematician, and inventor. 1934 - Jerzy Neyman's paper is presented to the Royal Statistical Society entitled "On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection." This paper was the one first presenting the concept of a “confidence interval" (interval estimate). 1945 - Day of death of Stefan Mazurkiewicz, Polish mathematician (b. 1888).

June, 20 1686 - Halley writes to Newton that Hooke has protested his "discovery" of the inverse square law should be noted in Principia. 1775 - Birthdate of Jacques Frederic Francais, French mathematician (d. 1833). 1788 - George Washington, thanking Nicholas Pike for the gift of a copy of his book "A New and Complete System of Arithmetic": "The

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science of figures, to a certain degree, is not only indispensably requisite in every walk of civilized life, but the investigation of mathematical truths accustoms the mind to method and correctness in reasoning and is an employment peculiarly worthy of rational beings." 1800 - Day of death of Abraham Gotthelf Kastner, German mathematician (b. 1719). 1806 - An essay by Abbe Buee Mémoire sur les quantités imaginaires was read before the Royal Society of London. 1808 - Poisson submitted his first paper on the stability of the planetary system. 1831 - Farkas Bolyai sent an off-print of his son's (Janos Bolyai) work "The Absolutely True Science of Space" (which would be published in 1832) to Gauss. 1838 - Birthdate of Theodor Reye, German mathematician (d. 1919). 1865 - Day of death of John William Lubbock, English astronomer, and mathematician (b. 1803). 1873 - Birthdate of Alfred Loewy, German mathematician (d. 1935). 1877 - Georg Cantor, in a letter to Dedekind, announced a proof that the points inside a square are in one-to-one correspondence with those on a line segment. 1915 - Birthdate of Adolph Winkler Goodman, American mathematician (d. 2004). 1917 - Birthdate of Helena Rasiowa, Austrian-Polish mathematician (d. 1994). 1936 - Nature publishes a poetic version of Descartes' theorem on Apollonian circles by Nobel laureate in chemistry F. Soddy* (see January 9 entry for generalization to N dimensions for N + 2 hyperspheres). 1942 - Birthdate of Neil Trudinger, Australian mathematician. 1946 - Birthdate of David Kazhdan, Russian-Israeli mathematician. 1963 - Day of death of Raphael Salem, Greek-French mathematician (b. 1898). 1969 - Birthdate of Misha Verbitsky, Russian mathematician. 2006 - Day of death of Dmytro Petryna, Soviet-Ukrainian mathematician (b. 1934). *

The Kiss Precise, by Frederick Soddy For pairs of lips to kiss maybe Involves no trigonometry. This not so when four circles kiss Each one the other three.

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To bring this off the four must be As three in one or one in three. If one in three, beyond a doubt Each gets three kisses from without. If three in one, then is that one Thrice kissed internally. Four circles to the kissing come. The smaller are the benter. The bend is just the inverse of The distance form the center. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of the squares of all four bends Is half the square of their sum. To spy out spherical affairs An oscular surveyor Might find the task laborious, The sphere is much the gayer, And now besides the pair of pairs A fifth sphere in the kissing shares. Yet, signs and zero as before, For each to kiss the other four The square of the sum of all five bends Is thrice the sum of their squares. In 2002, Lagarias, Mallows and Wilks published a continuation of Soddy's poem entitled “The Complex Kiss Precise" [98] Yet more is true: if all four discs Are sited in the complex plane, Then centers over radii Obey the self-same rule again

June, 21 1669 - Christopher Wren, in the Philosophical Transactions of the Royal Society, gives the first proof that the hyperboloid of one sheet is doubly ruled. 1677 - Leibniz, in a letter to Newton, explains his method of drawing tangents to curves, which he says proceeds "not by uxions of lines, but

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by the differences of numbers." He introduces his notation of dx and dy for the infinitesimal differences between the coordinates of two consecutive points on a curve. He also gives a solution to the problem of finding a curve whose subtangent is constant, demonstrating his ability to integrate. 1710 - Birthdate of James Short, Scottish-English mathematician, and optician (d. 1768). 1781 - Birthdate of Simeon Denis Poisson, French mathematician, and physicist (d. 1840). 1820 - Day of death of Alexis Therese Petit, French mathematician (b. 1791). 1894 - Birthdate of Harry Schmidt, German mathematician (d. 1951). 1913 - Day of death of Gaston Tarry, French mathematician (b. 1843). 1918 - Birthdate of Tibor Szele, Hungarian mathematician (d. 1955). 1928 - Birthdate of Wolfgang Haken, German-American mathematician. 1929 - Kazimierz Kuratowski announced at a meeting of the Warsaw Section of the Polish Mathematical Society that a graph is planar if and only if it does not contain a subgraph homeomorphic to either K5, the complete graph on 5 vertices, or K3,3, the complete bipartite graph on a bipartite set of (3, 3) vertices.* 1929 - Day of death of Ferdinand Rudio, Swiss mathematician (b. 1856). 1938 - Birthdate of Michael M. Richter, German mathematician, and computer scientist. 1940 - Day of death of Wolfgang Döblin, German-French mathematician (b. 1915). 1964 - Birthdate of David Rios Insua, Spanish mathematician. 1976 - Kenneth Appel and Wolfgang Haken at the University of Illinois announced that with the aid of a computer they had proved the fourcolor problem. 1993 - Andrew Wiles begins the three days of lectures leading to a solution of the Taniyama-Shimura conjecture, completing the proof of Fermat's last theorem (see June 23). 2007 - Day of death of John (Jack) Todd, Northern Irish mathematician (b. 1911). 2017 - Day of death of Yuri Zelinski, Ukrainian mathematician (b. 1947). *

A dedication of Frank Harary's book [71] is To KASIMIR KURATOWSKI, Who gave K5 and K3,3 To those who thought planarity Was nothing but topology.

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June, 22 1429 - Day of death of Jamshid al-Kashi, Persian astronomer, and mathematician (b. 1380). 1633 - Under the threat of torture, Galileo was forced by the Inquisition to recant Copernicanism. 1837 - Birthdate of Paul Gustav Heinrich Bachmann, German mathematician (d. 1920). 1852 - Birthdate of Eduard Weyr, Czech mathematician (d. 1903). 1860 - Birthdate of Mario Pieri, Italian mathematician (d. 1913). 1864 - Birthdate of Hermann Minkowski, German mathematician (d. 1909). 1866 - Birthdate of Kazimierz Zorawski, Polish mathematician (d. 1953). 1880 - Birthdate of Alfred Rosenblatt, Polish mathematician (d. 1947). 1892 - Day of death of Pierre Ossian Bonnet, French mathematician (b. 1819). 1902 - Gottlob Frege responded to the June 16th letter of Bertrand Russell (about a missing point in Frege's Grundgesetze der Arithmetik) saying that "your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build arithmetic." 1906 - Birthdate of Eduard Ott-Heinrich Keller, German mathematician (d. 1990). 1921 - Birthdate of Andrew Ronald Mitchell, British mathematician (d. 2007). 1925 - Day of death of Felix Klein, German mathematician (b. 1849). 1940 - Birthdate of Daniel Gray Quillen, American mathematician (d. 2011). 1950 - Birthdate of Benedict Hyman Gross, American mathematician. 1953 - Birthdate of Mauro Francaviglia, Italian mathematician (d. 2013). 1959 - According to Steven Krantz's Mathematical Apocrypha Redux, it was Marshall McLuhan who created the phrase "Publish or Perish." In a letter to Ezra Pound, he wrote about "beaneries," which was Pound's favorite term for a university: "The beaneries are on their knees to these gents (foundation administrators). They regard them as Santa Claus. They will do 'research on anything' that Santa approves. They will think his thoughts as long as he will pay the bill for getting them before the public signed by the profesorry-rat. 'Publish or perish' is the beanery motto." 1977 - Day of death of Harold Calvin Marston Morse, American mathematician (b. 1892).

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2018 - Day of death of Grigory Barenblatt, Soviet-Russian mathematician (b. 1927).

June, 23 1612 - Birthdate of Andre Tacquet, Flemish mathematician, and Jesuit Priest (d. 1660). 1676 - Newton sent his Epistola prior to Leibniz via Henry Oldenburg. 1756 - Birthdate of Thomas Jones, English mathematician (d. 1807). 1783 - The first meeting of the Royal Society of Edinburgh took place in the Old Library of Edinburgh University. 1835 - Möbius received a letter from Bellavitis with a method for adding and subtracting noncollinear vectors. 1858 - Birthdate of William Ernest Johnson, British logician (d. 1931). 1892 - Day of death of Pierre Ossian Bonnet, French mathematician (b. 1819). 1912 - Birthdate of Alan Turing, English mathematician, and computer scientist (d. 1954). 1941 - Birthdate of Ivor Owen Grattan-Guinness, British historian of mathematics and logic (d. 2014). 1944 - Birthdate of Richard Peter Stanley, American mathematician. 1993 - Over the course of three lectures delivered at the Isaac Newton Institute for Mathematical Sciences on June 21, 22, and 23 of 1993, Wiles announced his proof of the Taniyama-Shimura conjecture, and hence of Fermat's Last Theorem. 2013 - Day of death of Kurt Leichtweiss, German mathematician (b. 1927).

June, 24 1634 - Gilles Personne de Roberval was proclaimed the winner of the triennial competition for the Ramus chair at the Collège Royal in Paris. Thereafter, he kept his mathematical discoveries secret so that he could continue to win the competition and keep the chair. 1644 - In a letter to Torricelli, Fr. Marin Mersenne gives a method to find a number with any number of factors. 1687 - In a letter to Huygens, Fatio de Duillier used an integrating factor to solve the differential equation 3xdy - 2ydx = 0. 1832 - Day of death of Timofei Fedorovich Osipovsky, Russian mathematician, physicist, astronomer, and philosopher (b. 1766). 1880 - Birthdate of Oswald Veblen, American mathematician (d. 1960).

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1880 - Day of death of Jules Antoine Lissajous, French mathematician (b. 1822). 1900 - Birthdate of Wilhelm Cauer, German mathematician (d. 1945). 1909 - Birthdate of William Penney, Baron Penney, English mathematician and physicist (d. 1991). 1912 - Birthdate of Wilhelm Cauer, German mathematician (d. 1945). 1915 - Birthdate of Sir Fred Hoyle, English mathematician, and astronomer (d. 2001). 2008 - Day of death of Gerhard Ringel, Austrian mathematician (b. 1919). 2012 - Day of death of Gu Chaohao, Chinese mathematician (b. 1926).

June, 25 1274 - Day of death of Khawaja Muhammad ibn Muhammad ibn Hasan Tusi (Nasir al-Din Tusi), Persian polymath and prolific writer (b. 1201). 1634 - Gilles Personne de Roberval was proclaimed the winner of the triennial competition for the Ramus chair at the Collège Royal in Paris. 1641 - John Pell began the work of expanding Walter Warner's table of anti-logarithms from 10,000 to 100,000 entries. 1730 - Euler observed in a letter to Goldbach that 104 + 1 is divisible by 37 and that 38 + 28 is divisible by 17. 1935 - Birthdate of Charles Sheffield, English-American mathematician and physicist (d. 2002). 1941 - Day of death of Alfred Pringsheim, German mathematician (b. 1850). 1951 - Birthdate of Eva Bayer-Fluckiger, Swiss mathematician. 1988 - Day of death of Grigory Michailowitch Fichtenholz, Soviet mathematician (b. 1888). 1937 - Birthdate of Valentyna Gorbachuk, Ukrainian mathematician. 1948 - Birthdate of Paul Allen Catlin, American mathematician (d. 1995). 1974 - Day of death of Cornelius Lanczos, Hungarian mathematician and physicist (b. 1893). 1978 - Day of death of Hsien Chung Wang, Chinese-American mathematician (b. 1918). 2006 - Day of death of Irving Kaplansky, Canadian-American mathematician (b. 1917). 2011 - Day of death of Annie Easley, American computer scientist, and mathematician (b. 1933).

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June, 26 1274 - Day of death of Nasir al-Tusi, Islamic astronomer, and mathematician (b. 1201). 1824 - Birthdate of Lord Kelvin, born as William Thomson, Scottish-Irish physicist, mathematician, and engineer (d. 1907). 1858 - Schering qualified as a professor at Göttingen [15]. 1878 - Birthdate of Leopold Löwenheim, German mathematician (d. 1957). 1911 - Birthdate of Ernst Witt, German mathematician (d. 1991). 1918 - Birthdate of Yudell Leo Luke, American mathematician (d. 1983). 1946 - Day of death of Béla KĘrösjárto, Hungarian mathematician (b. 1898). 1963 - Day of death of Henry Morgan Ward, American mathematician (b. 1901). 1967 - Day of death of Henry Thomas Herbert Piaggio, British mathematician (b. 1884). 1969 - Birthdate of Andrei Yuryevich Okounkov, Russian mathematician.

June, 27 1806 - Birthdate of Augustus De Morgan, English mathematician (d. 1871). 1831 - Day of death of Sophie Germain, French mathematician, and physicist (b. 1776). 1834 - Birthdate of Erastus Lyman De Forest, American mathematician (d. 1888). 1850 - Birthdate of Jørgen Pedersen Gram, Danish mathematician (d. 1919). 1880 - Day of death of Carl Borchardt, German mathematician (b. 1817). 1881 - Poincaré asks Klein for details about the classification of groups according to genera [90]. 1883 - Day of death of William Spottiswoode, English mathematician, and physicist (b. 1825). 1899 - Birthdate of Lois Wilfred Griffiths, American mathematician (d. 1981). 1908 - The Academy of Sciences of Göttingen announced a prize of one hundred thousand marks, according to the will of Dr. Paul Wolfskehl, of Darmstadt, for the proof of Fermat's great theorem. 1952 - Day of death of Max Dehn, German-American mathematician (b. 1878).

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1966 - A conjecture of Leonhard Euler that, in the fashion that x2 + y2 = z2 it always takes n terms to sum to an n-th power: two squares, three cubes, four fourth powers, etc., is proven wrong: L.J. Lander and T.R. Parkin found the first counterexample: four fifth powers that sum to a fifth power: 275 + 845 + 1105 + 1335 = 1445. [99].

1975 - Day of death of G.I. Taylor, English mathematician, and physicist (b. 1886). 1977 - Italy issued a postage stamp honoring Filippo Brunelleschi (13771446).

June, 28 International Tau Day is celebrated by those who believe that 2ʌ (or 6.28…) is more appropriate or a nice addition to ʌ-day, which is celebrated on March 14 (or 3.14…).

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1751 - The first volume of Diderot's and d'Alembert's Encyclopédie appeared [67].

1830 - The Grand Prix was awarded by the French Academy of Sciences to Abel (posthumously) and Jacobi for their outstanding work on elliptic functions. 1875 - Birthdate of Henri Lebesgue, French mathematician (d. 1941). 1884 - Sofia Kovalevskaya was officially appointed an extraordinary professor at Stockholm University. 1894 - Birthdate of Einar Hille, American mathematician (d. 1980). 1920 - Birthdate of Nicolaas Hendrik Kuiper, Dutch mathematician (d. 1994). 1948 - Birthdate of Kenneth Alan Ribet, American mathematician. 1972 - Birthdate of Ngo Bao Chau, Vietnamese-French mathematician. 1984 - Day of death of Claude Chevalley, French mathematician (b. 1909). 1989 - Day of death of Charles Wilderman Trigg, American engineer, and mathematician (b. 1898). 1997 - The Wolfskehl Prize for the proof of Fermat's Last Theorem was awarded to Andrew Wiles. 2015 - Day of death of Louis Norberg Howard, American mathematician (b. 1929).

June, 29 1716 - Birthdate of Joseph Stepling, Czech astronomer, physicist, and mathematician (d. 1778).

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1728 - D. Bernoulli wrote to Goldbach: “I will finish with a problem which appears to me very curious and which I have solved. Thus: to find two unequal numbers x and y so that xy = yx. There is one solution among the whole numbers, namely x = 2, y = 4 (because 24 = 42), but one can give an infinite number of real numbers which solve this problem. There are other questions of this type of which I will say nothing." 1877 - After proving that the set of points of a square has the same cardinality as that of the points on just an edge of the square, Cantor wrote to his friend Richard Dedekind, “Je le vois, mais je ne le crois pas" (“I see it, but I don't believe it"). 1893 - Birthdate of Eduard ýech, Czech mathematician (d. 1960). 1895 - Birthdate of Cyrus Colton MacDuffee, American mathematician (d. 1961). 1900 - Day of death of Ivan Mikheevich Pervushin, Russian mathematician (b. 1827). 1904 - Birthdate of Witold Hurewicz, Polish mathematician (d. 1956). 1914 - Birthdate of Christos Papakyriakopoulos, Greek-American mathematician (d. 1976). 1924 - Day of death of Robert Simpson Woodward, American physicist, and mathematician (b. 1849). 1934 - Day of death of Francesco Gerbaldi, Italian mathematician (b. 1858). 1942 - Birthdate of K. Jon Barwise, American mathematician, philosopher, and logician (d. 2000). 2016 - Day of death of James William Cooley, American mathematician (b. 1926).

June, 30 1660 - Day of death of William Oughtred, English minister, and mathematician (b. 1575). 1742 - Christian Goldbach communicated to Leonhard Euler his "theorem" that every even integer is the sum of two primes. The "Goldbach conjecture" is still open. 1742 - Euler claimed that prime numbers of the form 4n + 1 are represented uniquely as a sum of two squares. He also mentioned that 641 divides 232 + 1, thereby disproving Fermat's claim that all numbers of the form 22n + 1 are prime. [104] 1748 - Birthdate of Dominique Cassini, French mathematician, and surveyor (d. 1845).

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1868 - Birthdate of Geoffrey Thomas Bennett, English mathematician (d. 1943). 1905 - Albert Einstein's paper, "On the Electrodynamics of Moving Bodies" (special relativity), is received at the Annalen der Physik. 1928 - Birthdate of Hassan Hassanzadeh Amoli, Islamic philosopher, theologian, mathematician, and mystic. 1950 - Birthdate of Alexander Andreevych Boichuk, Ukrainian mathematician. 1952 - Birthdate of Athanassios S. Fokas, Greek-English mathematician. 1972 - Day of death of Yuri Vladimirovich Linnik, Soviet mathematician (b. 1915).

CHAPTER SEVEN JULY

July, 1 1646 - Birthdate of Gottfried Wilhelm Leibniz, German mathematician, and philosopher (d. 1716). 1694 - Opening of the University of Halle in Germany. 1788 - Birthdate of Jean-Victor Poncelet, French mathematician, and engineer (d. 1867). 1818 - William George Horner's (1786-1837) method of solving equations (an algorithm for the efficient evaluation of polynomials in monomial form) was presented to the Royal Society in London. 1848 - Birthdate of Emil Weyr, Czech-Austrian mathematician (d. 1894). 1852 - Dirichlet delivered a memorial lecture at the Berlin Academy in honor of his close friend Jacobi in which he called Jacobi the greatest member of the Academy since Lagrange [43]. 1856 - Weierstrass was appointed Professor of Mathematics at the Royal Polytechnic School in Berlin. 1873 - Peirce wrote, “Newcomb, in a paper ... says he finds that pendulums hung by springs twist and untwist as they oscillate and says this will affect the time of oscillation." 1894 - The New York Mathematical Society changed its name to the American Mathematical Society [5]. 1906 - Birthdate of Jean Dieudonne, French mathematician (d. 1992). 1918 - Florian Cajori (1859-1930) was appointed professor of the history of mathematics at the University of California, Berkeley, one of the few such chairs in the world. During the next twelve years, he published 159 papers on the history of mathematics. 1948 - The Bell System Technical Journal published the first part of Claude Shannon's "A Mathematical Theory of Communication," regarded as a foundation of information theory, introducing the concept of Shannon entropy and adopting the term Bit. 1957 - Day of death of Donald McIntosh, Scottish mathematician (b. 1868).

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1963 - Day of death of Bevan Braithwaite Baker, Scottish mathematician (b. 1890). 1980 - A method of trisecting any given acute angle using Origami was demonstrated by Hisashi Abe, who published it in the Japanese journal "Suugaku Seminar" (Mathematics Seminar).

2010 - Grigori Yakovlevich Perelman refused the Clay Millennium prize of one million dollars, saying that he considers his contribution to proving the Poincaré conjecture to be no greater than that of Richard Hamilton, who introduced the theory of Ricci flow. 2015 - Day of death of Czesáaw Olech, Polish mathematician (b. 1931).

July, 2 1613 - Day of death of Bartholomaeus Pitiscus, German trigonometrist, astronomer, and theologian (b. 1561). 1621 - Day of death of Thomas Harriot, English astronomer, mathematician, and ethnographer (b. 1560). 1622 - Birthdate of Rene-Francoise Walter de Sluse, Walloon mathematician and churchman (d. 1685). 1644 - Day of death of William Gascoigne, English astronomer, mathematician, and maker of scientific instruments (b. 1612). 1823 - Birthdate of Bailie Hugh Blackburn, Scottish mathematician (d. 1909). 1832 - Legendre writes to Nathaniel Bowditch regarding his translation of Laplace's Mécanique Céleste: “Your work is not merely a translation with a commentary; I regard it as a new edition, augmented and improved, and such a one as might have come from the hands of the author himself, ... if he had been solicitously studious of being clear."

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1850 - Stokes's theorem first appeared for the first time as a postscript to a letter from Sir William Thompson (Lord Kelvin) to Stokes. 1852 - Birthdate of William Burnside, English mathematician (d. 1927). 1862 - Birthdate of William Henry Bragg, English physicist, chemist, and mathematician, Nobel Prize laureate (d. 1942). 1881 - Klein informs Poincaré that some of his work on theta functions is not new, and that a large number of young mathematicians are working to find conditions that distinguish Riemann's theta functions from the more general ones. 1919 - Day of death of Theodor Reye, German mathematician (b. 1838). 1925 - Birthdate of Olga Arsenevna Oleinik, Soviet-Russian mathematician (d. 2001). 1947 - Day of death of Nikolai Grigorievich Chebotaryov, Soviet mathematician (b. 1894). 1982 - Science reported that Steven Smale had proved that the averagecase behavior of the simplex algorithm for linear programming is far better than the worst-case behavior, which is exponential. 2014 - Day of death of Harold W. Kuhn, American mathematician (b. 1925).

July, 3 1749 - Day of death of William Jones, Welsh-English mathematician (b. 1675). 1789 - Day of death of Jakob II Bernoulli, Swiss-Russian mathematician (b. 1759). 1820 - Birthdate of Ernest de Jonquieres, French naval officer and mathematician (d. 1901). 1822 - Charles Babbage described his ideas for a "difference engine" to the Royal Society in London. 1866 - Birthdate of Henry Frederick Baker, English mathematician (d. 1956). 1879 - Birthdate of Alfred Korzybski, Polish-American mathematician, linguist, and philosopher (d. 1950). 1881 - Day of death of Hasan Tahsini, Albanian astronomer, mathematician, and philosopher (b. 1811). 1897 - Birthdate of Jesse Douglas, American mathematician (d. 1965). 1933 - Birthdate of Edward Brandt, Jr., American physician and mathematician (d. 2007). 1933 - Birthdate of Frederick Justin Almgren, American mathematician (d. 1997). 1933 - Birthdate of William Parry, English mathematician (d. 2006).

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1945 - Birthdate of Saharon Shelah, Israeli mathematician. 1977 - Day of death of Alexander Volkov, Soviet mathematician, and writer (b. 1891). 1991 - Day of death of Ernst Witt, German mathematician (b. 1911).

July, 4 1662 - Samuel Pepys wrote in his diary: "By and by comes Mr. Cooper ... of whom I intend to learn Mathematics; and so begin with him today... After an hour's being with him at Arithmetic, my first attempt being to learn the Multiplication table, then we parted till tomorrow." 1742 - Day of death of Luigi Guido Grandi, Italian monk, mathematician, and engineer (b. 1671). 1744 - Euler wrote to Christian Goldbach that he has finished his book "Introductio in Analysin Infinitorum."

1831 - Poisson declared Galois' work on solutions of equations as "incomprehensible," stating that "[Galois'] argument is neither sufficiently clear nor sufficiently developed to allow us to judge its rigor." However, the rejection report ends on an encouraging note: "We would then suggest that the author should publish the whole of his work in order to form a definitive opinion." 1843 - Liouville began an address to the Academy of Sciences with the words: "I hope to interest the Academy in announcing [that in] the papers of Évariste Galois, I have found a solution, as precise as it is profound, of this beautiful problem: whether or not [the general equation of fifth degree] is solvable by radicals." This work of Galois was published in 1846. 1862 - Charles Lutwidge Dodgson, a mathematics teacher at Oxford, went boating on the Isis, a tributary of the Thames, with the three daughters

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of Henry George Liddell, dean of Christ Church, Oxford. He was especially fond of Alice Liddell, then ten, and it was mainly for her that he began the story of another Alice's tumble down a rabbit hole. The work was published exactly three years later as "Alice's Adventures Under Ground" under the pseudonym Lewis Carroll, with the famous illustrations by John Tenniel. 1901 - Day of death of Peter Guthrie Tait, Scottish physicist, and mathematician (b. 1831). 1906 - Birthdate of Dan Rutherford, Scottish mathematician (d. 1966). 1921 - Birthdate of Gerard Debreu, French economist, and mathematician, Nobel Prize laureate (d. 2004). 1928 - Birthdate of Juergen Kurt Moser, German-American mathematician (d. 1999). 1941 - Day of death of Antoni Lomnicki, Polish mathematician (b. 1881). 1963 - The San Francisco Chronicle carried a report entitled, "A Milestone in Math: Professor's New Concept," by David Perlman. This popular account of Paul J. Cohen's proof of the independence of the axiom of choice was probably the first published. 1981 - Day of death of Niels Erik Norlund, Danish mathematician (b. 1885). 1986 - Day of death of Oscar Zariski, Belarusian-American mathematician (b. 1899). 2002 - Day of death of Laurent-Moïse Schwartz, French mathematician (b. 1915). 2006 - Day of death of Nathan Saul Mendelsohn, American-born Canadian mathematician (b. 1917).

July, 5 1687 - Isaac Newton published Philosophiae Naturalis Principia Mathematica.

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1698 - Johann Bernoulli defined the term "function" in a letter to Leibniz. Leibniz had coined the term. 1820 - Birthdate of William John Macquorn Rankine, Scottish physicist, mathematician, and engineer (d. 1872). 1926 - Day of death of Peter Redford Scott Lang, Scottish mathematician (b. 1850). 1932 - Day of death of René-Louis Baire, French mathematician (b. 1874). 1942 - Day of death of Oskar Bolza, German mathematician (b. 1857). 1953 - Birthdate of Caryn Navy, American mathematician, and computer scientist. 2015 - Day of death of Uffe Haagerup, Danish mathematician (b. 1949). 2018 - Day of death of Evgeny S. Golod, Soviet-Russian mathematician (b. 1935).

July, 6 1423 - Birthdate of Antonio Manetti, Italian mathematician, and architect (d. 1497). 1476 - Day of death of Regiomontanus, German mathematician, and astrologer (b. 1436). 1656 - Huygens, in a letter to Carcavi, gives the solution, without proof, to a dice-throwing probability problem posed by Fermat (If A wins for throwing a six, and B wins by throwing a seven, and after A throws once, B and A each roll twice in turns. What are the odds of A winning?). 1708 - De Moivre wrote to Johann Bernoulli about Machin's series, giving two different proofs that it converged to ʌ. 1849 - Birthdate of Alfred Bray Kempe, British mathematician (d. 1922). 1854 - Day of death of Georg Ohm, German physicist, and mathematician (b. 1789). 1863 - Marx wrote to Engels: “In my free time, I do differential and integral calculus. Apropos! I have a surplus of books and will send one to you if you want to study this topic. I deem it almost indispensable for your military studies. By the way, it is a much easier part of mathematics (involving mere technique) than the higher parts of algebra, for instance. Outside of knowledge of the usual algebra and trigonometry, there is nothing else necessary to study, except for general familiarity with the conic sections." 1909 - Einstein resigns his position at the Bern Patent Office to move to Zurich to take up his first full-time academic position in the chair of theoretical physics at the University of Zurich.

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1910 - Birthdate of Lothar Collatz, German mathematician (d. 1990). 1928 - Birthdate of Bernard Malgrange, French mathematician. 1976 - Birthdate of Ioana Dumitriu, Romanian-American mathematician. 2020 - Day of death of Ronald Lewis Graham, American mathematician (b. 1935).

July, 7 1668 - Isaac Newton received his M.A. from Trinity College in Cambridge. 1742 - Goldbach's conjecture was sent in a letter to Leonhard Euler. 1746 - Birthdate of Giuseppe Piazzi, Italian mathematician, and astronomer (d. 1826). 1752 - Birthdate of Joseph-Marie Jacquard, French mathematician (d. 1834). 1823 - William Rowan Hamilton passed into Trinity College, Dublin. 1887 - Michelson and Morley's experiment supported special relativity. 1900 - Day of death of Eduard Wiltheiss, German mathematician (b. 1855). 1905 - Birthdate of Marie-Louise Dubreil-Jacotin, French mathematician (d. 1972). 1906 - Birthdate of William Feller, Croatian-American mathematician (d. 1970). 1927 - Day of death of Gösta Mittag-Lefler, Swedish mathematician (b. 1846). 1942 - Day of death of William Henry Young, English mathematician (b. 1863). 1947 - Day of death of Alfred Rosenblatt, Polish mathematician (b. 1880). 1936 - Birthdate of Egbert Brieskorn, German mathematician (d. 2013). 1975 - Day of death of William Vallance Douglas Hodge, English mathematician (b. 1903). 1982 - Day of death of Raymond Louis Wilder, American mathematician (b. 1896). 2018 - Day of death of Alexander Bogomolny, Soviet-born IsraeliAmerican mathematician (b. 1948).

July, 8 Math 2.0 Day is a reminder that math is far more than the subject you might have found dull in school and college. Mathematics is the language that governs the world through numbers and equations.

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1390 - Day of death of Albert of Saxony, a German philosopher, physicist, and mathematician (b. appr. 1316). 1672 - Newton's first publication appears in a letter to the Philosophical Transactions. It presents "A Series of Queries Propounded by Mr. Isaac Newton," aiming to be determined through experiments, thus concluding his new theory of light and colors. Newton's work is recommended to those passionate about experimental philosophy. 1695 - Day of death of Christian Huygens, a Dutch mathematician, astronomer, and physicist (b. 1629). 1706 - De Moivre writes to Johann Bernoulli regarding Machin's unproven result on Machin's series for ʌ. 1760 - Birthdate of Christian Kramp, a French mathematician (d. 1826). 1777 - Birthdate of Daniel Friedrich Hecht, a German mathematician (d. 1833). 1892 - Birthdate of Torsten Carleman, a Swedish mathematician (d. 1949). 1902 - Day of death of John Daniel Runkle, an American educator, and mathematician (b. 1822). 1904 - Birthdate of Henri Cartan, a French mathematician (d. 2008). 1915 - Birthdate of Kenneth O. May, an American mathematician, and historian of mathematics (d. 1977). 1971 - Day of death of Kurt Reidemeister, a German mathematician connected to the Vienna Circle (b. 1893). 2002 - Donald Coxeter delivers the keynote address at the Janos Bolyai Conference on Hyperbolic Geometry, presenting a new paper on the Descartes circle theorem as extended by Phillip Beecroft. In his opening remarks, Coxeter attributes the discovery of this theorem to Phillip Beecroft and discusses the elegant proof that extends Descartes' four-circle theorem to an eight-circle theorem. 2008 - Day of death of Sixto Rios Garcia, a Spanish mathematician (b. 1913). 2010 - Day of death of David Harold Blackwell, an American statistician, and mathematician (b. 1919).

July, 9 1716 - Day of death of Joseph Sauveur, French mathematician and physicist (b. 1653). 1743 - Euler, in a letter to Goldbach, described to Goldbach a manor by which numbers of the form n2 + 1 might be divisible. 1814 - Gauss made his 146th and last entry in his scientific diary. He observed a connection between biquadratic residues and the lemniscate

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functions, later proved by Gauss and by Chowla (1940). More precisely, Gauss observed that if a + bi is a (Gaussian) prime and a1 + bi is divisible by 2 + 2i, then the number of solutions to the congruence 1 = xx + yy + xxyy (mod a+bi), including x = ’, y=±i and x = ±i, y = ’, is (a1)2 +b2. This entry in the diary led to the Weil conjectures. 1845 - Birthdate of George Howard Darwin, mathematical astronomer and fifth child of the evolutionist Charles Darwin (d. 1912). 1857 - Weierstrass, in his inaugural speech to the Berlin Academy, stated that mathematics occupies an especially high place because only through its aid can a truly satisfying understanding of natural phenomena be obtained. 1917 - Birthdate of Boris Shabat, Soviet mathematician (d. 1987). 1918 - Birthdate of Nicolaas Govert de Bruijn, Dutch mathematician (d. 2012). 1931 - Birthdate of Valentina Mikhailovna Borok, Soviet-Ukrainian mathematician (d. 2004). 1941 - British cryptologists break the secret code used by the German army to direct ground-to-air operations on the Eastern front during World War II. 1943 - Birthdate of Masahiko Fujiwara, Japanese mathematician, best known as an essayist. 1946 - D. Lehmer delivered the talk "Computing Machines for Pure Mathematics" as part of the Moore School Lectures, in which he introduced computing as an experimental science. 1953 - Day of death of Henri Pade, French mathematician (b. 1863). 1953 - France issued a stamp picturing Gaspard Monge, a notable mathematician known for his contributions to geometry.

1980 - Day of death of Arend Heyting, Dutch mathematician known for his work in intuitionistic logic (b. 1898).

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1984 - Day of death of Edna Ernestine Kramer Lassar, American mathematician (b. 1902). 1986 - In a letter to Jun-Ichi Yamashita, Grothendieck reported on his work: “I have been intensely busy for about a month now, with writing down some altogether different foundations of 'topology,' starting with the 'geometrical objects' or 'figures,' rather than with a set of 'points' and some kind of notion of 'limit' or (equivalently) 'neighborhoods.' Like the language of topoi (and unlike the so-called 'moderate space' theory foreshadowed in the Esquisse, still waiting for someone to take hold of the work in store...), it is a kind of topology 'without points' – a direct approach to 'shape.' I do hope the language I have started developing will be appropriate for dealing with finite spaces, which come off very poorly in 'general topology' (even when working with non-Hausdorff spaces). After all, presumably the space-time space we are living in is finite – at any rate there is no philosophical evidence whatever that it isn't, and still less, that it is adequately represented as a mathematical 'continuum' (more specifically, as a topological or differentiable or Riemannian or pseudo-Riemannian 'manifold') – and as for physical evidence; it is clear there cannot be any by the very nature of things, as measurements never yield anything else but approximate locations of the would-be (ideal) 'points.' These 'points' however do not have any empirical existence whatever. As Riemann pointed out, I believe, the mathematical continuum is a convenient fiction for dealing with physical phenomena, and the mathematics of infinity are just a way of approximating (by simplification through 'idealization') an understanding of finite aggregates, whose structures seem too elusive or too hopelessly intricate for a more direct understanding (at least it has been so up to now)." [155] 1996 - Day of death of Douglas George Chapman, Canadian-born American mathematical statistician (b. 1920). 2006 - Tesla Memorial at the Canadian side of Niagara Falls is unveiled.

July, 10 1610 - Galileo receives a letter from Cosimo II agreeing to his salary requests, and confirming him as “First Mathematician of our Stadium in Pisa" but with no requirements that he live or lecture in Pisa, "except when it may please you as an honor." 1682 - Birthdate of Roger Cotes, English mathematician and astronomer (d. 1716).

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1796 - Gauss wrote “EYPHKA! num = ǻ+ǻ+ǻ" in his scientific diary, recording his discovery that every positive integer is the sum of three triangular numbers.

1826 - Cauchy presented to the Academie a proof of existence theorems for first-order differential equations. 1843 - Jacques Philippe Marie Binet, age 57, elected to the Academie des Sciences to succeed Lacroix. 1878 - Birthdate of Oliver Dimon Kellogg, American mathematician (d. 1932). 1916 - Day of death of John Emory McClintock, American mathematician (b. 1840). 1927 - Birthdate of Grigory Barenblatt, Russian mathematician (d. 2018). 1936 - Day of death of Salvatore Pincherle, Italian mathematician (b. 1853). 1950 - France honors Lazar Carnot (1753-1823) with a postage stamp.

1950 - The German Democratic Republic, to celebrate the 250th anniversary of the founding of the Academy of Sciences, Berlin, issued postage stamps picturing some scientists, including Leonhard Euler and Gottfried von Leibniz.

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2007 - Day of death of Paulette Libermann, French mathematician (b. 1919).

July, 11 1382 - Day of death of Nicole Oresme, French mathematician (d. 1382). 1663 - John Wallis, Savilian Professor of Geometry at Oxford, gave a specious proof of Euclid's parallel postulate. 1672 - Leibniz gave correct rules for the differentiation of sums, products, quotients, powers, and roots. 1686 - Leibniz published his first paper on the integral calculus in Acta eruditorum. 1700 - Prince Elector Frederick I established the Royal Prussian Academy of Sciences at Berlin and named Gottfried Leibniz its President for life. 1731 - Alexis-Claude Clairaut elected to the French academy at age eighteen. 1733 - Day of death of Jakob Hermann, Swiss mathematician (b. 1678). 1738 - Isaac Greenwood, the first Hollis Professor at Harvard College, was "ejected" for drunkenness. 1747 - Benjamin Franklin writes to Peter Collinson, member of the Royal Society, to describe the "wonderful effects of pointed bodies, both in drawing off and throwing off the electrical fire." 1778 - Day of death of Joseph Stepling, Czech astronomer, physicist, and mathematician (b. 1716). 1807 - Day of death of George Atwood, English mathematician (b. 1745). 1814 - Ampere submitted a paper on general solutions of differential equations. 1890 - Birthdate of Giacomo Albanese, Italian mathematician (d. 1947). 1908 - Birthdate of Alfred Hoblitzelle Clifford, American mathematician (d. 1992).

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1909 - Day of death of Simon Newcomb, Canadian-American astronomer, and mathematician (b. 1835). 1920 - Birthdate of Roman Sikorski, Polish mathematician (d. 1983). 1922 - Birthdate of John William Scott Cassels, British mathematician (d. 2015). 1934 - Birthdate of Leonid Volevich, Soviet-Russian mathematician (d. 2007). 1995 - Day of death of Andrzej Alexiewicz, Polish mathematician (b. 1917). 2013 - Day of death of Egbert Brieskorn, German mathematician (b. 1936).

July, 12 1831 - Gauss to Schumacher: “I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits to which certain ratios can come as near as desired, while others are permitted to increase without bound." 1875 - Birthdate of Ernst Fischer, Austrian mathematician (d. 1954). 1879 - Birthdate of Margherita Piazzola Beloch, Italian mathematician (d. 1976). 1880 - Birthdate of Zygmunt Janiszewski, Polish mathematician (d. 1920). 1925 - Heisenberg announced the basic principles of quantum mechanics. 1945 - Day of death of Boris Galerkin, Soviet mathematician, and engineer (b. 1871). 1983 - Day of death of Ernst Gabor Straus, German-American mathematician (b. 1922).

July, 13 1527 - Birthdate of John Dee, English-Welsh mathematician, astronomer, and astrologer (d. 1609). 1672 - Newton writes to John Collins, “… about the infinite series I am not yet resolved, not knowing when I shall proceed to finish it." [143]. 1741 - Birthdate of Carl Friedrich Hindenburg, German mathematician (d. 1808). 1773 - Gerolamo Saccheri, a Jesuit priest, received the imprimatur of the Inquisition for his Euclides ab Omni Naevo Vindicatus (Euclid Cleansed of Every Blemish), an important forerunner of non-Euclidean geometry. [111].

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1807 - Day of death of Johann (III) Bernoulli, Swiss mathematician (b. 1744). 1832 - Charles Babbage became the first recipient of the Royal Astronomical Society's Gold Medal. 1880 - Boncompagni informed Genocchi that he had received a copy of the five unedited letters and all the mathematical notes of Germain [15]. 1904 - Birthdate of Alfred Leon Foster, American mathematician (d. 1994). 1941 - Day of death of Ivan Ivanovich Privalov, Soviet mathematician (b. 1891). 1944 - Birthdate of Erno Rubik, Hungarian mathematician, educator, and inventor (1974) of Rubik's Cube.

July, 14 1671 - Birthdate of Jacques d'Allonville, French astronomer, and mathematician (d. 1732). 1686 - Newton replies to a letter of Halley (June 20, 1686) about Hook protesting against Newton's work on the inverse square law: “And now having sincerely told you the case between Mr. Hooke and me, I hope I shall be free for the future from the prejudice of his letters. I have considered how best to compose the present dispute, and I think it may be done by the enclosed scholium to the fourth proposition." This scholium was “The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke, and Halley." 1793 - Birthdate of George Green, British mathematical physicist (d. 1841). 1800 - Day of death of Lorenzo Mascheroni, Italian mathematician (b. 1750). 1831 - On Bastille Day, Galois was at the head of a protest, wearing the uniform of the disbanded artillery and came heavily armed with several pistols, a loaded rifle, and a dagger. He was again arrested and received a nine-month sentence. During his stay in prison, Galois at one point drank alcohol for the first time at the goading of his fellow inmates. 1865 - Day of death of Benjamin Gompertz, British self-educated mathematician and actuary (b. 1779). 1868 - Tape measure patented. Alvin J. Fellows of New Haven, Connecticut, received patent no. 79,965 for the first tape measure. The

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tape measure was enclosed in a circular base with a spring lock to hold the tape at any desired point.

1905 - Birthdate of Laurence Chisholm Young, British mathematician (d. 2000). 1928 - Birthdate of Errett Albert Bishop, American mathematician (d. 1983). 1953 - Day of death of Richard von Mises, Austrian-American mathematician and aerodynamicist (b. 1883). 1954 - At a Conference for California Teachers of Mathematics, a Los Angeles dentist named Leon Bankoff presented a talk proving that the 2000-year-old proof of Archimedes that there were a pair of congruent “Archimedean Twin Circles" in the Arbelos was, in fact, false. He produced a third identical circle, now usually called the "Bankoff triplet circle." 1956 - Day of death of John Miller, Scottish mathematician (b. 1871). 1993 - Joan Ginther, a former mathematics teacher, first won $5.4 million in the Lotto Texas. Her next win came in 2006 when she won $2 million in the Holiday Millionaire scratch-off. Her third win happened in 2008 when she won $3 million from a Millions and Millions ticket. In 2010, she won $10 million, her largest prize yet, bringing her total winnings to $20.4 million. The odds of winning this many times are one in 18 septillions (10^42). All of her winning tickets were purchased in Texas, and two of them were bought from the same convenience store in Bishop, Texas. Some people suppose that she has solved the algorithm of the lottery. 2017 - Day of death of Maryam Mirzakhani, Iranian mathematician (b. 1977).

July, 15 998 - Day of death of Abu al-Wafa Buzjani, Persian mathematician, and astronomer (b. 940).

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1636 - Euler wrote to Mersenne that "a number n is a sum of exactly three integral squares if and only if a2n is" [104]. 1662 - The Royal Society of London (founded in 1660) received its charter from King Charles II. 1834 - St. Vladimir University in Kiev (now Kyiv National Taras Shevchenko University) was founded. 1865 - Birthdate of Wilhelm Wirtinger, Austrian-German mathematician (d. 1945). 1906 - Birthdate of Adolph-Andrei Pavlovich Yushkevich, Soviet historian of mathematics (d. 1993). 1922 - Birthdate of Leon M. Lederman, American physicist, and mathematician, Nobel Prize laureate (d. 2018). 1928 - The ENIGMA machine encodes its first message. 1930 - Birthdate of Stephen Smale, American mathematician, and computer scientist. 1931 - Day of death of Ladislaus Bortkiewicz, Russian-German economist, and mathematician (b. 1868). 1961 - Day of death of Nina Karlovna Bari, Soviet mathematician (b. 1901). 1998 - A biography of the famous mathematician Paul Erdos, "The Man Who Loved Only Numbers," written by Paul Hoffman, was first published.

July, 16 1678 - Birthdate of Jakob Hermann, Swiss mathematician (d. 1733). 1748 (July 5 by old style) - Michail Lomonosov, in a letter to Euler, stated the idea of the conservation of matter: "All changes in nature are such that inasmuch is taken from one object, insomuch is added to another. So, if the amount of matter decreases in one place, it increases elsewhere. This universal law of nature embraces laws of motion as well, for an object moving others by its own force, in fact, imparts to another object the force it loses." 1749 - Goldbach knows how to prove the following special case of Euler's missing lemma: If 8m + 4 is a sum of four odd squares, then 2m + 1 is a sum of four squares [104]. 1819 - Birthdate of Siegfried Heinrich Aronhold, German mathematician (d. 1884). 1848 - The 50th anniversary of Gauss' doctorate was celebrated. As part of the celebration, Gauss was to light his pipe with a manuscript page from his "Disquisitiones Arithmeticae." His student Dirichlet was

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outraged by this sacrilege and boldly snatched the paper as a treasured memento. 1903 - Birthdate of Irmgard Flugge-Lotz, German mathematician, and engineer (d. 1974). 1995 - Amazon.com sells its first book. 2010 - Day of death of Michail Michailovich Lavrentiev, Soviet-Russian mathematician (b. 1932).

July, 17 Yellow Pig Day, a celebration of the number 17. 1698 - Birthdate of Pierre Louis Maupertuis, French mathematician, and philosopher (d. 1759). 1790 - Day of death of Johann (II) Bernoulli, Swiss mathematician (b. 1710). 1831 - Birthdate of Victor Mayer Amedee Mannheim, French mathematician (d. 1906). 1863 - Birthdate of Herbert Richmond, British mathematician (d. 1948). 1868 - Birthdate of Peter Comrie, Scottish mathematician (d. 1944). 1877 - Birthdate of Archibald Henderson, American mathematician, and writer (d. 1963). 1879 - It was announced in Nature that Kempe had proved the four-color conjecture. A correct proof was first obtained by Appel and Haken (1977). 1909 - Birthdate of Geoffrey Walker, British mathematician (d. 2001). 1911 - Day of death of Hermann Caesar Hannibal Schubert, German mathematician (b. 1848). 1912 - Day of death of Henri Poincaré, French mathematician, physicist, and engineer (b. 1854). 1929 - Birthdate of Sergei K. Godunov, Soviet-Russian mathematician. 1917 - Day of death of Giuseppe Veronese, Italian mathematician (b. 1854). 1935 - The first problem was entered into the Scottish Book, a large bound notebook that Stefan Banach brought to the Scottish Cafe in Lwow for mathematicians to record research problems. 1944 - Day of death of William James Sidis, American mathematician, and anthropologist (b. 1898). 1975 - Birthdate of Terence Chi-Shen Tao, Australian mathematician. 1980 - Day of death of Boris Delaunay, Soviet mathematician (b. 1890). 1993 - Day of death of Adolph-Andrei Pavlovich Yushkevich, Soviet historian of mathematics (b. 1906).

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1998 - Day of death of Michael James Lighthill, British mathematician (b. 1924). 2014 - A few years after his retirement, when brushing his teeth, Thomas Royen had a flash of insight: how to use the Laplace transform of the multivariate gamma distribution to achieve a relatively simple proof for the Gaussian correlation inequality.

July, 18 1013 - Birthdate of Hermann of Reichenau, German mathematician (d. 1054). 1635 - Birthdate of Robert Hooke, English natural philosopher, architect, and polymath (d. 1703). 1742 - Day of death of Abraham Sharp, English mathematician (b. 1653). 1768 - Birthdate of Jean Robert Argand, Swiss-French amateur mathematician (d. 1822). 1807 - Day of death of Thomas Jones, English mathematician (b. 1756). 1813 - Birthdate of Pierre Laurent, French mathematician (d. 1854). 1856 - Birthdate of Giacinto Morera, Italian engineer, and mathematician (d. 1909). 1863 - Birthdate of Kelly Miller, American mathematician, the first black man to attend Johns Hopkins University (d. 1939). 1872 - In a lecture to the Berlin Academy, Karl Weierstrass gave the classic example of a continuous nowhere differential function.

1899 - Birthdate of Robert Schlapp, Scottish mathematician (d. 1991) 1908 - Birthdate of Beatrice Aitchison, American mathematician, statistician, and transportation economist (d. 1997) 1930 - Day of death of Karl Emmanuel Robert Fricke, German mathematician (b. 1861) 1979 - Great Britain issued a stamp honoring "Alice's Adventures in Wonderland"

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July, 19 1739 - D'Alembert made his first contribution to the field of mathematics, pointing out the errors he had detected in "Analyse démontrée" (published 1708 by Charles-Rene Reynaud) in a communication addressed to the Académie des Sciences. 1767 - Birthdate of Francois-Joseph Servois, French mathematician (d. 1847). 1819 - Poisson submitted a paper on the solution of the wave equation. He used the method of power series in this work. 1878 - Day of death of Yegor Ivanovich Zolotarev, Russian mathematician (b. 1847). 1817 - Birthdate of Charles Auguste Briot (d. 1882). 1865 - Birthdate of Wilhelm Wirtinger, Austrian mathematician (d. 1945). 1886 - Birthdate of Michael Fekete, Hungarian-Israeli mathematician (d. 1957). 1894 - Birthdate of Aleksandr Khinchin, Russian mathematician (d. 1959). 1895 - George Cantor first uses Aleph-null in a letter to Felix Klein. 1913 - Birthdate of Mary Cannell, British historian of mathematics (d. 2000). 1939 - Birthdate of Yves Meyer, French mathematician. 1947 - Day of death of John Clark, Scottish mathematician (b. 1861). 1982 - Day of death of Hugh Everett III, American physicist and mathematician (b. 1930). 1997 - Day of death of Eric Charles Milner, British mathematician (b. 1928).

July, 20 1632 - Pierre de Carcavi became a member of the parliament of Toulouse. 1819 - Day of death of John Playfair, Scottish mathematician, physicist, and geologist (b. 1748). 1876 - Birthdate of Otto Blumenthal, German mathematician (d. 1944).

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1882 - Birthdate of Olga Hahn-Neurath, Austrian mathematician and philosopher (d. 1937). 1866 - Day of death of Bernhard Riemann, German mathematician (b. 1826). 1922 - Day of death of Andrey Markov, Russian mathematician (b. 1856). 1937 - Day of death of Olga Hahn-Neurath, Austrian mathematician and philosopher from the Vienna Circle (b. 1882). 1959 - The first International Mathematical Olympiad began in Brasov, Romania. 1977 - Day of death of Fritz Joachim Weyl, Swiss mathematician (b. 1915). 1997 - Day of death of Eric Charles Milner, English-born mathematician (b. 1928).

July, 21 1849 - Birthdate of Robert Simpson Woodward, American physicist and mathematician (d. 1924). 1861 - Birthdate of Herbert Ellsworth Slaught, American mathematician (d. 1937). 1873 - Day of death of Delfino Codazzi, Italian mathematician (b. 1824). 1924 - Birthdate of Robert Simpson Woodward, American physicist and mathematician (d. 1924). 1925 - Day of death of Giovanni Frattini, Italian mathematician (b. 1852). 1926 - Birthdate of John Leech, British mathematician (d. 1992). 1932 - Birthdate of Michail Michailovich Lavrentiev, Soviet-Russian mathematician (d. 2010). 1937 - Day of death of Edwin Bailey Elliott, British mathematician (b. 1851). 1966 - Day of death of Francesco Cantelli, Italian mathematician (b. 1875). 1966 - Day of death of Philipp Frank, Austrian-American physicist, mathematician, and philosopher, Vienna Circle member (b. 1884). 1967 - Brazil issued a stamp with a Möbius strip on it to commemorate the 6th Brazilian Mathematical Congress.

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1993 - Day of death of Edwin James George Pitman, Australian mathematician (b. 1897). 2011 - Day of death of Franz Leopold Alt, Austrian-born American mathematician (b. 1910). 2016 - Day of death of Roger Godement, French mathematician (b. 1921). 2017 - Day of death of Myhailo Yosypovych Yadrenko, Ukrainian mathematician (b. 1932).

July, 22 Pi Approximation Day, also known as Casual Pi Day, is dedicated to the mathematical constant ʌ, which denotes the relationship between a circle's circumference and its diameter and is approximated by the fraction 22/7, which calculates to approximately 3.14. 1575 - Day of death of Francisco Maurolico, Italian Benedictine and mathematician (b. 1494). 1694 - Johann Bernoulli sent "L'Hospital's rule" to L'Hospital under the terms of their agreement of 17 March 1694. 1755 - Birthdate of Gaspard de Prony, French mathematician and engineer (d. 1839). 1784 - Birthdate of Friedrich Bessel, German mathematician and astronomer (d. 1846). 1795 - Birthdate of Gabriel Lame, French mathematician (d. 1870). 1826 - Day of death of Giuseppe Piazzi, Italian mathematician and astronomer (b. 1746). 1882 - Birthdate of Konrad Hermann Theodor Knopp, German mathematician (d. 1957). 1902 - Birthdate of Reinhold Baer, German mathematician (d. 1979). 1925 - Norbert Wiener wrote to his friend Phillip Franklin: “As to the state of the market: differential geometry seems rather quiet, and some of the principal operators have deserted it for other securities. Real and complex variables continue firm, without much change. Analysis situs has a bull market. Bull operators have been very active in differential equations, also. Quantum theory continues speculative, with chances of a very sharp rise, but the market contains a lot of wildcat stock. Hilbert, Brouwer, and Co. are doing well with mathematical logic." 1935 - Birthdate of John Robert Stallings, American mathematician (d. 2008). 1936 - Birthdate of Geraldine Claudette Darden, American mathematician. 1943 - Day of death of William Fogg Osgood, American mathematician (b. 1864).

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1954 - Birthdate of Ingrid Daubechies, Belgian physicist and mathematician. 1959 - Day of death of David van Dantzig, Dutch mathematician (b. 1900). 1966 - Day of death of Philipp Frank, Austrian-American physicist and mathematician (b. 1884). 1978 - Roger Apery gave a talk entitled “Sur l'irrationalite de ȗ(3)" to outline proofs that ȗ(3) and ȗ(2) were irrational. 1983 - Science reported that Gerd Faltings proved the Mordell conjecture (often called now Faltings' theorem). 1999 - Day of death of Otakar Boruvka, Czech mathematician (b. 1899).

July, 23 1754 - Lagrange published his first work in the form of a letter in Italian. 1775 - Birthdate of Etienne-Louis Malus, French physicist and mathematician (d. 1812). 1854 - Birthdate of Ivan Vladislavovich Sleszynski, Ukrainian-Polish mathematician (d. 1931). 1856 - Birthdate of Bal Gangadhar Tilak, Indian mathematician, philosopher, and militant nationalist (d. 1920). 1888 - Birthdate of Fritz Carlson, Swedish mathematician (d. 1952). 1903 - Day of death of Eduard Weyr, Czech mathematician (b. 1852). 1918 - Emmy Noether first presented her famous theorem in a lecture to the Göttingen Mathematical Society [33]. 1920 - Birthdate of Herbert Federer, American mathematician (d. 2010). 1927 - The English term "eigenvalue" first appears in a letter to Nature from A. S. Eddington beginning: “Among those ... trying to acquire a general acquaintance with Schrödinger’s wave mechanics there must be many who find their mathematical equipment insufficient to follow his first great problem – to determine the eigenvalues and eigenfunctions for the hydrogen atom" (the term was derived from Hilbert's use of Eigenwert in 1904) [118]. 1932 - Birthdate of Derek Thomas Whiteside, British historian of mathematics, best known for editing the 8-volume Mathematical Papers of Isaac Newton (d. 2008). 1936 - The Physical Review received Einstein's submission on 1 June 1936, according to the journal's logbook. Tate returned the manuscript to Einstein on 23 July with a critical review and the mild request that he “would be glad to have [Einstein's] reaction to the various comments and criticisms the referee has made." Einstein wrote back on 27 July in high dudgeon, withdrawing the paper and dismissing out of

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hand the referee's comments. In the paper, it seems Einstein thought he had a proof that gravity waves, something of his own creation, could not exist. 1960 - Birthdate of Juha Heinonen, Finnish-American mathematician (b. 1960). 1964 - Day of death of Werner Wolfgang Rogosinski, German-British mathematician (b. 1894). 1964 - Day of death of Samarendra Nath Roy, Indian-American mathematician and an applied statistician (b. 1906). 1987 - Day of death of Boris Shabat, Soviet mathematician (b. 1917).

July, 24 1786 - Birthdate of Joseph Nicollet, French mathematician and explorer (d. 1843). 1851 - Birthdate of Friedrich Schottky, Polish-German mathematician (d. 1935). 1854 - Birthdate of Ivan Vladislavovich Sleszynski, Ukrainian-Polish mathematician (d. 1931). 1856 - Birthdate of Émile Picard, French mathematician (d. 1941). 1860 - Yale University authorized the granting of Doctor of Philosophy degrees. 1871 - Birthdate of Paul Epstein, German mathematician (d. 1939). 1888 - Birthdate of Dunham Jackson, American mathematician (d. 1946). 1923 - Birthdate of Christine Mary Hamill, English mathematician (d. 1956). 1934 - Day of death of Hans Hahn, Austrian mathematician (b. 1879). 1983 - Day of death of Eberhard Frederich Ferdinand Hopf, Austrian mathematician (b. 1902). 1999 - Day of death of Alexander (Smbat) Abian, Iranian-born ArmenianAmerican mathematician (b. 1923).

July, 25 1741 - Euler arrives in Berlin to become director of Mathematics at Frederick the Great's newly formed Academy of Science. 1783 - Founding of the Royal Academy of Science in Turin. 1807 - Gauss named Professor of Astronomy and director of the new observatory in Göttingen. 1808 - Birthdate of Johann Benedict Listing, German mathematician (d. 1882).

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1825 - Birthdate of Henry Wilbraham, English mathematician (d. 1883). 1831 - A comrade of Galois, Raspail quoted Galois in a letter from prison: "And I tell you, I will die in a duel over some low-class coquette. Why? Because she will invite me to avenge her honor which another has compromised." [163] Raspail continues that Galois, still in a delirium, attempted suicide, and that he would have succeeded if his fellow inmates hadn't forcibly stopped him. 1915 - Birthdate of Ivan Petrovich Egorov, Soviet mathematician (d. 1990). 1923 - Birthdate of Edgar Gilbert, American mathematician (d. 2013). 1980 - Day of death of Euphemia Lofton Haynes, American mathematician (b. 1890). 1992 - Day of death of Ralph Philip Boas Jr., American mathematician, teacher, and journal editor (b. 1912).

July, 26 1271 - Birthdate of Zhao Youqin, Chinese astronomer, mathematician, and physicist (d. 1335). 1684 - Day of death of Elena Cornaro Piscopia, Italian mathematician, and philosopher (b. 1646). 1711 - Birthdate of Lorenz Christoph Mizler, German physician, mathematician, and historian (d. 1778). 1712 - Brooke Taylor describes what we now call a "Taylor series" in a letter to John Machin. 1749 - Euler observes that the Four-Squares Theorem follows if it can be shown to hold for all numbers of the form m = 8n + 1 (or, more generally, for all numbers of any of the forms 8n + a with a = 1, 3, 5, or 7). [104] 1766 - Frederick the Great wrote to d'Alembert, thanking him for his suggestion of hiring Lagrange to succeed Euler at the Berlin Academy: "To your care and recommendation am I indebted for having replaced a half-blind mathematician by a mathematician with both eyes, which will especially please the anatomical members of the academy." 1902 - Birthdate of Stanislaw Golab, Polish mathematician (d. 1980). 1903 - Birthdate of Kurt Mahler, German-Australian mathematician (d. 1988). 1907 - Birthdate of Nachman Aronszajn, Polish-American mathematician (d. 1980). 1912 - Birthdate of Tadashi Nakayama or Tadasi Nakayama, Japanese mathematician (d. 1964).

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1918 - The famous paper "Invariante Variationprobleme" by Emmy Noether is published in Göttingen Nachrichten.

1925 - Day of death of Gottlob Frege, German mathematician, and philosopher (b. 1848). 1932 - Day of death of Oliver Dimon Kellogg, American mathematician (b. 1878). 1937 - Birthdate of Ernest Vingerg, Soviet-Russian mathematician (d. 2020). 1941 - Day of death of Henri Lebesgue, French mathematician (b. 1875). 1942 - Day of death of Alfred Tauber, Hungarian-born Austrian mathematician (b. 1866). 1942 - Day of death of Georg Alexander Pick, Austrian mathematician (b. 1859). 1955 - Day of death of Raymond Clare Archibald, American mathematician (b. 1875). 1976 - Kenneth Appel and Wolfgang Haken of the University of Illinois communicated their proof of the Four-Color Theorem to the Bulletin of the American Mathematical Society. 1977 - Day of death of Oskar Morgenstern, German-American economist, and mathematician (b. 1902). 1984 - Day of death of George Gallup, American mathematician, and statistician (b. 1901).

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1997 - Day of death of Kunihiko Kodaira, Japanese mathematician (b. 1915). 2000 - Day of death of John Tukey, American mathematician (b. 1915). 2006 - Day of death of Andrei Roiter, Soviet-Ukrainian mathematician (b. 1937). 2013 - Day of death of Harley Flanders, American mathematician (b. 1925). 2016 - Day of death of Solomon Feferman, American philosopher, and mathematician (b. 1928).

July, 27 1667 - Birthdate of Johann Bernoulli, Swiss mathematician (d. 1748). 1759 - Day of death of Pierre Louis Maupertuis, French mathematician, and philosopher (b. 1698). 1829 - By a remarkable coincidence, both Cauchy and Sturm sent papers to the Académie des Sciences dealing with differential equations. Both of them used techniques which we recognize as matrix methods. 1837 - Dirichlet presented his first analytic number theory paper at a meeting of the Berlin Academy of Sciences. He proved the fundamental theorem that bears his name: Every arithmetical sequence an+b, n = 0, 1, 2, … of integers, where a and b are relatively prime, contains infinitely many primes. 1844 - Day of death of Agoston Scholtz, Hungarian mathematician (b. 1916). 1861 - The Athenaeum magazine carried a review of Charles Dodgson's pamphlet entitled "The Formula of Plane Trigonometry" in which he suggested new symbols for the six basic trigonometric functions. The reviewer was not convinced. 1867 - Birthdate of Derrick Norman Lehmer, American mathematician (d. 1938). 1871 - Birthdate of Ernest Friedrich Ferdinand Zermelo, German mathematician (d. 1953). 1901 - The University of Edinburgh conferred the honorary degree of Doctor of Laws on Professor P. G. Tait M.A. D.Sc. 1907 - Birthdate of Irene Fischer, Austrian-American geodesist, and mathematician (d. 2009). 1931 - Day of death of Jacques Herbrand, French mathematician (b. 1908). 1936 - Einstein writes to John Tate, editor of the Physical Review, angrily withdrawing a paper that he had submitted for publication but had been rejected after peer review. Einstein and Rosen's paper claimed that

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gravitational waves did not exist. It was Einstein who introduced gravitational waves in his theory of general relativity in 1916, within a few months of finding the correct form of the field equations for it. However, by 1936 he had changed his mind. 1953 - Birthdate of Pantelis Damianou, Cypriot mathematician (d. 2020). 1999 - Day of death of Aleksandr Danilovich Aleksandrov, Russian mathematician, physicist, and mountaineer (b. 1912). 2015 - Day of death of John William Scott Cassels, British mathematician (b. 1922).

July, 28 1619 - Kepler wrote to Napier expressing his enthusiasm for Napier's invention of logarithms. 1818 - Day of death of Gaspard Monge, French mathematician, and engineer (b. 1746). 1829 - Galois' father committed suicide after a bitter political dispute with the village priest. A couple of days later, Galois made his second and last attempt to enter the Polytechnique, and failed yet again. 1849 - Birthdate of Robert Forsyth Scott, British mathematician (d. 1933). 1899 - Cantor asked Dedekind in a letter: “The big question was whether, besides the alephs, there were still other cardinalities of sets; for two years now I have been in possession of a proof that there are no others." (The proof came in a letter dated 3 August 1899). 1934 - Hans Zassenhaus completed his doctoral dissertation "Kennzeichnung endlicher linearer Gruppen als Permutationsgruppen." 1948 - A. Turing writes to Jack Good with an estimate of the number of neurons in the human brain: “I have repeatedly looked in books on neurology … and never found any numbers offered. My own estimate is 3 × 108 to 3 × 109." 1954 - Birthdate of Gerd Faltings, German mathematician. 1956 - Day of death of Luigi Fantappie, Italian mathematician (b. 1901). 1999 - Day of death of Trygve Haavelmo, Norwegian economist and mathematician, Nobel Prize laureate (b. 1911).

July, 29 1654 - Pascal wrote to Fermat, questioning his solution to the 'problem of the points,' a probability problem: “Impatience has seized me as well as it has you, and although I am still abed, I cannot refrain from telling you that I received your letter in regard to the problem of the points

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yesterday evening from the hands of M. Carcavi, and that I admire it more than I can tell you. I do not have the leisure to write at length, but, in a word, you have found the two divisions of the points and of the dice with perfect justice. I am thoroughly satisfied as I can no longer doubt that I was wrong, seeing the admirable accord in which I find myself with you." In the same letter, the term "number theory" was introduced. 1698 - In a letter to John Bernoulli, Leibniz introduces the dot for multiplication: “I do not like × as a symbol for multiplication, as it is easily confounded with x; … often I simply relate two quantities by an interposed dot and indicate multiplication by ·." Hence, in designating a ratio, I use not one point but two points, which I use at the same time for division." 1739 - D'Alembert, age 21, submitted his first mathematical paper to the Academy of Sciences. 1781 - Day of death of Johann Kies, German astronomer, and mathematician (b. 1713). 1839 - Day of death of Gaspard de Prony, French mathematician, and engineer (b. 1755). 1840 - Ada Lovelace reported to her mother that a tutor had been found, and that her mathematical studies were once more underway. She was now working under the tutelage of Augustus De Morgan (1806-1871). 1858 - Birthdate of Francesco Gerbaldi, Italian mathematician (d. 1934). 1867 - Thomas Hill, president of Harvard College, wrote to Benjamin Peirce: “I have the honor of informing you that the University, on Commencement Day, conferred on you the Degree of Doctor of Laws in recognition of the transcendent ability with which you have pursued mathematical physical investigations, and in particular for the luster which she has herself for so many years borrowed from your genius." 1912 - Birthdate of Noel Bryan Slater, British mathematician, and physicist (d. 1973). 1925 - Birthdate of Harold W. Kuhn, American mathematician (d. 2014). 1944 - Day of death of David Eugene Smith, American mathematician, educator, and editor (b. 1860). 1996 - Day of death of Marcel-Paul Schützenberger, French mathematician (b. 1920). 2004 - Day of death of Walter Feit, Austrian mathematician (b. 1930). 2015 - A 15th type of pentagon that would tile the plane was announced by Casey Mann, Jennifer McLoud, and David Von Derau of the University of Washington Bothell.

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July, 30 1738 - Euler sends a letter to John Bernoulli with the solution to a question from Daniel Bernoulli regarding isoperimetric curves, particularly the one for which the integral of rm gave a maximum or minimum. 1806 - Gauss wrote to Schumaher: “It seems to be my fate to concur in nearly all my theoretical works with Legendre. So it is in the higher arithmetic, in the research in transcendental functions connected with the rectification of the ellipse, in the foundations of geometry and now again here [in the method of least squares, which] ... is also used in Legendre's work and indeed right gallantly carried through." 1859 - Bernhard Riemann is appointed a full professor at Göttingen, succeeding his two former teachers, Gauss and Dirichlet. 1907 - The Axiom of Choice is usually given as created by Zermelo in 1908, presumably because that was the year it appeared in Mathematische Annalen, but the date on the actual paper is 30 July 1907. The paper contains “AXIOM VI. (Axiom of choice). If T is a set whose elements all are sets that are different from 0 and mutually disjoint, its union “union of T" includes at least one subset S1 having one and only one element in common with each element of T." 1918 - Richard Courant with Ferdinand Springer signed a contract for the series of books now famous as the “Yellow Series." 1978 - Day of death of Rufus Bowen, American mathematician (b. 1947). 1985 - Day of death of Julia Robinson, American mathematician (b. 1919). 2004 - Day of death of Adolph Winkler Goodman, American mathematician (b. 1915).

July, 31 1321 - Day of death of Ibn Al-Banna, Moroccan-Berber mathematician, astronomer, Islamic scholar, Sufi, and a one-time astrologer (b. 1256). 1669 - Lucasian professor Isaac Barrow sent John Collins a manuscript of Newton's De analysi, which was a summary of Newton's work on calculus and was written after Newton saw Nicholas Mercator's Logarithmotechnia (1668), which contained a series for log(1+x), in order that Newton would not lose credit for his work on infinite series. Although this manuscript was not published until 1704, it led to Newton's appointment as Lucasian professor on 29 October 1669. 1704 - Birthdate of Gabriel Cramer, Swiss mathematician, and physicist (d. 1752). 1712 - Birthdate of Samuel König, German mathematician (d. 1757).

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1726 - Day of death of Nicolaus II Bernoulli, Swiss mathematician, and theorist (b. 1695). 1730 - Goldbach proves that Fermat numbers are pairwise coprime. He claims that 1 is the only square among the triangular numbers. 1826 - Birthdate of Daniel Friedrich Ernst Meissel, German mathematician (d. 1895). 1851 - Gauss witnessed the opening ceremonies when the newly constructed railway from Cassel reached Gottingen. 1863 - Birthdate of George Abram Miller, American mathematician (d. 1951). 1896 - Day of death of Ludwig Christian Wiener, German mathematician, physicist, and philosopher (b. 1826). 1926 - Birthdate of Hilary Putnam, American mathematician, computer scientist, and philosopher (d. 2016). 1943 - Ireland issued two stamps to celebrate the centenary of the discovery of quaternions by Sir William Rowan Hamilton.

1927 - Birthdate of Felix Browder, American mathematician (d. 2016). 1945 - Birthdate of John O'Connor, British mathematician. 2016 - Day of death of Seymour Papert, South African mathematician (b. 1928).

CHAPTER EIGHT AUGUST

August, 1 1861 - Birthdate of Ivar Otto Bendixson, Swedish mathematician (d. 1935). 1881 - Birthdate of Otto Toeplitz, German mathematician (d. 1940). 1920 - Day of death of Bal Gangadhar Tilak, Indian mathematician, philosopher, and militant nationalist (b. 1856). 1937 - Birthdate of Barry Edward Johnson, British mathematician (d. 2002). 1944 - The MARK I computer started to work at Harvard. 1947 - The Netherlands issued a postage stamp honoring J. de Witt (16251672).

1950 - Birthdate of Eric Schechter, American mathematician. 1955 - Birthdate of Bernadette Perrin-Riou, French mathematician. 1970 - Birthdate of Elon Lindenstrauss, Israeli mathematician. 1980 - Michael Aschbacher wrote to Daniel Gorenstein that he had completed the classification of the finite simple groups. 1987 - Day of death of Evelyn Merle Nelson, Canadian mathematician (b. 1943). 1990 - Day of death of Dmitrii Alexeevich Suprunenko, Soviet mathematician (b. 1915). 1992 - Day of death of Leslie Fox, British mathematician (b. 1918).

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August, 2 1641 - Freicle de Bessy proposed a problem to Fermat involving the factorization of 221, using the fact that 221 = 10² + 11² = 5² + 14² [128]. 1733 - Benjamin Franklin suggested that writers could improve their literary style if they learned some mathematics in The Pennsylvania Gazette: "If a writer would persuade, he should proceed gradually from things already allowed to those from which assent is yet withheld, and make their connection manifest. ...Perhaps a habit of using good method cannot be better acquired than by learning a little geometry or algebra." 1823 - Day of death of Lazare Carnot, French mathematician, general, and politician, President of the National Convention (b. 1753). 1856 - Birthdate of Ferdinand Rudio, Swiss mathematician (d. 1929). 1887 - Birthdate of Oskar Anderson, Russian-German mathematician, and statistician (d. 1960). 1892 - Day of death of Italian mathematician and politician (b. 1822). 1902 - Birthdate of Mina Spiegel Rees, American mathematician (d. 1997). 1906 - R. D. Carmichael proved that there are no triple perfect odd numbers that are the product of three distinct prime factors [39]. 1912 - Birthdate of Joel Lee Brenner, American mathematician (d. 1997). 1927 - Birthdate of Peter Swinnerton-Dyer, English mathematician (d. 2018). 1943 - Birthdate of Melvin Hochster, American mathematician. 1970 - Day of death of Angus MacFarlane-Grieve, English mathematician, rower, and soldier (b. 1891). 1971 - Birthdate of Ruth Elke Lawrence-Naimark, Israeli mathematician. 1976 - Day of death of Laszlo Kalmar, Hungarian mathematician (b. 1905).

August, 3 1746 - Euler and d'Alembert began their correspondence. 1747 - Diderot and d'Alembert replaced de Gua, who had earlier done much to systematize analytic geometry, as directors of the publishing project, which was to become the celebrated Encyclopédie. 1835 - Birthdate of Artemas Martin, American mathematician (d. 1918). 1899 - Cantor succeeded in proving the problem stated in his July 28 letter to Dedekind, where Cantor asked whether the set of all cardinal

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numbers is itself a set because, if it is, it would have a cardinal number larger than any other cardinal. 1914 - Birthdate of Mark Kac, Polish mathematician (d. 1984). 1917 - Day of death of Ferdinand Georg Frobenius, German mathematician (b. 1849). 1922 - Day of death of Mathias Lerch, Czech mathematician (b. 1860). 1926 - Birthdate of Maurice Auslander, American mathematician (d. 1994). 1943 - Birthdate of Béla Bollobás, Hungarian-English mathematician. 2018 - Italy issued a stamp honoring Maria Gaetana Agnesi.

August, 4 1753 - Euler mentions "another very beautiful theorem" in Fermat's work: "Fermat's Last Theorem." He remarks that he has found a proof for the exponent 3. However, his proof in Algebra (1770) contains a fallacy. 1805 - Birthdate of William Rowan Hamilton, Irish physicist, astronomer, and mathematician (d. 1865). 1810 - Gauss married his second wife, Minna Waldeck, who bore him two sons and a daughter. 1811 - Thomas Jefferson writes to Nicolas G. Duef to thank him for a French Dictionary and adds, "I am anxious to get a copy of La Croix's Cours de Mathematiques." 1812 - Day of death of Georg Klugel, German mathematician (b. 1739). 1834 - Birthdate of John Venn, English mathematician and philosopher (d. 1923). 1874 - Day of death of Ludwig Otto Hesse, German mathematician (b. 1811). 1893 - Birthdate of Francis Dominic Murnaghan, Irish mathematician (d. 1976). 1906 - Day of death of Joseph Marie de Tilly, Belgian military man, and mathematician (b. 1837). 1909 - Birthdate of Saunders MacLane, American mathematician (d. 2005).

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1912 - Birthdate of Aleksandr Danilovich Aleksandrov, Russian mathematician, physicist, and mountaineer (d. 1999). 1920 - Day of death of Karl Friedrich Wilhelm Rohn, German mathematician (b. 1855). 1945 - Day of death of Gerhard Gentzen, German mathematician (b. 1909). 1950 - Birthdate of Jacqueline Anne Stedall, British historian of mathematics (d. 2014). 1980 - Day of death of Georg Aumann, German mathematician (b. 1906). 2009 - Day of death of James Wiegold, Welsh mathematician (b. 1934).

August, 5 1802 - Birthdate of Niels Henrik Abel, Norwegian mathematician (d. 1829). 1855 - Birthdate of Alfredo Capelli, Italian mathematician (d. 1910). 1872 - Day of death of Charles-Eugene Delaunay, French mathematician, and astronomer (b. 1816). 1889 - Birthdate of Hans Ludwig Hamburger, German mathematician (d. 1956). 1900 - In The Weekly Dispatch, the famous puzzler Henry E. Dudeney challenged readers to find a magic square with all prime numbers that had the lowest sum for rows and columns. He had already solved it, and his example had that "prime one" sitting right there front and center in the top row: 67 13 31

1 37 73

43 61 7

1910 - Day of death of Julius Petersen, Danish mathematician (b. 1839). 1981 - Day of death of Jerzy Neyman, Russian-American mathematician (b. 1894).

August, 6 1618 - Johannes Kepler determined the distance to the sun to be 22.5 million km. 1667 - Birthdate of Johann Bernoulli, Swiss mathematician (d. 1748). 1694 - Day of death of Antoine Arnauld, French mathematician, and philosopher (b. 1612).

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1741 - Birthdate of John Wilson, English lawyer, and mathematician (d. 1793). 1855 - Thomas Penyngton Kirkman presented a paper on the general question of determining a condition under which a graph is Hamiltonian. 1925 - Day of death of Gregorio Ricci-Curbastro, Italian mathematician (b. 1853). 1926 - Day of death of Constantin Climescu, Romanian mathematician (b. 1844). 1936 - Birthdate of Harold Mortimer Edwards, Jr., American mathematician. 1945 - Day of death of Paul Koebe, German mathematician (b. 1882). 1986 - Day of death of Banesh Hoffmann, British physicist, and mathematician (b. 1906). 1998 - Day of death of André Weil, French-American mathematician (b. 1906). 2007 - Day of death of Atle Selberg, Norwegian mathematician (b. 1917).

August, 7 1620 - Kepler's mother was arrested for witchcraft. 1639 - Day of death of Martin van den Hove, Dutch astronomer, and mathematician (b. 1605). 1645 - The modern notation for the square of the number (t^2) appeared in a letter by J. Pell [29]. 1799 - The second, greatly augmented edition of Montucla's Histoire des Mathématiques appeared. 1834 - Day of death of Joseph-Marie Jacquard, French mathematician (b. 1752). 1868 - Birthdate of Ladislaus Josephowitsch Bortkiewicz, RussianGerman mathematician (d. 1931). 1928 - Birthdate of Dikran Tahta, British-Armenian mathematician (d. 2006). 1985 - Day of death of Gabor Szego, Hungarian-American mathematician (b. 1895). 2010 - Day of death of John Nelder, English mathematician, and statistician (b. 1924).

August, 8 National Abacus (Soroban) Day in Japan 1555 - Day of death of Oronce Fine, French mathematician, and cartographer (b. 1494).

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1627 - Birthdate of Joseph Moxon, English printer of mathematical books and maps, a maker of globes and mathematical instruments, and mathematical lexicographer (d. 1691). 1802 - William Herschel describes in his Diary a conversation between Napoleon and Laplace that took place on this day: “Napoleon took a moment during the brief peace of 1802 to engage in a bit of intellectual banter. He entertained a few savants – Sir William Herschel himself, the distinguished physicist Count Rumford, his minister of the interior – a chemist by profession – Jean Antoine Chaptal, and Laplace. After exchanging pleasantries with Herschel, the First Consul turned to Laplace, who had just published the third volume of Celestial Mechanics. Released from matters of state, Napoleon delighted in posing challenging questions to his guests. He told his mathematical friend that he had read Newton and noticed that Newton's great book mentioned God frequently. However, he stated, "I have perused yours, but failed to find His name even once." He asked Laplace why that was. In the grand tradition of this story, Laplace is reported to have replied, "I have no need of that hypothesis." 1853 - Day of death of Josef-Maria Hoene de Wronski, Polish mathematician (b. 1776). 1900 - David Hilbert addressed the second International Congress of Mathematicians in Paris: “We hear within us the perpetual call: There is a problem. Seek its solution. You can find it by pure reason, for in mathematics there is no 'ignorabimus.'" Hilbert also presented ten problems (1, 2, 6, 7, 8, 13, 16, 19, 21, and 22) at the Paris conference of the ICM, speaking at the Sorbonne. 1912 - Birthdate of Ralph Philip Boas Jr., American mathematician, teacher, and journal editor (d. 1992). 1921 - Birthdate of Edwin Henry Spanier, American mathematician (d. 1996). 1931 - Birthdate of Roger Penrose, English physicist, mathematician, and philosopher. 1931 - George Birkhoff publishes “A Set of Postulates for Plane Geometry Based on Scale and Protractor" in the Annals of Mathematics. 1973 - Birthdate of Ilka Agricola, German mathematician. 1974 - Birthdate of Manjul Bhargava, Canadian-American mathematician. 1977 - Derek T. Whiteside received the Sarton Medal, the highest honor that the History of Science Society can bestow, for his editorship of The Mathematical Papers of Isaac Newton. 1979 - Day of death of Jacob Lionel Bakst Cooper, South African mathematician (b. 1915).

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1987 - Day of death of Danilo Blanuša, Croatian mathematician, and physicist (b. 1903). 1989 - Day of death of Taro Morishima, Japanese mathematician (b. 1903).

August, 9 1537 - Birthdate of Francesco Barozzi, Italian mathematician, and astronomer (d. 1604). 1611 - Day of death of John Blagrave, English mathematician, and astronomer. 1654 - Fermat wrote to Carcavi: “Monsieur, I was overjoyed to have had the same thoughts as those of M. Pascal, for I greatly admire his genius and I believe him to be capable of solving any problem he attempts. The friendship he offers is so dear to me and so precious that I shall not scruple to take advantage of it in publishing an edition of my Treatises. If it does not shock you, you could both help in bringing out this edition, and I suggest that you should be the editors: you could clarify or augment what seems too brief and thus relieve me of a care which my work prevents me from taking. I would like this volume to appear without my name even, leaving to you the choice of designation which would indicate the author, whom you could qualify simply as a friend" [102]. 1726 - Birthdate of Francesco Cetti, Italian priest, zoologist, and mathematician (d. 1778). 1853 - Day of death of Josef-Maria Hoene de Wronski, Polish Messianist philosopher, mathematician, physicist, inventor, lawyer, and economist (b. 1776). 1932 - Day of death of John Charles Fields, Canadian mathematician, founder of the Fields Medal (b. 1863). 1940 - Birthdate of Linda Keen, American mathematician. 1994 - Day of death of Helena Rasiowa, Polish mathematician (b. 1917). 2007 - Day of death of Graham Robert Allan, English mathematician (b. 1936).

August, 10 1548 - Tartaglia and Ferrari debated in Milan over solutions to cubic and quartic equations in a mathematical contest. 1602 - Birthdate of Gilles de Roberval, French mathematician (d. 1675).

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1929 - Day of death of Pierre Fatou, French mathematician, and astronomer (b. 1878). 1730 - Euler mentions that Fermat and Wallis studied the equation ap² + 1 = q², and mentions a method for solving it which he credits to Pell [104]. 1732 - Pell equations (x² - Ay² = 1) are named in the letter of Euler to Goldbach. 1806 - Birthdate of Julius Ludwig Weisbach, German mathematician, and engineer (d. 1871). 1843 - Day of death of Robert Adrain, American mathematician (b. 1775). 1846 - The Smithsonian Institution established in Washington, DC. 1859 - Birthdate of Ivan Vsevolodovich Meshchersky, Soviet mathematician (d. 1935). 1859 - Birthdate of Georg Alexander Pick, Austrian mathematician (d. 1942). 1869 - Day of death of Victoire Louis Athanase Dupre, French mathematician, and physicist (b. 1808). 1888 - Engels wrote to Marx: "Yesterday I found the courage at last to study your mathematical manuscripts even without reference books, and I was pleased to find that I did not need them. I compliment you on your work. The thing is as dear as daylight, so that we cannot wonder enough at the way the mathematicians insist on mystifying it." [113]. 1926 - Birthdate of Carol Karp, American mathematician (d. 1972). 1929 - Day of death of Pierre Joseph Louis Fatou, French mathematician (b. 1878). 1960 - Day of death of Oswald Veblen, American mathematician (b. 1880). 1995 - Day of death of Zhou Weiliang, Chinese mathematician (b. 1911). 2014 - Day of death of Kathleen Ollerenshaw, English mathematician, astronomer, and politician, Lord Mayor of Manchester (b. 1912).

August, 11 1464 - Day of death of Nicholas von Cusa, German polymath (b. 1401). 1578 - Day of death of Pedro Nunes, Portuguese mathematician (b. 1502). 1591 - Kepler received his master's degree from Tübingen. 1730 - Birthdate of Charles Bossut, French mathematician (d. 1814). 1829 - Birthdate of Norman Macleod Ferrers, English mathematician (d. 1903). 1842 - Birthdate of Enrico D'Ovidio, Italian mathematician (d. 1933).

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1859 - Bernhard Riemann was made a corresponding member of the Berlin Academy based on his 1857 paper on Abelian Functions. 1889 - Birthdate of Andrei Mikhailovich Razmadze, Georgian mathematician (d. 1929). 1892 - Day of death of Enrico Betti, Italian mathematician (b. 1813). 1912 - Birthdate of Norman Levinson, American mathematician (d. 1975). 1956 - Birthdate of Pierre-Louis Lions, French mathematician. 1983 - Grothendieck noted in Pursuing Stacks: "It has been over three weeks now I haven't been working on the notes. Most part of the time was spent wandering in the Pyrenees with some friends (a kind of thing I hadn't been doing since I was a boy), and touring some other friends living the simple life around there, in the mountains. I was glad to meet them and happy to wander and breeze the fresher air of the mountains | and very happy too after two weeks to be back in the familiar surroundings of my home amidst the gentle hills covered with vineyards..." [155]. 1995 - Day of death of Alonzo Church, American mathematician, and logician (b. 1903). 2003 - Day of death of Armand Borel, Swiss-American mathematician (b. 1923).

August, 12 1452 - Birthdate of Abraham Zacuto, Jewish astronomer, astrologer, mathematician, rabbi, and historian (d. 1515). 1755 - Lagrange sent Euler solutions to some famous problems using a technique that was later to be called the calculus of variations [55]. 1769 - Birthdate of Johann Christian Martin Bartels, German mathematician (d. 1836). 1862 - Birthdate of Jules Antoine Richard, French mathematician (d. 1956). 1887 - Birthdate of Erwin Schrödinger, Austrian theoretical physicist (d. 1961). 1901 - Day of death of Ernest de Jonquières, French naval officer, and mathematician (b. 1820). 1926 - Birthdate of Horace Chandler Davis, American-Canadian mathematician, writer, and educator. 1930 - Birthdate of Jacques Tits, Belgian-French mathematician. 1935 - Day of death of Friedrich Schottky, German mathematician (b. 1851).

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2014 - BBC announces the first Female Fields Medal winner, Maryam Mirzakhani.

August, 13 1625 - Birthdate of Rasmus Bartholin, Danish physician, mathematician, and physicist (d. 1698). 1704 - Birthdate of Alexis Fontaine des Bertins, French mathematician (d. 1771). 1819 - Day of death of Sir George Stokes, 1st Baronet, Anglo-Irish mathematician, and physicist (d. 1903). 1822 - Day of death of Jean Robert Argand, Swiss-French amateur mathematician (b. 1768). 1849 - Gauss writes to his former student, Möbius, to thank him for sending a copy of Möbius' paper on third-order curves and advises him to investigate the form of analytic curves from Gauss' 1799 dissertation. 1849 - George Boole writes to De Morgan to tell him he has received the math professorship at Queen's College Cork. In spite of stating clearly in his application, "I am not a member of any university and have never studied at a college." 1861 - Birthdate of Cesare Burali-Forti, Italian mathematician (d. 1931). 1887 - Birthdate of Otton Marcin Nikodym, Polish-American mathematician (d. 1974). 1896 - Day of death of Philipp Ludwig von Seidel (b. 1821). 1914 - Birthdate of Grace Bates, American mathematician (d. 1996). 1936 - Birthdate of Graham Robert Allan, English mathematician (d. 2007). 1957 - Day of death of Fredrik Carl Mülertz Størmer, Norwegian geophysicist, and mathematician (b. 1874). 1959 - Birthdate of Steven Henry Strogatz, American mathematician, and popular writer. 1968 - Day of death of Øystein Ore, Norwegian mathematician (b. 1899). 1977 - Day of death of John Hamilton Curtiss, American mathematician (b. 1909). 2008 - Day of death of Henri Cartan, French mathematician (b. 1904).

August, 14 1530 - Birthdate of Giambattista Benedetti, Italian mathematician, and physicist (d. 1590).

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1659 - Fermat, in a letter to Carcavi, claimed to be able to prove the following five theorems by the method of infinite descent: (1) The area of a right-angled triangle whose sides are integers cannot be a square number. (2) The equation x3 + y3 = z3 has no solutions in integers. (3) The equation y2 + 2 = x3 admits no solutions in integers except x = 3, y = 5. (4) The equation y² + 4 = x³ admits no solutions in integers except x = 2, y = 2, and x = 5, y = 11. (5) Each prime number of the form p = 4n + 1 is uniquely expressible as the sum of two squares. 1737 - Birthdate of Charles Hutton, English mathematician (d. 1823). 1834 - Day of death of Edmond Nicolas Laguerre, French mathematician (b. 1834). 1842 - Birthdate of Jean-Gaston Darboux, French mathematician (d. 1917). 1850 - Birthdate of Walter William Rouse Ball, British mathematician, and lawyer (d. 1925). 1865 - Birthdate of Guido Castelnuovo, Italian mathematician (d. 1952). 1866 - Birthdate of Charles Jean de la Vallée-Poussin, Belgian mathematician (d. 1962). 1886 - Day of death of Edmond N. Laguerre, French mathematician (b. 1834). 1888 - Birthdate of Julio Rey Pastor, Spanish mathematician, and historian of science (d. 1962). 1894 - The first summer meeting of the American Mathematical Society was held. 1906 - Birthdate of Eugene Lukacs, Hungarian statistician (d. 1987). 1930 - Day of death of Florian Cajori, Swiss-American educator, and mathematician (b. 1859). 1956 - Birthdate of Erica Flapan, American mathematician. 1956 - Day of death of Hans Ludwig Hamburger, German mathematician (b. 1889). 1959 - Birthdate of Peter Williston Shor, American mathematician. 1967 - Day of death of Jovan Karamata, Serbian mathematician (b. 1902). 1987 - Day of death of Shigeo Sasaki, Japanese mathematician (b. 1912). 2000 - Day of death of Vera Nikolaevna Maslennikova, Soviet mathematician (b. 1926).

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August, 15 1758 - Day of death of Pierre Bouguer, French mathematician, geophysicist, and astronomer (b. 1698). 1768 - Lagrange, in a letter to D'Alembert, expressed his difficulty in solving the problem: Given a nonsquare positive integer n, to find a square integer x² such that nx² + 1 shall also be a square. In the same letter, he showed that x² = 3 could be expanded in a trigonometric series. [93]. 1789 - Day of death of Jacob (II) (Jacques (II)) Bernoulli, Swiss-Russian mathematician (b. 1759). 1795 - Birthdate of Emile Leger, French mathematician (d. 1838). 1798 - Day of death of Edward Waring, English mathematician (b. 1736). 1841 - In a series of letters, Ada Lovelace sent De Morgan four papers she had written on the subject of accelerating force. The first of which accompanied a letter given by Toole as dating from 15 August 1841. Subsequent letters referring to these papers on force date from 16, 21, and 28 August 1841; the last one, however, was actually transcribed by Toole as dating from August 1842, along with another from 4 September. [82]. 1863 - Birthdate of Aleksey Krylov, Soviet mathematician, and engineer (d. 1945). 1901 - Birthdate of Pyotr Novikov, Soviet mathematician, and theorist (d. 1975). 1922 - Day of death of Pierre Léon Boutroux, French mathematician, and historian of science (b. 1880). 1951 - USSR issued a postage stamp with a portrait of Sofia Kovalevskaya.

1978 - Day of death of Viggo Brun, Norwegian mathematician (b. 1885). 1981 - Day of death of Viktor Vladimirovich Wagner (Vagner), Soviet mathematician (b. 1908). 2002 - Day of death of Heinz Bauer, German mathematician (b. 1928).

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August, 16 1705 - Day of death of Jacob Bernoulli, Swiss mathematician, and theorist (b. 1654). 1821 - Birthdate of Arthur Cayley, English mathematician (d. 1895). 1836 - Day of death of Marc-Antoine Parseval, French mathematician, and theorist (b. 1755). 1837 - Birthdate of Joseph Marie de Tilly, Belgian military man, and mathematician (d. 1906). 1842 - Birthdate of Jakob Rosanes, Ukrainian-German mathematician, and chess player (d. 1922). 1905 - Birthdate of Marian Adam Rejewski, Polish mathematician, and cryptologist (d. 1980). 1907 - Birthdate of Dušan "Duro" Kurepa, Yugoslav mathematician (d. 1993). 1918 - Birthdate of Paul Olum, American mathematician (d. 2001). 1920 - Birthdate of Richard Ernest Bellman, American applied mathematician (d. 1984). 1966 - Stephen Smale, University of California, Berkeley, received the Fields Medal at the International Congress of Mathematicians in Moscow for his work on dynamical systems. 1983 - Poland issued a stamp celebrating the 50th anniversary of the Enigma Decoding Machine.

1995 - Day of death of Thomas Brooke Benjamin, English mathematical physicist, and mathematician (b. 1929). 2013 - Day of death of David Rees, Welsh mathematician (b. 1918).

August, 17 1607 - Birthdate of Pierre de Fermat, French lawyer, and mathematician (d. 1665). 1655 - William Oughtred writes to John Wallis to praise his methods in Arithmetica Infinitorum [176].

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1750 - Euler returns to his idea of using generating functions for proving the Four-Squares Theorem [104]. 1811 - Jefferson writes to his grandson, Benjamin Rush: “Having to conduct my grandson through his course of mathematics, I have resumed that study with great avidity. It was always my favorite one. We have no theories there, no uncertainties remain on the mind; all is demonstration and satisfaction." [45]. 1825 - A royal decree granted Niels Henrik Abel a year's travel in France and Germany. 1904 - Birthdate of Giovanni Ricci, Italian mathematician (d. 1973). 1924 - Day of death of Pavel Samuilovich Urysohn, Soviet mathematician (b. 1898). 1927 - Day of death of Erik Ivar Fredholm, Swedish mathematician (b. 1866). 1954 - Birthdate of Ingrid Daubechies, Belgian physicist, and mathematician. 1975 - Day of death of Sergei Vasilyevich Fomin, Soviet mathematician (b. 1917). 1993 - Day of death of Feng Kang, Chinese mathematician (b. 1920). 2004 - Day of death of Shizuo Kakutani, Japanese-American mathematician (b. 1911). 2007 - Day of death of Victor L. Klee, Jr., American mathematician (b. 1925). 2015 - Day of death of William Bowen Bonnor, British mathematician, and gravitation physicist (b. 1920).

August, 18 1652 - Day of death of Florimond de Beaune, French mathematician (b. 1601). 1685 - Birthdate of Brook Taylor, English mathematician (d. 1731). 1832 - Birthdate of Eugène Rouche, French mathematician (d. 1910). 1910 - Birthdate of Paul Turán, Hungarian mathematician (d. 1976). 1881 - Engels wrote to Marx to praise Marx's manuscript on the differential calculus: "The matter is so perfectly clear that we cannot be amazed enough at how the mathematicians so stubbornly insist on mystifying it." 1978 - Henri Cohen gives a lecture to confirm Roger Apéry's proof that Apéry’s constant ȗ(3) is irrational. 1960 - Day of death of Carlo Emilio Bonferroni, Italian mathematician (b. 1892).

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August, 19 1584 - Birthdate of Pierre Vernier, French mathematician (d. 1638). 1662 - Day of death of Blaise Pascal, French mathematician, physicist, and philosopher (b. 1623). 1703 - Day of death of John Wallis, British mathematician (b. 1616). 1736 - Birthdate of Erland Bring, Swedish mathematician (d. 1798). 1739 - Birthdate of Georg Klugel, German mathematician (d. 1812). 1758 - Étienne Montucla received the censor's approbation for his Histoire des mathématiques. 1877 - Correspondence between Hermite and Lipschitz begins [15]. 1822 - Day of death of Jean Baptiste Joseph Delambre, French mathematician, and astronomer (b. 1749). 1872 - Birthdate of Théophile Ernest de Donder, Belgian mathematician, and physicist (b. 1872). 1874 - Day of death of Friedrich Moritz Hartogs, Jewish-German mathematician (b. 1844). 1910 - Day of death of Eugène Rouche, French mathematician (b. 1832). 1925 - Birthdate of Volodymyr Semenovych Korolyuk, Soviet-Ukrainian mathematician (d. 2020). 1939 - Birthdate of Alan Baker, British mathematician. 1939 - Day of death of Paul Epstein, German mathematician (b. 1871). 1947 - Birthdate of Anuška Ferligoj, Slovenian mathematician. 1957 - Day of death of Maurice Kraitchik, Belgian mathematician, and game designer (b. 1882). 1973 - Birthdate of Olga Holtz, Russian mathematician.

August, 20 1622 - Day of death of BahƗ‫ ގ‬al-DƯn Muতammad ibn ণusayn al-‫ޏ‬ƖmilƯ, Syrian-Iranian theologian, mathematician, and astronomer (b. 1546). 1672 - Day of death of Johan de Witt, Dutch mathematician, and politician (b. 1625). 1669 - Barrow had brought Newton a copy of Nicholas Mercator's Logarithmotechnia, which included the infinite series for ln(1 + x). Newton recognized this as a simple example of his more general work on infinite series during his annus mirabilis in Woolsthorpe. Newton began to share some of his work with Barrow, who convinced him to send some of it, anonymously, to John Collins, which he did. When Collins received highly favorable responses, Newton allowed Barrow to identify him to Collins. Barrow's letter to Collins on this date was

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the first time Newton became known to the mathematical community outside Cambridge [53]. 1677 - Day of death of Pierre Petit, French astronomer, physicist, mathematician, and instrument maker (b. 1594). 1710 - Birthdate of Thomas Simpson, English mathematician (d. 1761). 1791 - Day of death of Jacques Charles, French mathematician (b. 1752). 1862 - Birthdate of Paul Gustav Samuel Stackel, German mathematician (d. 1919). 1863 - Birthdate of Corrado Segre, Italian mathematician (d. 1924). 1899 - Birthdate of Salomon Bochner, Galician-born American mathematician (d. 1982). 1901 - Birthdate of Henry Morgan Ward, American mathematician (d. 1963). 1915 - Day of death of Fred Hoyle, English mathematician, and astronomer (b. 1915). 1955 - 2500th anniversary of the Pythagorean school of philosophy. Observances were held on the island of Samos to honor the anniversary of the founding of the school by Pythagoras. Four postage stamps were issued by Greece, one showing the celebrated 47th Proposition of Euclid, the Pythagorean Theorem.

1957 - Birthdate of Simon Kirwan Donaldson, British mathematician. 1972 - Day of death of Carol Karp, American mathematician (b. 1926). 2006 - Day of death of William Parry, English mathematician (b. 1934). 2008 - Day of death of Sergey Mergelyan, Soviet-Armenian mathematician (b. 1928).

August, 21 1660 - Birthdate of Hubert Gautier, French mathematician, and engineer (d. 1737).

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1665 - Birthdate of Giacomo F. Maraldi, French-Italian astronomer, and mathematician (d. 1729). 1706 - Hermann wrote to Leibniz a proof that Machin's series converges to ʌ and showed that some other series also converge to ʌ. 1738 - Euler wrote a letter to Goldbach complaining that the eyestrain of working with the Atlas of Russia was causing him to go blind. Goldbach replied on the very same day and got Euler relieved of the most tedious mapmaking tasks. It was Euler's first letter to Goldbach in German; all previous letters had been in the more formal language, Latin, and this change was an acknowledgment that Euler had become more than just a colleague of the older Goldbach, but also a friend. [151] 1757 - Day of death of Samuel König, German mathematician (b. 1712). 1771 - Day of death of Alexis Fontaine des Bertins, French mathematician (b. 1704). 1789 - Birthdate of Augustin-Louis Cauchy, French mathematician (d. 1857). 1836 - Day of death of Claude Louis Marie Henri Navier, French mathematician (b. 1785). 1881 - Birthdate of Archibald Read Richardson, British mathematician (d. 1954). 1888 - William Seward Burroughs of St. Louis obtained a patent for his adding machine, the first successfully marketed.

1893 - The zeroth International Mathematical Congress, with representatives from seven countries, was held in conjunction with the Chicago World's Fair from August 21-25. 1901 - Birthdate of Edward Copson, English mathematician (d. 1980). 1909 - Birthdate of Nikolay Bogolyubov, Soviet mathematician, and physicist (d. 1992).

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1917 - Birthdate of Leonid Hurwicz, Russian economist, and mathematician (d. 2008). 1924 - Birthdate of Lajos Takacs, Hungarian mathematician (d. 2015). 1927 - Day of death of William Burnside, English mathematician (b. 1852). 1932 - Birthdate of Louis de Branges de Bourcia, French-American mathematician. 1940 - Birthdate of Endre Szemeredi, Hungarian-American mathematician, and computer scientist. 1951 - Birthdate of Eric Goles, Chilean mathematician, and computer scientist. 1961 - Day of death of Cyrus Colton MacDuffee, American mathematician (b. 1895). 1972 - Peru issued an Air Post Stamp picturing a Quipu (cotton or camelid fiber strings used for collecting data and keeping records, monitoring tax obligations, properly collecting census records, calendrical information, and for military organization).

1995 - Day of death of Subrahmanyan Chandrasekhar, Indian-American astrophysicist, and mathematician, Nobel Prize laureate (b. 1910). 2012 - Day of death of William Thurston, American mathematician (b. 1946).

August, 22 1450 - Gutenberg borrowed 800 guilders in gold at 6% interest to develop his invention of printing from movable metal type. 1647 - Birthdate of Denis Papin, French physicist, and mathematician, the forerunner of the pressure cooker and the steam engine (d. 1712). 1676 - Ole Rømer's conjecture that the speed of light was finite may have appeared in a presentation to the Royal Academy of Sciences in Paris. 1752 - Day of death of William Whiston, English mathematician, historian, and theologian (b. 1667). 1794 - Day of death of Achille-Pierre Dionis du Séjour, French mathematician, astronomer, and politician (b. 1734).

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1796 - Birthdate of Baden Powell, English mathematician (d. 1860). 1883 - Sylvester writes Cayley that, “I have been recovering my theory of multiple algebras – by slow degrees." Thus begins his first sustained assault on Matrix Theory [131]. 1907 - Day of death of Platon Sergeevich Poretsky, Russian mathematician (b. 1846). 1917 - E. Noether writes to Ernst Fischer, “I have actually been able now to reduce the differential invariants – which up to last spring I still had not completely proved – to a problem of equivalence between linear families; it would be nice if this could be incorporated into your theory"; and, “You can see that things are coming out, after all, as I had envisioned them already last spring; my things are to be subordinated to yours, not the other way around." [38]. 1923 - Birthdate of Hidehiko Yamabe, Japanese mathematician (d. 1960). 1924 - Birthdate of Gerard Laman, Dutch mathematician (d. 2009). 1925 - Day of death of Emanuel Czuber, Austrian mathematician (b. 1851). 1974 - Day of death of Jacob Bronowski, Polish-English mathematician, biologist (b. 1908). 1975 - Day of death of Andrzej Mostowski, Polish mathematician (b. 1913). 2006 - Grigori Perelman is awarded the Fields Medal for his proof of the Poincaré conjecture in mathematics but refuses to accept the medal.

August, 23 1638 - Descartes, in a letter to Mersenne, proposed his folium (x3 + y3 = 2axy) as a test case to challenge Fermat's differentiation techniques. To Descartes' embarrassment, Fermat's method worked. 1683 - Birthdate of Giovanni Poleni, Italian mathematician (d. 1761). 1735 - Abraham de Moivre elected to the Berlin Academy. 1778 - Birthdate of Josef-Maria Hoene de Wronski, Polish Messianist philosopher, mathematician, physicist, inventor, lawyer, and economist (d. 1853). 1797 - Adhémar Jean Claude Barre de Saint-Venant, French mechanician, and mathematician (d. 1886). 1829 - Birthdate of Moritz Cantor, German mathematician, and historian (d. 1920). 1842 - Birthdate of Osborne Reynolds, Irish mathematician (d. 1912). 1873 - Birthdate of Zoard Geocze de Szendro, Hungarian mathematician (d. 1916).

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1893 - Birthdate of Joseph Fels Ritt, American mathematician (d. 1951). 1908 - Birthdate of John Arthur Todd, British mathematician (d. 1994). 1919 - Birthdate of Vladimir Abramovich Rokhlin, Soviet mathematician (d. 1984). 1923 - Day of death of Phoebe Sarah Hertha Ayrton, British engineer, mathematician, physicist, and inventor (b. 1854). 1954 - Day of death of Jaan Sarv, Estonian mathematician (b. 1877). 1956 - Birthdate of Andreas Floer, German mathematician (d. 1991). 1973 - Day of death of Helmuth Kneser, Baltic German mathematician (b. 1898). 1988 - Day of death of Hans Lewy, American mathematician (b. 1904). 2001 - A year prior to the Abel Bicentenary, it was announced that the Norwegian Government would establish an Abel Fund worth NOK 200 million. Part of the fund's money would be used by the Norwegian Academy of Science and Letters to award an annual Abel Prize for mathematics worth about $750,000, which is of the order of magnitude of the Nobel Prize and a long-awaited one. Unlike the Fields Medal, the Abel Prize is for lifelong contributions to mathematics. 2009 - Day of death of Pierre Samuel, French mathematician (b. 1921). 2012 - Day of death of James B. Serrin, American mathematician (b. 1926).

August, 24 1561 - Birthdate of Bartholomaeus Pitiscus, German trigonometrist, astronomer, and theologian (d. 1613). 1595 - Day of death of Thomas Digges, English mathematician, and astronomer (b. 1546). 1654 - Pascal wrote to Fermat, describing his solution to the Problem of the Points (a probability problem) and asking Fermat to critique it: “I was not able to tell you my entire thoughts regarding the problem of the points by the last post, and at the same time, I have a certain reluctance at doing it for fear lest this admirable harmony which obtains between us and which is so dear to me should begin to flag, for I am afraid that we may have different opinions on this subject. I wish to lay my whole reasoning before you and to have you do me the favor to set me straight if I am in error or to endorse me if I am correct. I ask you this in all faith and sincerity for I am not certain even that you will be on my side. When there are but two players, your theory which proceeds by combinations is very just. But when there are three, I believe I have a proof that it is unjust that you should proceed in any

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other manner than the one I have. But the method which I have disclosed to you and which I have used universally is common to all imaginable conditions of all distributions of points, in the place of that of combinations (which I do not use except in particular cases when it is shorter than the general method), a method which is good only in isolated cases and not good for others. I am sure that I can make it understood, but it requires a few words from me and a little patience from you. (I wish I had known this phrase early in my teaching career; it seems it would have been frequently handy)." 1670 - Day of death of William Neile, English mathematician, and founder member of the Royal Society (b. 1637). 1739 - Day of death of Takebe Katahiro, Japanese mathematician (b. 1664). 1743 - Euler sketches the idea of infinite descent [104]. 1846 - Birthdate of Enoch Beery Seitz, American mathematician (d. 1883). 1873 - Day of death of Hermann Hankel, German mathematician (b. 1839). 1888 - Day of death of Rudolf Clausius, German physicist, and mathematician (b. 1822). 1923 - Birthdate of Viktor Mikhaylovich Glushkov, Soviet mathematician (d. 1982). 1932 - Birthdate of Glen Eugene Bredon, American mathematician (d. 2000). 1942 - Birthdate of Karen Uhlenbeck, American mathematician, the first female Abel Prize winner. 1971 - The USSR issued a stamp for the centenary of the birth of the British physicist, Ernest Rutherford. Beside his picture is a diagram of the movement of atomic particles which involves a hyperbola.

1975 - Day of death of Anna Margaret Mullikin, American mathematician (b. 1893).

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August, 25 1561 - Birthdate of Philippe van Lansberge, Dutch astronomer, and mathematician (d. 1632). 1699 - Birthdate of Charles-Etienne Camus, French mathematician (d. 1768). 1679 - Day of death of Jonas Moore, English mathematician, and physicist (b. 1627). 1844 - Birthdate of Thomas Muir, British mathematician (d. 1934). 1867 - Birthdate of Hendrik de Vries (d. 1954). 1867 - Birthdate of Yury Vasilievich Kolosov, Russian-Soviet mathematician (d. 1936). 1893 - Eliakim Hastings Moore was apparently the first person to use the English word “field" in its modern mathematical sense and the first to allow for a finite field. He coined the expressions “field of order s" and "Galois-field of order s = qn." [118] 1898 - Birthdate of Helmut Hasse, German mathematician (d. 1975). 1955 - The People's Republic of China issued stamps honoring the mathematician Tsu Chung-chih (429-500), astronomers Chang Heng (78-139), and Chong Sui (683-727), and physicist Li Shih-chen (15181593).

1959 - The National Medal of Science was authorized by an act of Congress (73 Stat. L. 431) for outstanding contributions in the physical, biological, mathematical, and engineering sciences on the basis of recommendations from the National Academy of Sciences. 1964 - Birthdate of Azmin Ali, Malaysian mathematician, and politician. 1964 - Birthdate of Maxim Kontsevich, Russian-American mathematician. 1976 - The Board of Governors of the MAA awarded an honorary life membership to Martin Gardner “for the substantial contributions he has made to the public appreciation of mathematics through his superb exposition in his texts and his column Mathematical Games in Scientific American." 2005 - Day of death of Ruth Aaronson Bari, American mathematician (b. 1917).

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August, 26 349 - Day of death of Thomas Bradwardine, English archbishop, mathematician, and physicist (b. 1290). 1572 - Day of death of Peter Ramus, French mathematician (b. 1515). 1728 - Birthdate of Johann Heinrich Lambert, Swiss mathematician, physicist, and astronomer (d. 1777). 1735 - Euler presented his solution to the Königsberg bridge problem, whether it was possible to find a route crossing each of the seven bridges of the city of Königsberg once and only once, in a lecture to his colleagues at the Academy of Sciences in St. Petersburg. 1770 - Lagrange, in a letter to d'Alembert, first used the notation f'(x) for the derivative. 1875 - Birthdate of Giuseppe Vitali, Italian mathematician (d. 1932). 1893 - Birthdate of Joseph Fels Ritt, American mathematician (d. 1951). 1899 - Birthdate of Wolfgang Krull, German mathematician (d. 1971). 1918 - Birthdate of Katherine Johnson, American physicist, and mathematician (d. 2020). 1921 - Birthdate of Shimshon Amitsur, Israeli mathematician (d. 1994). 1929 - Day of death of Thomas John l'Anson Bromwich, English mathematician (b. 1875). 1950 - Gödel addressed the International Congress of Mathematicians in Cambridge, Massachusetts, on his work in relativity theory. 1965 - Birthdate of Marcus du Sautoy, English mathematician. 1961 - Day of death of Howard Percy Robertson, American mathematician (b. 1903). 1977 - Day of death of Robert Schatten, American mathematician (b. 1911). 1992 - Day of death of Daniel E. Gorenstein, American mathematician (b. 1923).

August, 27 1760 - Leonhard Euler, in his “Letters to a German Princess on various topics of physics and philosophy," explained how a surveyor uses a level. As an example, he asked which end of the straight line between their homes is higher. He discussed the flow of the rivers that connect their homes but gave the wrong answer to his question! 1787 - T. Jefferson advised his future son-in-law, Thomas Mann Randolph, on the role mathematics should play in his education: “The foundations that you have laid in languages and mathematics are

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proper for every superstructure. The former exercises our memory while that and no other faculty is yet matured, and prevents our acquiring habits of idleness, the latter gives exercise to our reason, as soon as that has acquired a certain degree of strength, and stores the mind with truths that are useful in other branches of science." [45] 1858 - Birthdate of Giuseppe Peano, Italian mathematician, and philosopher (d. 1932). 1912 - Day of death of Mikhail Vashchenko-Zakharchenko, Ukrainian mathematician (b. 1825). 1923 - Birthdate of Jacob Willem Cohen, Dutch mathematician (d. 2000). 1925 - Birthdate of Ernest A. Michael, a prominent American mathematician (d. 2013). 1963 - Day of death of Inayatullah Khan Mashriqi, Pakistani mathematician (b. 1888). 1988 - Day of death of John Francis Riordan, American mathematician (b. 1903).

August, 28 1413 - A Papal Bull of Foundation of St Andrews University was issued by Pope Benedict XIII, who wrote: “… considering also the peace and quietness which flourish in the said city of St Andrews and its neighborhood, its abundant supply of victuals, the number of its hospices and other conveniences for students, which it is known to possess, we are led to hope that this city, which the divine bounty has enriched with so many gifts, may become the fountain of science... " 1666 - John Evelyn records in his diary: “To the Royal Society, where one Mercator, an excellent mathematician, produced his rare clock and new motion to perform the equations, and Mr. Rooke, his new pendulum." 1742 - In a letter from Euler to Goldbach, Euler proves no number of the form 4n^4 + 1 can be a prime (more precisely, he showed that 1 + 4x4 = (2x2 + 2x + 1)(2x2 - 2x + 1)). 1801 - Birthdate of Antoine Augustin Cournot, French mathematician, and philosopher (d. 1877). 1867 - Birthdate of Maxime Bochner, American mathematician (d. 1918). 1883 - Birthdate of Jan Arnoldus Schouten, Dutch mathematician (d. 1971). 1884 - Birthdate of Herman Muntz, German mathematician (d. 1956). 1893 - The first day of the Evanston Colloquial lectures by Felix Klein, which would continue until September 9.

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1910 - Birthdate of Tjalling Koopmans, Dutch-American mathematician, and economist Nobel Prize laureate (d. 1985). 1911 - Birthdate of Shizuo Kakutani, Japanese-American mathematician (d. 2004). 1939 - Birthdate of John Kingman, English mathematician. 1961 - The Board of Governors of the MAA voted to name Dr. Mina S. Rees, Dean of Graduate Studies at the City University of New York, the first recipient of their Award for Distinguished Service to Mathematics. 1965 - Day of death of Giulio Racah, Italian-Israeli physicist, and mathematician (b. 1909). 1974 - Sweden issued a stamp picturing a spool and thread, with the thread stretched to form a string figure of a hyperbola.

2005 - Day of death of Esther Szekeres, Hungarian-Australian mathematician (b. 1910). 2005 - Day of death of George Szekeres, Hungarian-Australian mathematician (b. 1911).

August, 29 1654 - Fermat wrote to Pascal: “Monsieur, Our interchange of blows still continues, and I am well pleased that our thoughts are in such complete adjustment as it seems since they have taken the same direction and followed the same road. Your recent Traite du triangle arithmétique and its applications are an authentic proof and if my computations do me no wrong, your eleventh consequence went by post from Paris to Toulouse while my theorem, on figurate numbers, which is virtually the same, was going from Toulouse to Paris. I have not been on the watch for failure while I have been at work on the problem and I am persuaded that the true way to escape failure is by concurring with you. But if I should say more, it would be of the nature of a compliment and we have banished that enemy of sweet and easy conversation. It is now my turn to give you some of my numerical discoveries, but the end of

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the parliament augments my duties and I hope that out of your goodness, you will allow me due and almost necessary respite." In the same letter, he states that, “Meditate however, if you find it convenient, on this theorem: The squared powers of 2 augmented by unity are always prime numbers. [That is,] The square of 2 augmented by unity makes 5 which is a prime number; The square of the square makes 16 which, when unity is added, makes 17, a prime number; The square of 16 makes 256 which, when unity is added, makes 257, a prime number; The square of 256 makes 65536 which, when unity is added, makes 65537, a prime number; and so to infinity. This is a property whose truth I will answer to you. The proof of it is very difficult (impossible, since the statement, as Euler would show later, is not true) and I assure you that I have not yet been able to find it fully." [102]. 1740 - In a letter to Euler, Philippe Naude (the Younger) asked Euler in how many ways a number n can be written as a sum of positive integers. 1756 - Birthdate of Jan Sniadecki, Polish mathematician, and astronomer (d. 1830). 1831 - Michael Faraday discovered his law of electrical induction. 1873 - Day of death of Hermann Hankel, German mathematician (b. 1839). 1899 - Dedekind sends a letter to Georg Cantor that includes a proof of the Schroder-Bernstein Theorem. 1904 - Birthdate of Leonard Roth, British mathematician (d. 1968). 1930 - Day of death of James Bolam, British mathematician (b. 1839). 1937 - Day of death of Otto Ludwig Holder, German mathematician (b. 1859). 1943 - Birthdate of Michele Vergne, French mathematician. 1959 - Birthdate of Stephen Wolfram, English-American physicist, and mathematician. 2012 - Day of death of Shoshichi Kobayashi, Japanese-American mathematician (b. 1932).

August, 30 1621 - Day of death of Baha' ad-Din al-Amili, Lebanese-born mathematician (b. 1547). 1804 - Birthdate of Ernst Wilhelm Grebe, German mathematician (d. 1874). 1819 - Birthdate of Joseph Alfred Serret, French mathematician (d. 1885). 1856 - Birthdate of Carl David Tolme Runge, German mathematician, physicist, and spectroscopist (d. 1927).

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1906 - Birthdate of Olga Taussky-Todd, Austrian-Czech-American mathematician (d. 1995). 1908 - Leonhard Euler's Opera omnia proposed. A committee appointed by the Swiss Society of Naturalists reported its willingness, provided sufficient financial assistance could be secured, to publish the complete works of Euler in about 40 volumes. 1935 - Birthdate of Alexandra Bellow, Romanian-American mathematician. 1940 - Day of death of Sir Joseph John Thomson, English physicist, and mathematician, Nobel Prize laureate (b. 1856).

August, 31 1682 - Michael Rolle published his solution to a problem posed by Ozanam: Find four integers such that the difference of any two of them is a perfect square, and the sum of the first three will also be a perfect square. 1721 - Day of death of John Keill, Scottish mathematician, and natural philosopher (b. 1671). 1811 - Day of death of Louis-Antoine de Bougainville, French soldier, explorer, and mathematician (b. 1729). 1821 - Birthdate of Hermann Ludwig Ferdinand von Helmholtz, German physiologist, physicist, mathematician, and meteorologist (d. 1894). 1880 - Birthdate of Heinrich Franz Friedrich Tietze, Austrian mathematician (d. 1964). 1885 - Birthdate of Herbert Westren Turnbull, English mathematician (d. 1961). 1899 - Cantor, in a letter to Dedekind, remarked that his "diagonal process" can be used to show that the power set of a set has more elements than the set itself [142]. 1918 - Day of death of Andre-Louis Cholesky, French military officer, and mathematician (b. 1875). 1945 - Day of death of Stefan Banach, Polish mathematician (b. 1892). 1950 - Kurt Gödel addressed the International Congress of Mathematicians in Cambridge, Massachusetts, on his work in relativity theory. The lecture was called “Rotating Universes in General Relativity Theory." 1950 - Day of death of Subbayya Sivasankaranarayana Pillai, Indian mathematician (b. 1901). 2013 - Day of death of Jan Camiel Willems, Belgian mathematician (b. 1939).

CHAPTER NINE SEPTEMBER

September, 1 1648 - Day of death of Marin Mersenne, French mathematician, theologian, and philosopher (b. 1588). 1659 - Birthdate of Joseph Saurin, French mathematician (d. 1737). 1716 - Day of death of Heinrich Meissner, German mathematician (b. 1644). 1742 - Euler wrote a letter to Niklaus I Bernoulli on the pentagonal number theorem. 1902 - The French film pioneer George Méliès presented the very first science fiction movie to the stunned public at the Paris Olympia theater. 1908 - Day of death of Aleksandr Nikolayevich Korkin, Russian mathematician (b. 1837). 1910 - Birthdate of Pao-Lu Hsu, Chinese mathematician (d. 1970). 1916 - The first summer meeting of the MAA was held at MIT. 1920 - The central limit theorem got its name in the paper by George Polya. 1932 - Birthdate of Jacobus Hendricus van Lint, Dutch mathematician (d. 2004). 1941 - Birthdate of Alfred Pringsheim, German mathematician. 1967 - Harvey Friedman was appointed Assistant Professor of Mathematics at Stanford University just three weeks before his nineteenth birthday. 1982 - Day of death of Haskell Curry, American mathematician (b. 1900). 1982 - Day of death of Ludwig Georg Elias Moses Bieberbach, German mathematician (b. 1886). 2008 - Day of death of Oded Schramm, Israeli-American mathematician (b. 1961).

September, 2 1636 - Euler wrote to Mersenne that "a number is a sum of three integral squares if and only if it is a sum of three rational squares" [104].

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1694 - Johann Bernoulli, in a letter to Leibniz, described a function as: "... a quantity somehow formed from indeterminate and constant quantities." 1756 - Lagrange was elected to the Berlin Academy on the recommendation of Euler. 1764 - Day of death of Nathaniel Bliss, English astronomer and mathematician (b. 1700). 1768 - Day of death of Antoine Deparcieux, French mathematician (b. 1703). 1808 - Gauss wrote to Wolfgang Bolyai: "It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment." 1841 - Birthdate of Paul Matthieu Hermann Laurent, French mathematician (d. 1908). 1850 - Birthdate of Alfred Pringsheim, German mathematician (d. 1941). 1854 - Day of death of Pierre Laurent, French mathematician (b. 1813). 1856 - Birthdate of Friedrich Wilhelm Franz Meyer (d. 1934). 1865 - Day of death of William Rowan Hamilton, Irish physicist, astronomer, and mathematician (b. 1805). 1878 - Birthdate of René-Maurice Fréchet, French mathematician (d. 1973). 1892 - Birthdate of Frank Wilcoxon, American mathematician (d. 1965). 1909 - Birthdate of Deane Montgomery, American mathematician (d. 1992). 1913 - Birthdate of Israel Gelfand, Soviet-American mathematician, and biologist (d. 2009). 1923 - Birthdate of René Thom, French mathematician, and biologist (d. 2002).

September, 3 1704 - Birthdate of Joseph de Jussieu, French explorer, geographer, and mathematician (d. 1779). 1805 - Gauss, in a letter to Olbers, mentioned his correspondent "Le Blanc" (S. Germain) with great appreciation [15]. 1814 - Birthdate of James Joseph Sylvester, English mathematician (d. 1897). 1874 - Birthdate of Fredrik Carl Mülertz Størmer, Norwegian geophysicist and mathematician (d. 1957). 1884 - Birthdate of Solomon Lefschetz, American mathematician (d. 1972).

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1908 - Birthdate of Lev Pontryagin, Soviet mathematician (d. 1988). 1945 - Birthdate of Peter Goddard, English physicist, and mathematician. 1967 - Day of death of William P. Milne, Scottish mathematician (b. 1881). 1970 - Birthdate of Stanislav Konstantinovich Smirnov, Russian-Swiss mathematician.

September, 4 1675 - John Collins, in a letter to James Gregory, wrote: "… there being present with [Tschirnhaus] a Dane named George Moorh [Georg Mohr] who lately published in low Dutch two little Books, the one named Euclides Danicus where he pretends to perform all Euclid’s problems with a pair of Compasses only without a Ruler, and another entitled Euclides Curiosus, wherein with a Ruler and a fork (or the Compasses at one opening) he performs the same…" 1740 - Philip Naude the younger (1684-1747) wrote Euler from Berlin to ask "how many ways can the number 50 be written as a sum of seven different positive integers?" (Euler gave his first answer on April 6, 1741, in a paper he read at the weekly meeting of the St. Petersburg Academy.) [150] 1751 - Euler had discussed the problem of decomposing regular polygons into triangles in a letter to Goldbach. 1848 - Birthdate of Heinrich Bruns, German astronomer, mathematician, and geodesist (d. 1919). 1751 - Euler wrote a letter to Goldbach, which among other things included his discovery of Catalan numbers [130]. 1893 - Felix Klein said, "The proof of the transcendence of ʌ will hardly diminish the number of circle-squarers; however, this class of people has always shown an absolute distrust of mathematicians and a contempt for mathematics that cannot be overcome by any amount of demonstration." [92] 1940 - The British government tasked A. Turing with breaking the German Enigma code. 1963 - India issued a stamp honoring Dadabhai Naoroji (1825–1917), mathematician, and statesman.

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1969 - Day of death of Marcel Riesz, Hungarian mathematician (b. 1886). 1984 - Day of death of Ernst Carl Gerlach Stueckelberg, Swiss mathematician, and physicist (b. 1905).

September, 5 973 - Birthdate of Al-Biruni, an Iranian scholar, and polymath (d. 1048). 1575 - Day of death of Federico Commandino, an Italian humanist and mathematician (b. 1509). 1667 - Birthdate of Giovanni Girolamo Saccheri, an Italian priest, mathematician, and philosopher (d. 1733). 1725 - Birthdate of Jean-Etienne Montucla, a French mathematician (d. 1799). 1857 - Day of death of Isidore Auguste Marie Francois Xavier Comte, a French philosopher, and mathematician (b. 1798). 1896 - Birthdate of Ivo Lah, a Slovenian mathematician and actuary (d. 1979). 1914 - Birthdate of Nicanor Parra, a Chilean physicist, mathematician, and poet (d. 2018). 1927 - Birthdate of William Moser, a Canadian mathematician (d. 2009). 1930 - The conference at Konigsberg started on September 5-7, 1930, where Gödel announced his revolutionary result [110]. 1935 - The Moscow Mathematical Society held a commemorative meeting to honor the memory of Emmy Noether [38]. 1945 - Romania issued two postage stamps to commemorate the 50th anniversary of the mathematics journal Gazeta Mathematica.

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1972 - Day of death of Tadeusz WaĪewski, Polish mathematician (b. 1896). 1994 - Day of death of Shimshon Amitsur, Israeli mathematician (b. 1921). 2014 - Day of death of Mara Neusel, German mathematician (b. 1964).

September, 6 1635 - Day of death of Metius, Dutch mathematician, and astronomer (b. 1571). 1859 - Birthdate of Boris Bukreev, Ukrainian Soviet mathematician (d. 1962). 1863 - Birthdate of Dmitry Aleksandrovich Grave, Russian and Soviet mathematician (d. 1939). 1906 - Birthdate of Banesh Hoffmann, British physicist, and mathematician (d. 1986). 1929 - Birthdate of Ljubov Rebane, Soviet physicist, and mathematician (d. 1991). 1930 - Kurt Gödel presented his Completeness Theorem at the annual meeting of the Deutsche Mathematiker-Vereinigung in Königsberg. Gödel proved this theorem for his doctoral dissertation under the direction of Hans Hahn in 1929. He would prove his Incompleteness Theorem one year later. 1940 - Birthdate of Elwyn Ralph Berlekamp, American mathematician (d. 2019). 1956 - Day of death of Witold Hurewicz, Polish mathematician (b. 1904). 1967 - Day of death of Albert Edward Ingham, English mathematician (b. 1900). 1977 - Day of death of John Edensor Littlewood, English mathematician (b. 1885). 1983 - A stamp was issued in the USSR commemorating the 1,200th anniversary (approximate) of Al-Khwarizmi's birth.

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2019 - Andrew Booker, from Bristol University and Andrew Sutherland, a mathematician at the Massachusetts Institute of Technology, found a sum of three cubes for 42 = (-80538738812075974)3 + 804357581458175153 + 126021232973356313. This leaves 114 as the lowest unsolved case.

September, 7 1460 - Founding of the University of Basel. 1707 - Birthdate of Georges-Louis Leclerc, Comte de Buffon, French mathematician, and cosmologist (d. 1788). 1819 - Birthdate of Jean Claude Bouquet, French mathematician (d. 1885). 1844 - In a letter to George Boole, Arthur Cayley indicated that he is "much interested" in a paper on quaternions by William Rowan Hamilton: "the remarkable part of which is evidently that the factors of the product are not commutable [commutative], but as he observes, why should they be?" [108]. 1884 - Birthdate of Georges Jean Marie Valiron, French mathematician (d. 1955). 1903 - Birthdate of Dudley Ernest Littlewood, British mathematician (d. 1979). 1915 - Birthdate of Kiyosi Ito, Japanese mathematician (d. 2008). 1918 - Day of death of Peter Ludwig Mejdell Sylow, Norwegian mathematician (b. 1832). 1923 - The AMS adopted a resolution "sanctioning the establishment of a lectureship to be known as the Josiah Willard Gibbs Lectureship, the lecture to deal in a semi-popular form with some aspect of mathematics or its applications." 1927 - The first Polish Mathematical Congress opened in Lwow. 1930 - Kurt Gödel announced his famous Incompleteness Theorem – that there are true but unprovable statements in arithmetic – in a discussion on the foundations of mathematics organized by the Vienna Circle (to be published in 1931). 1936 - Day of death of Marcel Grossmann, Swiss mathematician (b. 1878). 1947 - Day of death of Michele Cipolla, Italian mathematician (b. 1880). 1948 - Birthdate of Cheryl Elisabeth Praeger, Australian mathematician. 1951 - Day of death of Harry Schmidt, German mathematician (b. 1894). 1955 - Birthdate of Efim Isaakovich Zelmanov, Soviet-American mathematician.

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1956 - Day of death of Otto Schmidt, Soviet scientist, mathematician, astronomer, geophysicist, statesman, academician (b. 1894). 1985 - Day of death of George Polya, Hungarian mathematician (b. 1887).

September, 8 1584 - Birthdate of Gregoire de Saint-Vincent, Flemish Jesuit, and mathematician (d. 1667). 1588 - Birthdate of Marin Mersenne, French mathematician, philosopher, and theologian (d. 1648). 1637 - Day of death of Robert Fludd, English physician, mathematician, and cosmologist (b. 1574). 1648 - Birthdate of Caspar (or Kaspar) Neumann, German professor, and clergyman (d. 1715). 1679 - Leibniz, in a letter to Huygens, explains his main ideas on analysis [36]. 1682 - Day of death of Juan Caramuel y Lobkowitz, Spanish mathematician, and philosopher (b. 1606). 1761 - Day of death of Bernard Forest de Belidor, French mathematician, and engineer (b. 1698). 1844 - The term "Abelian integral" seems to have first occurred in a letter from William Henry Fox Talbot to John Frederick William Herschel: “What is the definition of an Abelian Integral? For it appears to me that most integrals possess the Abelian property." 1861 - Birthdate of Percy John Heawood, British mathematician (d. 1955). 1882 - Day of death of Joseph Liouville, French mathematician (b. 1809). 1894 - Day of death of Hermann Ludwig Ferdinand von Helmholtz, German physiologist, physicist, mathematician, and meteorologist (b. 1821). 1927 - Birthdate of Marguerite Frank, American-French mathematician. 1938 - Day of death of Norman Levinson, American mathematician (b. 1867). 1963 - Day of death of Robert Smith, Scottish mathematician (b. 1876). 1969 - Day of death of Gordon Thomas Whyburn, American mathematician (d. 1904).

September, 9 1713 - The St. Petersburg paradox (or St. Petersburg lottery) was invented by Nicolas Bernoulli, who first stated it in a letter to Pierre Raymond de Montmort. (The paradox takes its name from its resolution by

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Daniel Bernoulli, a one-time resident of the eponymous Russian city, who published his arguments in the Commentaries of the Imperial Academy of Science of Saint Petersburg [12]). 1741 - In a letter to Mersenne, Euler studied the prime divisors of x2 + y2, x2 - 2y2, and x2 - 3y2 [104]. 1751 - The proof of Euler's formula "Vertices + Faces - 2 = Edges" was read to the Berlin Academy. 1860 - Birthdate of Frank Morley, British mathematician (d. 1937). 1883 - Day of death of Victor Alexandre Puiseux, French mathematician and astronomer (b. 1820). 1885 - Day of death of Jean Claude Bouquet, French mathematician (b. 1819). 1913 - Einstein gave a lecture in Frauenfeld titled "Physical Foundations of a Theory of Gravitation." In this lecture, Einstein could not yet deal with the fact that his gravitational field equations were not covariant with respect to arbitrary transformations but only covariant with respect to linear transformations [179]. 1914 - Birthdate of Marjorie Lee Browne, American mathematician (d. 1979). 1920 - Birthdate of Feng Kang, Chinese mathematician and physicist (d. 1993). 1967 - The Soviet Union issued a postage stamp showing checker players with part of a board in the background.

1973 - Day of death of Giovanni Ricci, Italian mathematician (b. 1904).

September, 10 1542 - In an apocryphal letter to Rabelais, Charles V of Spain offered 1000 escudos for the solution of the quadrature of the circle problem. 1635 - Day of death of Johann Faulhaber, German mathematician (b. 1580). 1749 - Day of death of Emilie du Chatelet, French mathematician, and physicist (b. 1706).

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1751 - Believing that he had been unfairly treated by Euler in the Berlin Academy Prize competition of 1750, d'Alembert broke off his correspondence with Euler in an angry letter. 1838 - C.G.J. Jacobi wrote to his brother Moritz Hermann Jacobi (18011874), a renowned physicist in St. Petersburg, with unreserved admiration: "Applying Fourier series to number theory, Dirichlet has recently found results touching the utmost of human acumen" [43]. 1839 - Birthdate of Charles Sanders Peirce, American mathematician, statistician, and philosopher (d. 1914). 1861 - Birthdate of Theodor Molien, Baltic-German mathematician (d. 1941). 1885 - Galton introduced regression [118]. 1890 - Day of death of Felice Casorati, Italian mathematician (b. 1835). 1903 - Birthdate of Georges de Rham, Swiss mathematician (d. 1990). 1915 - Day of death of John Howard Van Amringe, American educator, and mathematician (b. 1835). 1930 - Birthdate of Anatoliy Volodymyrovych Skorokhod, SovietUkrainian mathematician (d. 2011). 1931 - Day of death of Dmitri Egorov, Russian mathematician (b. 1869). 1931 - Ernst Eduard Kummer (1810-1893) solved a prize problem dealing with the expanding sin(nx) in powers of sin x and cos x, which was posed by his professor Heinrich Ferdinand Scherk, and consequently was awarded his Ph.D. degree at age 21 from the University of Halle. 1948 - Day of death of Walther Mayer, Austrian mathematician (b. 1887). 1966 - Day of death of Emil Julius Gumbel, German mathematician, and statistician (b. 1891). 2005 - Day of death of Hermann Bondi, Austrian mathematician, and cosmologist (b. 1919). 2008 - Large Hadron Collider particle accelerator switched on at CERN near Geneva, Switzerland. 2009 - UK apologizes to Turing. Alan Turing committed suicide in 1954 because he was persecuted by the British Government for his homosexuality. The Government feared he might be a security risk as many (almost all) of his actions on behalf of the war effort at Bletchley Park were still classified. On September 10, 2009, following an Internet campaign, British Prime Minister Gordon Brown made an official public apology on behalf of the British government for the way in which Turing was treated after the war. 2014 - Day of death of Edward Nelson, American mathematician (b. 1932).

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September, 11 1798 - Birthdate of Franz Ernst Neumann, German mineralogist, physicist, and mathematician (d. 1895). 1822 - It was announced by the College of Cardinals that henceforth "the printing and publication of works treating the motion of the earth and the stability of the sun, in accordance with the opinion of modern astronomers, is permitted." 1831 - Carl Jacobi was appointed a professor at the University of Königsberg. 1843 - Day of death of Joseph Nicollet, French mathematician, and explorer (b. 1786). 1877 - Birthdate of James Hopwood Jeans, English physicist, astronomer, and mathematician (d. 1946). 1890 - Birthdate of Euphemia Lofton Haynes, American mathematician (d. 1980). 1890 - Day of death of Felice Casorati, Italian mathematician (b. 1835). 1917 - Birthdate of Kenkichi Iwasawa, Japanese mathematician (d. 1998). 1923 - Sixteen-year-old Donald Coxeter wrote to Eric H. Neville (who had worked with Ramanujan) at the request of Literary scholar and suffragette, Edith Morley. “I am going to buy your book on the Fourth Dimension as I am awfully keen on that sort of thing. I am writing a book on 'Dimensional Analogy' of which I enclose an outline." Neville met with Coxeter, and after a brief interview, advised that, “You must leave school at once! They're not teaching you right!" He had him tutored by Alan Robson, a Master at Marlborough College near Stonehenge. [144]. 1940 - The first remote computation – from Dartmouth College to AT&T Bell Laboratories – was demonstrated during a meeting of the American Mathematical Association. 1943 - Day of death of Oswald Teichmuller, German mathematician (b. 1913). 1951 - Birthdate of Richard D. Gill, English-Dutch mathematician. 1972 - Day of death of Johannes de Groot, Dutch mathematician (b. 1914). 2002 - Day of death of Howard Levi, American mathematician (b. 1916). 2011 - Day of death of Daniel M. Lewin, American mathematician and businessman, co-founder of Akamai Technologies (b. 1970). 2012 - Day of death of Irving Stoy Reed, American mathematician and engineer (b. 1923). 2013 - Day of death of Andrzej Trybulec, Polish mathematician, and computer scientist (b. 1941).

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September, 12 1771 - Birthdate of Antoine-Andre-Louis Reynaud, French mathematician (d. 1844). 1876 - Johns Hopkins University, the first true graduate school in the USA, formally opened its doors with an address – and without the benefit of a prayer – by the evolutionist T. H. Huxley. A Presbyterian minister wrote, “It is bad enough to invite Huxley. It were better to have asked God to be present. It would have been absurd to ask them both." 1877 - Birthdate of Georg Karl Wilhelm Hamel, German mathematician (d. 1954). 1883 - Sylvester writes to Johns Hopkins President Gilman of his intent to resign his chair effective January 1 of the following year. 1894 - Birthdate of Dorothy Maud Wrinch, Argentinian-English mathematician, biochemist, and philosopher (d. 1976). 1900 - Birthdate of Haskell Curry, American mathematician (d. 1982). 1906 - Day of death of Ernesto Cesaro, Italian mathematician (b. 1859). 1918 - Day of death of Maxime Bochner, American mathematician (b. 1867). 1921 - Birthdate of Pierre Samuel, French mathematician (d. 2009). 1933 - Day of death of Leonard James Rogers, British mathematician (b. 1862). 1935 - Institute of Mathematical Statistics founded in Ann Arbor, Michigan. 1983 - Day of death of Roman Sikorski, Polish mathematician (b. 1920). 2005 - Day of death of Serge Lang, French-American mathematician (b. 1927).

September, 13 1296 - Day of death of Johannes Campanus (of Novara), Italian mathematician (b. 1220). 1724 - In a letter to D. Bernoulli, Goldbach mentioned that J. Ozanam proved the difference of two fourth powers could not be a square (equivalent to Fermat's Last Theorem for n = 4) [20]. 1826 - Gauss wrote in his very first letter to Dirichlet about his plan to write three memoirs on biquadratic residues [43]. 1840 - Soon after starting her math lessons with De Morgan, Ada Lovelace wrote: “I could wish I went on quicker. That is, I wish a human head, or my head at all events, could take in a great deal more

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& a great deal more rapidly than is the case; and if I had made my own head, I would have proportioned its wishes & ambition a little more to its capacity. … When I compare the very little I do, with the very much – the infinite I may say that there is to be done; I can only hope that hereafter in some future state, we shall be cleverer than we are now." [82] (see Sept. 15 entry for De Morgan's reply). 1873 - Birthdate of Constantin Caratheodory, Greek-German mathematician (d. 1950). 1883 - Opening of the University of Texas at Austin and Galveston. 1885 - Birthdate of Wilhelm Blaschke, Austrian-German mathematician (d. 1962). 1913 - Birthdate of Herman Heine Goldstine, American mathematician, computer scientist, and scientific administrator (d. 2004). 1920 - Birthdate of William Bowen Bonnor, British mathematician and gravitation physicist (d. 2015). 1923 - Birthdate of Peter Karl Henrici, Swiss mathematician (d. 1987). 1940 - Day of death of Myron Mathisson, Polish physicist, and mathematician (b. 1897). 2002 - Jason Padgett (born 1970) was attacked and robbed by two men outside a karaoke bar in Tacoma, Washington. Before the attack, Padgett was a college dropout who worked at a futon store. His primary passions in life were partying and chasing girls. He had no interest in maths – at school, he didn't even get into an algebra class. After the attack, he became a well-known professional mathematician [89].

September, 14 1638 - Day of death of Pierre Vernier, French mathematician (b. 1584). 1712 - Day of death of Giovanni Domenico Cassini, Italian-French mathematician, astronomer, and engineer (b. 1625). 1713 - Birthdate of Johann Kies, German astronomer and mathematician (d. 1781). 1837 - Birthdate of Nikolai Bugaev, Russian mathematician and philosopher (d. 1903). 1858 - Birthdate of Henry Burchard Fine, American mathematician (d. 1928). 1891 - Birthdate of Ivan Matveyevich Vinogradov, Soviet mathematician (d. 1983). 1906 - Birthdate of Franz Rellich, Austrian-Italian mathematician (d. 1955).

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1910 - Day of death of Jacob Loroth, German mathematician (b. 1844). 1912 - Day of death of Georg Landsberg, German mathematician (b. 1865). 1916 - Day of death of Pierre (-Maurice-Marie) Duhem, French physicist, mathematician, and philosopher of science (b. 1861). 1916 - Day of death of Jose Echegaray, Spanish engineer, mathematician, and playwright, Nobel Prize laureate (b. 1832). 1920 - Birthdate of Alberto Calderon, Argentinian-American mathematician (d. 1998). 1926 - Birthdate of Hans-Joachim Bremermann, German-American mathematician and biophysicist (d. 1996). 1932 - Day of death of Ernest Julius Wilczynski, American mathematician (b. 1876).

September, 15 973 - Birthdate of Abu Arrayhan Muhammad ibn Ahmad al-Biruni, Islamic mathematician (d. 1048). 1736 - Birthdate of Jean Sylvain Bailly, French astronomer, mathematician, and politician, 1st Mayor of Paris (d. 1793). 1739 - Euler wrote Johann Bernoulli about the general treatment of the homogeneous linear differential equation with constant coefficients. 1782 - Lagrange, in a letter to Laplace, told of finishing his Mecanique analytique. Legendre undertook the editing of the work for the press. 1840 - De Morgan replied to Lovelace's September 13 letter: "...never estimate progress by the number of pages. You can hardly be a judge of the progress you make, and I should say that it is more likely you progress rapidly upon a point that makes you think for an hour than upon an hour's quick reading, even when you feel satisfied. That which you say about the comparison of what you do with what you see can be done was equally said by Newton when he compared himself to a boy who had picked up a few pebbles from the shore... so that you have respectable authority for supposing that you will never get rid of that feeling, and it is no use trying to catch the horizon" [82] (see September 13 entry for Lovelace's letter). 1846 - George Boole, age 30, applied for a professorship at "any of her Majesty's colleges, now in the course of being established in Ireland." Although he had "never studied at a college," he had been a teacher for 15 years and was "familiar with the elementary and the practical as well as the higher Mathematics." Although he was self-taught, the testimonies of DeMorgan, Cayley, and William Thomson showed that

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he was an accomplished mathematician. In August 1849, he was appointed the first professor of mathematics at Queen's College Cork [108]. 1855 - Sylvester began his duties as a professor of mathematics and lecturer in natural philosophy at the Royal Military Academy, Woolwich, England. 1883 - Birthdate of Esteban Terradas i Illa, Spanish mathematician, and engineer (d. 1950). 1886 - Birthdate of Paul Levy, French mathematician (d. 1971). 1901 - Birthdate of Luigi Fantappie, Italian mathematician (d. 1956). 1923 - Birthdate of Georg Kreisel, Austrian-born mathematical logician (d. 2015). 1926 - Birthdate of Jean-Pierre Serre, French mathematician. 1938 - Birthdate of Rudolf F. Ahlswede, German mathematician (d. 2010). 1947 - Association for Computing Machinery (ACM) founded in New York City, USA. 2003 - Day of death of Alexander Ivanovich Skopin, Soviet mathematician (b. 1927). 2008 - GIMPS announced two largest-known primes up to that time: 243,112,609 - 1 and 237,156,667 - 1.

September, 16 1494 - Birthdate of Francisco Maurolico, Italian Benedictine, and mathematician (d. 1575). 1636 - Fermat wrote to Roberval that "If a and b are rational, and if a2 + b2 = 2(a + b)x + x2, then x and x2 are irrational" [104]. 1666 - Birthdate of Antoine Parent, French mathematician (d. 1716). 1848 - Weierstrass became a mathematics teacher at the Catholic Gymnasium (high school) in Braunsberg, Germany, his third such position. That year he taught mathematics for 19 hours per week, took over the geography class after Easter, and received a special note of thanks for helping out in the gym! 1895 - Pearson writes to Yule: "I had a most kindly and encouraging letter from Francis Galton about my Heredity paper. He really is a fine old fellow to take my modification of his views so well" [162]. 1925 - Day of death of Alexander Friedmann, Russian physicist, and mathematician (b. 1888). 1931 - Day of death of Niels Nielsen, Danish mathematician (b. 1865). 1932 - Day of death of Ronald Ross, Indian-English physician and mathematician, Nobel Prize laureate (b. 1857).

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1946 - Day of death of James Hopwood Jeans, English physicist, astronomer, and mathematician (b. 1877). 1979 - Day of death of Marion Gray, British mathematician (b. 1902). 1989 - Day of death of Allen Lowell Shields, American mathematician (b. 1927).

September, 17 1743 - Birthdate of Marquis de Condorcet, French mathematician, and political scientist (d. 1794). 1826 - Birthdate of Bernhard Riemann, German-Italian mathematician (d. 1866). 1877 - Day of death of William Henry Fox Talbot, English inventor, mathematician, chemist, physicist, philologist, and Egyptologist (b. 1800). 1891 - Day of death of Jozef Maximilian Petzval, Hungarian mathematician (b. 1807). 1905 - Birthdate of Hans Freudenthal, Dutch mathematician (d. 1990). 1931 - L. Scnirelman presents his results concerning the Goldbach conjecture to the Deutsche Mathematiker-Vereinigung, showing that every number can be expressed as a sum of fewer than twenty primes. 1937 - Birthdate of Moshe Flato, Israeli-French mathematician, and theoretical physicist (d. 1998). 1944 - Birthdate of Jean Taylor, American mathematician. 1999 - Day of death of Leonard Carlitz, American mathematician (b. 1907).

September, 18 1752 - Birth of Adrien-Marie Legendre, French mathematician (d. 1833). 1783 - Day of death of Leonhard Euler, Swiss-Russian mathematician and physicist (b. 1707). 1863 - Birth of William Henry Metzler, Canadian mathematician (d. 1943). 1913 - Day of death of Samuel Roberts, British mathematician (b. 1827). 1925 - Birth of Victor L. Klee, Jr., American mathematician (d. 2007). 1926 - Birth of James William Cooley, American mathematician (d. 2016). 1939 - Birth of Jan Camiel Willems, Belgian mathematician (d. 2013). 1948 - Alan Turing writes to Jack Good and mentions a chess machine “designed by Champ and myself”.

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1977 - Day of death of Paul Bernays, English-Swiss mathematician and philosopher (b. 1888).

September, 19 1648 - Blaise Pascal performed experiments to confirm the theory of atmospheric pressure and the existence of a vacuum. 1749 - Birthdate of Jean Baptiste Joseph Delambre, French mathematician, and astronomer (d. 1822). 1761 - Day of death of Pieter van Musschenbroek, Dutch mathematician, and physicist (b. 1692). 1811 - Birthdate of Orson Pratt, American mathematician, and religious leader (d. 1881). 1840 - Day of death of John Emory McClintock, American mathematician (d. 1916). 1843 - Day of death of Gaspard-Gustave de Coriolis, French mathematician, physicist, and engineer (b. 1792). 1888 - Birthdate of James Waddell Alexander II, American mathematician (d. 1971). 1894 - Peano wrote to Klein, “The purpose of mathematical logic is to analyze the ideas and reasoning that especially figure in the mathematical sciences." 1950 - Birthdate of Michael Proctor, English physicist, mathematician. 1994 - Andrew Wiles realized that the specific reason why the Flach approach would not work directly suggested a new approach with the Iwasawa theory which resolved all of the previous issues with the latter and resulted in a CNF that was valid for all of the required cases. This was a simplification of his proof of Fermat's Last Theorem. 2010 - Day of death of Joseph Bernard Kruskal, Jr., American mathematician, statistician, computer scientist, and psychometrician (b. 1928). 2019 - Item number MR4000000 was added to MathSciNet.

September, 20 1623 - Schickard wrote to Kepler about his new calculating machine: “What you have done by calculation I have just tried to do by way of mechanics. I have conceived a machine consisting of eleven complete and six incomplete sprocket wheels; it calculates instantaneously and automatically from given numbers, as it adds, subtracts, multiplies, and divides. You would enjoy seeing how the machine accumulates and

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transports spontaneously a ten or a hundred to the left and, vice-versa, how it does the opposite if it is subtracting… " 1882 - Day of death of Charles Auguste Briot, French mathematician (b. 1817). 1842 - Birthdate of Alexander Wilhelm von Brill, German mathematician (d. 1935). 1861 - Birthdate of Frank Nelson Cole, American mathematician (d. 1926). 1887 - Birthdate of Erich Hecke, German mathematician (d. 1947). 1906 - Birthdate of Vera Faddeeva, Soviet mathematician (d. 1983). 1910 - Birthdate of Dorothy Vaughan, American mathematician, and computer programmer (d. 2008). 1930 - Birthdate of Richard Montague, American mathematician, and philosopher (d. 1971). 1930 - Birthdate of Moritz Pasch, German mathematician (b. 1843). 1948 - John von Neumann gave his first lecture on the theory of automata. 1956 - Birthdate of Jennifer Tour Chayes, American mathematician, and computer scientist. 1996 - Day of death of Paul Erdos, Hungarian-Polish mathematician (b. 1913).

September, 21 1576 - Day of death of Gerolamo Cardano, an Italian mathematician, physician, and astrologer (b. 1501). 1623 - Birthdate of Stephano Angeli, an Italian mathematician (d. 1697). 1781 - Lagrange wrote to d'Alembert expressing concern that mathematics was reaching its creative end. "It appears to me also that the mine [of mathematics] is already very deep and that unless one discovers new veins it will be necessary sooner or later to abandon it." 1842 - Day of death of Sir James Ivory, a Scottish mathematician (b. 1765). 1884 - Birthdate of Denes Konig, a Hungarian mathematician (d. 1944). 1895 - Birthdate of Joseph Leonard Walsh, an American mathematician (d. 1973). 1899 - Birthdate of Juliusz Pawel Schauder, a Polish mathematician (d. 1943). 1908 - In the 80th annual general meeting of the German Society of Scientists and Physicians in Cologne, Minkowski presented his famous talk, "Raum und Zeit" ("Space and Time"). 1917 - Birthdate of Phyllis Nicolson, an English mathematician (d. 1968).

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1968 - Birthdate of Kevin Buzzard, a British mathematician. 1981 - Day of death of Henry George Forder, a New Zealander mathematician (b. 1889). 1984 - Science reported (pp. 1379-1380) that Narendra Karmarkar of AT&T Bell Labs found a practical polynomial-time algorithm that is far faster than the simplex algorithm for linear programming problems.

September, 22 1547 - Birthdate of Philipp Nicodemus Frischlin, a German philologist, mathematician, astronomer, and poet (d. 1590). 1703 - Day of death of Vincenzo Viviani, an Italian mathematician and physicist (b. 1622). 1711 - Birthdate of Thomas Wright, an English astronomer, mathematician, instrument maker, architect, and garden designer (d. 1786). 1765 - Birthdate of Paolo Runi, an Italian mathematician and philosopher (d. 1822). 1837 - Day of death of William George Horner, a British mathematician and schoolmaster (b. 1786). 1970 - Day of death of VojtČch Jarník, a Czech mathematician (b. 1897). 1979 - Day of death of Charles Ehresmann, a French mathematician (b. 1905). 2000 - Day of death of Alexei I. Kostrikin, a Soviet-Russian mathematician (b. 1929). 2009 - Day of death of Gerard Laman, a Dutch mathematician (b. 1924). 2012 - Day of death of Irving Adler, an American mathematician (b. 1913).

September, 23 1647 - Descartes met with Pascal on September 23rd or 24th when Descartes visited France from Holland. On this occasion, Descartes may have recommended to Pascal the experiment of noting the variation of the heights of the barometer with altitude. 1657 - Day of death of Joachim Jungius, a German mathematician, logician, and philosopher of sciences (b. 1587). 1768 - Birthdate of William Wallace, a Scottish mathematician (d. 1843). 1851 - Birthdate of Ellen Hayes, an American mathematician and astronomer (d. 1930).

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1877 - Day of death of Urbain Le Verrier, a French mathematician and astronomer (b. 1811). 1884 - Patent filed for the Hollerith tabulating machine. 1900 - Birthdate of David van Dantzig, a Dutch mathematician (d. 1959). 1902 - Birthdate of Su Buqing, a Chinese mathematician (d. 2003). 1919 - Day of death of Heinrich Bruns, a German astronomer, mathematician, and geodesist (b. 1848). 1968 - Birthdate of Wendelin Werner, a German-born French mathematician. 1971 - Day of death of James Waddell Alexander II, an American mathematician (b. 1888). 1983 - The Los Angeles Times reported that David Slowinski of Cray Research had found the 29th Mersenne prime, 2132,049 - 1. It turned out that this was actually the 30th, as the 29th would turn out to be 2110,503 1 found by Walter Colquitt and Luke Welsh almost five years later on January 28, 1988.

September, 24 1054 - Day of death of Hermann of Reichenau, a German composer, mathematician, and astronomer (b. 1013). 1501 - Birthdate of Gerolamo Cardano, an Italian mathematician, physician, and astrologer (d. 1576). 1625 - Birthdate of Johan de Witt, a Dutch mathematician and politician (d. 1672). 1651 - Day of death of Etienne Pascal, a French mathematician (b. 1588). 1742 - Day of death of Johann Matthias Hase, a German mathematician, astronomer, and cartographer (b. 1684). 1801 - Birthdate of Mikhail Ostrogradsky, a Ukrainian-Russian mathematician and physicist (d. 1862). 1844 - Birthdate of Max Noether, a German mathematician (d. 1921). 1861 - Birthdate of Karl Emmanuel Robert Fricke, a German mathematician (d. 1930). 1894 - Birthdate of Werner Wolfgang Rogosinski, a German-British mathematician (d. 1964). 1896 - Birthdate of Tadeusz Wazewski, a Polish mathematician (d. 1972). 1904 - Birthdate of Evan Tom Davies, a British mathematician (d. 1973). 1923 - Birthdate of Raoul Bott, a Hungarian-American mathematician (d. 2005). 1930 - Birthdate of Anatoliy Volodymyrovych Skorokhod, a SovietUkrainian mathematician (d. 2011).

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1938 - Day of death of Lev Schnirelmann, a Soviet mathematician (b. 1905). 1945 - Birthdate of Ian Nicholas Stewart, a British mathematician and a popular-science and science-fiction writer. 1967 - Day of death of Pauline Sperry, an American mathematician (b. 1885). 1999 - Day of death of Anneli Cahn Lax, an American mathematician (b. 1922).

September, 25 1654 - Fermat wrote to Pascal to defend a combinatorial method that Pascal had previously regarded as incorrect. 1777 - Day of death of Johann Heinrich Lambert, a Swiss mathematician, physicist, and astronomer (b. 1728). 1819 - Birthdate of George Salmon, an Irish mathematician (d. 1904). 1825 - Birthdate of Carl Harald Cramer, a Swedish mathematical statistician (d. 1985). 1852 - Day of death of Christoph Gudermann, a German mathematician (b. 1798). 1888 - Birthdate of Stefan Mazurkiewicz, a Polish mathematician (d. 1945). 1893 - Birthdate of Harald Cramer, a Swedish mathematician and statistician (d. 1985). 1931 - Birthdate of Bryan John Birch, an English mathematician. 1933 - Day of death of Paul Ehrenfest, an Austrian and Dutch physicist and mathematician (b. 1880). 1944 - Denmark issued a stamp commemorating the 300th anniversary of the birth of Ole Roemer.

1949 - Birthdate of Volodymyr Sharko, Ukrainian mathematician (d. 2014). 1955 - Day of death of Franz Rellich, Austrian-Italian mathematician (b. 1906).

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September, 26 1688 - Birthdate of Willem Gravesande, a Dutch mathematician (d. 1742). 1716 - Day of death of Antoine Parent, a French mathematician (b. 1666). 1731 - Birthdate of Gianfrancesco Malfatti, an Italian mathematician (b. 1807). 1732 - Euler shows that F5, the fifth Fermat "prime," is, in fact, not prime, but divisible by 1641. 1766 - Day of death of Giulio Carlo Fagnano dei Toschi, an Italian mathematician (b. 1682). 1802 - Day of death of Jurij Vega, a Slovene mathematician and physicist (b. 1754). 1854 - Birthdate of Percy Alexander MacMahon, a British mathematician (d. 1929). 1868 - Day of death of August Ferdinand Möbius, a German mathematician and astronomer (b. 1790). 1877 - Day of death of Hermann Grassmann, a German mathematician and physicist (b. 1809). 1904 - The German mathematician Ernst Zermelo, a student of Max Planck in statistical physics, wrote a letter to David Hilbert telling him that he had solved the problem of the Continuum. His proof made use of what would soon become well known to mathematicians as the "Axiom of Choice": "For any family of non-empty sets, there exists a correspondence that associates to each of these sets one of its elements." [58] 1905 - Albert Einstein published his annus mirabilis paper on what is now called special relativity. 1910 - Day of death of Thorvald Nicolai Thiele, a Danish astronomer, actuary, and mathematician (b. 1838). 1926 - Birthdate of Colin Brian Haselgrove, an English mathematician (d. 1964). 1927 - Birthdate of Brian Griffiths, an English mathematician (d. 2008). 1976 - Day of death of Paul Turan, a Hungarian mathematician (b. 1910). 1990 - Day of death of Lothar Collatz, a German mathematician (b. 1910).

September, 27 1677 - Birthdate of Johann Doppelmayr, a German mathematician (d. 1750). 1719 - Birthdate of Abraham Gotthelf Kastner, a German mathematician and epigrammatist (d. 1800).

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1783 - Day of death of Etienne Bezout, a French mathematician (b. 1730). 1814 - Birthdate of Daniel Kirkwood, an American mathematician and astronomer (d. 1895). 1843 - Birthdate of Gaston Tarry, a French mathematician (d. 1913). 1855 - Birthdate of Paul Emile Appell, a French mathematician (d. 1930). 1876 - Birthdate of Earle Raymond Hedrick, an American mathematician (d. 1943). 1879 - Birthdate of Hans Hahn, an Austrian mathematician and philosopher (d. 1934). 1892 - Birthdate of Mykhailo Pilipovich Krawtchouk, a Ukrainian Soviet mathematician (d. 1942). 1894 - F. Klein, in his address in Vienna whose theme was "Riemann and his importance for the development of modern mathematics," noticed: "Riemann was one of these out-of-the-way scholars who let their profound thoughts ripen silently in their mind." 1889 - Birthdate of Henry George Forder, a New-Zealandian mathematician (d. 1981). 1919 - Birthdate of James H. Wilkinson, an American mathematician and computer scientist (d. 1986). 1972 - Day of death of S. R. Ranganathan, an Indian mathematician and librarian (b. 1892). 1997 - Day of death of William Leonard Edge, a British mathematician (b. 1904). 2014 - Day of death of Jacqueline Anne Stedall, a British historian of mathematics (b. 1950).

September, 28 1605 - Birthdate of Ismael Bullialdus, a French astronomer, and mathematician (d. 1694). 1664 - Leibniz was awarded his bachelor's degree in Law. 1694 - Day of death of Gabriel Mouton, a French mathematician, and theologian (b. 1618). 1698 - Birthdate of Pierre-Louis Moreau de Maupertuis, a French mathematician, biologist, and astronomer (d. 1759). 1743 - Goldbach, with considerable help from Euler, gave a new proof of Euler's result that primes p = 4n + 3 do not divide numbers of the form a2 + 1. [104] 1761 - Birthdate of Francois Budan de Boislaurent, a Haitian-born amateur mathematician (d. 1840).

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1824 - Birthdate of George Johnston Allman, an Irish mathematician and historian of ancient Greek mathematics (d. 1904). 1845 - Apelt, in a letter to Möbius, wrote that he believed Grassman's Ausdehnungslehre was based on a false philosophy of mathematics. 1869 - Day of death of Guglielmo Libri Carucci dalla Sommaja, an Italian count and mathematician (b. 1803). 1873 - Birthdate of Julian Lowell Coolidge, an American mathematician, and educator (d. 1954). 1881 - Birthdate of Edward Ross, a Scottish mathematician (d. 1947). 1901 - Birthdate of Kurt Otto Friedrichs, a German-American mathematician (d. 1982). 1917 - Richard Courant wrote to his future wife Nina Runge that he got the opportunity to talk to Ferdinand Springer about "a publishing project," and that things looked promising. This meeting led to a contract and a series of books now called the "Yellow Series." 1925 - Birthdate of Martin David Kruskal, an American physicist, and mathematician (d. 2006). 1939 - Day of death of Samuel Dickstein, a Polish mathematician (b. 1851). 1947 - Birthdate of Rhonda Hughes, an American mathematician. 1956 - Birthdate of Martha Isabel Fandino Pinilla, a Colombian-Italian mathematician. 1961 - Birthdate of Enrique Zuazua Iriondo, a Spanish mathematician. 1992 - Day of death of John Leech, a British mathematician (b. 1926). 2004 - Day of death of Jacobus Hendricus van Lint, a Dutch mathematician (b. 1932). 2009 - mathoverflow.net goes online.

September, 29 1561 - Birthdate of Adriaan van Roomen, Flemish priest, and mathematician (d. 1615). 1801 - Gauss's Disquisitiones Arithmeticae published.

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1803 - Birthdate of Jacques Charles Francois Sturm, a French mathematician (d. 1850). 1812 - Birthdate of Gustav Adolph Gopel, a German mathematician (d. 1847). 1895 - Birthdate of Harold Hotelling, an American mathematician (d. 1973). 1928 - Day of death of Ernst Steinitz, a German mathematician (b. 1871). 1935 - Birthdate of Hillel (Harry) Furstenberg, an American-Israeli mathematician. 1941 - Day of death of Friedrich Engel, a German mathematician (b. 1861). 1945 - Birthdate of Valentin Zaitsev, a Russian mathematician (d. 2018). 2003 - Day of death of Ovide Arino, a French mathematician (b. 1947).

September, 30 1550 - Birthdate of Michael Maestlin, a German astronomer, and mathematician (d. 1631). 1717 - Maclaurin, at the age of 19, was appointed to the Mathematics Chair at Marischal College, Aberdeen, Scotland. In 1725, he was made a Professor at Edinburgh University on the recommendation of Newton. 1775 - Birthdate of Robert Adrain, an American mathematician (d. 1843). 1810 - The University of Berlin opened. 1883 - Birthdate of Ernst David Hellinger, a Jewish German-American mathematician (d. 1950).

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1891 - Birthdate of Otto Schmidt, a Soviet scientist, mathematician, astronomer, geophysicist, statesman, and academician (d. 1956). 1894 - Birthdate of Dirk Jan Struik, a Dutch mathematician (d. 2000). 1910 - Day of death of Maurice Levy, a French mathematician, and engineer (b. 1838). 1913 - Birthdate of Samuel Eilenberg, a Polish-American mathematician (d. 1998). 1915 - Day of death of William Watson, an American mathematician (b. 1834). 1916 - Birthdate of Richard Kenneth Guy, a British mathematician (d. 2020). 1918 - Birthdate of Leslie Fox, a British mathematician (d. 1992). 1953 - Day of death of Lewis Fry Richardson, an English mathematician, physicist, meteorologist, psychologist, and pacifist (b. 1881). 2017 - Day of death of Vladimir Voevodsky, a Russian mathematician (b. 1966).

CHAPTER TEN OCTOBER

October, 1 1386 - The University of Heidelberg was founded. 1648 - In a letter to Samuel Hartlib, Sir Balthazar Gerbier sent a description of Pascal's mechanical calculator. 1658 – This day was the closing date for submitting solutions to Pascal's prize problems on the cycloid. A toothache earlier that year caused him to return to mathematics and to study the cycloid. 1670 - James Gregory wrote to John Collins, with the first use of what would come to be called the Newton-Gregory interpolation formula. [10] 1671 - Birthdate of Luigi Guido Grandi, an Italian monk, mathematician, and engineer (d. 1742). 1768 - Day of death of Robert Simson, a Scottish mathematician (b. 1687). 1814 - The terms "commutative" and "distributive" were used (in French) by Francois Joseph Servois in a memoir published in Annales de Gergonne (volume V, no. IV). [118] 1828 - Dirichlet began teaching at the Military School. [43] 1873 - Birthdate of Alfreds Arnolds Adolfs Meders, a Latvian mathematician (d. 1944). 1894 - Birthdate of Edgar Krahn, an Estonian mathematician (d. 1961). 1898 - Birthdate of Bela Kerekjarto, a Hungarian mathematician (d. 1946). 1910 - H. Muntz was awarded a doctorate, Dr. Phil., magna cum laude. His official reviewers were Schwarz and Schottky. His dissertation, under the title of "On boundary value problems of partial differential equations of minimal surfaces," was published in Crelle's journal. [129] 1911 - Birthdate of Zhou Weiliang, a Chinese mathematician (d. 1995). 1912 - Birthdate of Kathleen Ollerenshaw, an English mathematician, astronomer, and politician who became Lord Mayor of Manchester (d. 2014). 1921 - Birthdate of Roger Godement, a French mathematician (d. 2016).

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1924 - Day of death of John Edward Campbell, a British mathematician (b. 1862). 1934 - Paul Erdos stopped in Cambridge to visit mathematical friends, particularly Harrold Davenport and Richard Rado, on his way to a position in Manchester. 1940 - Day of death of Chiungtze C. Tsen, a Chinese mathematician (b. 1898). 1957 - Birthdate of Eva Tardos, a Hungarian mathematician and educator. 1972 - Day of death of Francisco Jose Duarte, a Venezuelan mathematician (b. 1883). 1994 - Day of death of Paul Lorenzen, a German mathematician and philosopher (b. 1915). 1996 - Day of death of Herbert Karl Johannes Seifert, a German mathematician (b. 1907).

October, 2 1568 - Birthdate of Marino Ghetaldi, a Croatian mathematician (d. 1626). 1667 - Newton became a fellow at Trinity College, Cambridge. 1759 - Birthdate of Jacob (II) (Jacques (II)) Bernoulli, a Swiss-Russian mathematician (d. 1789). 1759 - Euler to the young Lagrange: “Your solution of the isoperimetric problems leaves nothing to be desired, and I rejoice that this subject, with which I have been so completely occupied since my first efforts, has been carried by you to such a high degree of perfection. The importance of the subject has stimulated me to develop, aided by your lights, an analytical solution that I will keep secret as long as your own meditations are not published, lest I take away from you a part of the glory you deserve." [157] 1791 - Birthdate of Alexis Therese Petit, a French mathematician (d. 1820). 1825 - Birthdate of John James Walker, an English mathematician (d. 1900). 1853 - Day of death of François Arago, a French mathematician, physicist, astronomer, and politician, who also served as the 25th Prime Minister of France (b. 1786). 1908 - Birthdate of Arthur Erdélyi, a Hungarian-born Scottish mathematician (d. 1977). 1912 - Ernest Rutherford presents his theory of the structure of the Atom to a session of the Manchester Literary and Philosophical Society. He

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rejected Thompson's “Plum Pudding" model for an atom with most of its mass concentrated into a tiny charged core in its center. 1926 - Birthdate of Michio Suzuki, a Japanese mathematician (d. 1998). 1929 - Day of death of Andrei Mikhailovich Razmadze, a Georgian mathematician (b. 1889). 1947 - Day of death of P. D. Ouspensky, a Russian-English mathematician, and philosopher (b. 1878). 1962 - Day of death of Boris Yakovlevich Bukreev, a Ukrainian-Soviet mathematician (b. 1859). 1977 - Day of death of Beniamino Segre, an Italian mathematician (b. 1903). 1990 - Day of death of Ivan Petrovich Egorov, a Soviet mathematician (b. 1915). 2006 - Day of death of Paul Halmos, a Hungarian-American mathematician (b. 1916). 2013 - Day of death of Abraham Nemeth, an American mathematician (b. 1918).

October, 3 1533 - Michael Stifel predicted that on this date, a chariot would touch down on a nearby hilltop and conduct him and his followers to heaven. Followers of the mathematical mystic quit their jobs, but as the day approached, they became sceptical. Stifel convinced the local constabulary to lock him in jail on the appointed date where he would be safe from his ruined, irate parishioners. 1842 - Arthur Cayley admitted to a fellowship at Trinity College, Cambridge, at the age of 21. 1846 - Birthdate of Platon Sergeevich Poretsky, a Russian mathematician (d. 1907). 1863 - Birthdate of Stanislaw Zaremba, a Polish mathematician (d. 1942). 1881 - Day of death of Orson Pratt, an American mathematician, and religious leader (b. 1811). 1891 - Day of death of Edouard Lucas, a French mathematician (b. 1842). 1896 - Einstein graduates from high school in Switzerland at the age of 17. 1914 - Day of death of Rene Eugene Gateaux, a French mathematician (b. 1889). 1944 - Birthdate of Pierre Deligne, a Belgian mathematician. 2006 - Day of death of John Crank, an English mathematician, and physicist (b. 1916).

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October, 4 1479 - University of Copenhagen founded. 1759 - Birthdate of Louis Francois Antoine Arbogast, a French mathematician (d. 1803). 1873 - Birthdate of Gheorghe Titeica, a Romanian mathematician (d. 1939). 1876 - Birthdate of Florence Eliza Allen, an American mathematician and suffrage activist (d. 1960). 1885 - Day of death of Heinrich Ferdinand Scherk, a German mathematician (b. 1798). 1906 - Birthdate of Mary Celine Fasenmyer, an American mathematician (d. 1996). 1914 - The manifesto known as “Aufruf an die Kulturwelt!" defending German military actions in the occupied zones was signed by 93 people (Felix Klein was the only mathematician among them). [7] 1938 - Paul Erdos, escaping from the Nazis, arrives at the Institute for Advanced Study at Princeton. 1947 - Day of death of Max Planck, a German physicist (b. 1858). 1954 - Day of death of Georg Karl Wilhelm Hamel, a German mathematician (b. 1877). 1974 - Day of death of Robert Lee Moore, an American mathematician (b. 1882). 2000 - Mathematics Magazine publishes "A proof that the Halting Problem is undecidable" in poetic form (in the fashion of Dr. Seuss) by Geoffrey K. Pullum, who was then at Stevenson College, University of California, Santa Cruz. “Scooping the loop snooper, A proof that the Halting Problem is undecidable", by Geoffrey K. Pullum (School of Philosophy, Psychology and Language Sciences, University of Edinburgh) No general procedure for bug checks succeeds. Now, I won’t just assert that, I’ll show where it leads: I will prove that although you might work till you drop, you cannot tell if computation will stop. For imagine we have a procedure called P that for specified input permits you to see whether specified source code, with all of its faults, defines a routine that eventually halts.

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You feed in your program, with suitable data, and P gets to work, and a little while later (in finite compute time) correctly infers whether infinite looping behavior occurs. If there will be no looping, then P prints out ‘Good.’ That means work on this input will halt, as it should. But if it detects an unstoppable loop, then P reports ‘Bad!’ — which means you’re in the soup. Well, the truth is that P cannot possibly be, because if you wrote it and gave it to me, I could use it to set up a logical bind that would shatter your reason and scramble your mind. Here’s the trick that I’ll use – and it’s simple to do. I’ll define a procedure, which I will call Q, that will use P’s predictions of halting success to stir up a terrible logical mess. For a specified program, say A, one supplies, the first step of this program called Q I devise is to find out from P what’s the right thing to say of the looping behavior of A run on A. If P’s answer is ‘Bad!’, Q will suddenly stop. But otherwise, Q will go back to the top, and start off again, looping endlessly back, till the universe dies and turns frozen and black. And this program called Q wouldn’t stay on the shelf; I would ask it to forecast its run on itself. When it reads its own source code, just what will it do? What’s the looping behavior of Q run on Q? If P warns of infinite loops, Q will quit; yet P is supposed to speak truly of it! And if Q’s going to quit, then P should say ‘Good’ — which makes Q start to loop! (P denied that it would.)

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No matter how P might perform, Q will scoop it: Q uses P’s output to make P look stupid. Whatever P says, it cannot predict Q: P is right when it’s wrong, and is false when it’s true! I’ve created a paradox, neat as can be — and simply by using your putative P. When you posited P you stepped into a snare; Your assumption has led you right into my lair. So where can this argument possibly go? I don’t have to tell you; I’m sure you must know. By reductio, there cannot possibly be a procedure that acts like the mythical P. You can never find general mechanical means for predicting the acts of computing machines. It’s something that cannot be done. So we users must find our own bugs. Our computers are losers!

October, 5 1565 - Day of death of Lodovico Ferrari, an Italian mathematician (b. 1522). 1750 - Maria Gaetana Agnesi received a response from Pope Benedict XIV on the publication of her book, "Instituzioni Analitiche," a twovolume presentation covering algebra, calculus, and differential equations. The pope sent her a gold medal and a wreath laid with precious stones, and named her an honorary professor at the University of Bologna. 1777 - Day of death of Johann Andreas Segner, a Slovak-German mathematician, physicist, and physician (b. 1704). 1781 - Birthdate of Bernard Bolzano, a Czech mathematician, and philosopher (d. 1848). 1854 - Bernhard Riemann gave his first lecture at Gottingen to eight students. Dedekind, his friend and fellow Privatdozent, relates that Riemann was a very poor lecturer whose intellect took such large leaps that students often found it impossible to follow. 1861 - Birthdate of Thomas Little Heath, a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer (d. 1940).

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1898 - Birthdate of Philip Franklin, an American mathematician (d. 1965). 1910 - Birthdate of Nathan Jacobson, an American mathematician (d. 1999). 1918 - Day of death of Matteo Bottasso, an Italian mathematician (b. 1878). 1930 - Birthdate of Reinhard Selten, a German economist and mathematician, Nobel Prize laureate (d. 2016). 1932 - Birthdate of Hyman Bass, an American mathematician. 1955 - Birthdate of Krishnaswami Alladi, an Indian-American mathematician. 1972 - Day of death of Solomon Lefshetz, an American mathematician (b. 1884). 1973 - Birthdate of Cedric Villani, a French mathematician. 1985 - Day of death of Harald Cramer, a Swedish mathematician, actuary, and statistician (b. 1893). 1985 - Day of death of Karl Menger, an Austrian-American mathematician from the Vienna Circle (b. 1902). 1986 - Day of death of James H. Wilkinson, an English mathematician, and computer scientist (b. 1919).

October, 6 1570 - Cardano was imprisoned for 87 days on charges of impiety, specifically for casting a horoscope of Christ. He spent the remaining five years of his life in Rome under the eye of a suspicious pope who nonetheless gave him a pension. 1651 - Sir Charles Cavendish wrote to John Pell about Thomas Harriot's "Doctrine of Triangular Numbers": "Sr. Th: Alesburie remembers him to you & desires to know if you would be pleased to show him the vse of Mr Hariots doctrine of triangular numbers; which if you will doe he will send you the originall; I confess I was so farre in love with it that I copied it out." [10] 1729 - Daniel Bernoulli wrote the first known letter which contains an interpolating function for the factorials. 1784 - Birthdate of Pierre Charles François Dupin, a French mathematician (d. 1873). 1795 - Birthdate of Benjamin Olinde Rodrigues, a French banker, mathematician, and social reformer (d. 1851). 1809 - Day of death of Benjamin Peirce, an American astronomer, mathematician, and educator (b. 1809). 1831 - Birthdate of Richard Dedekind, a German mathematician and philosopher (d. 1916).

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1840 - Day of death of François Budan de Boislaurent, a Haitian-born amateur mathematician (b. 1761). 1855 - Day of death of August Leopold Crelle, a German mathematician and engineer (b. 1780). 1860 - J. J. Sylvester, in a dinner invitation for Thomas Archer Hirst to join him with Arthur Cayley and Sylvester's "young French mathematical friend" (Camille Jordan), entices him with a bit of mathematics: "I shall have something very striking to tell you about algebraic quantities of any order of irrationality and their representation by multiple definite integrals when we meet." [132] 1880 - Day of death of Benjamin Peirce, an American astronomer, mathematician, and educator (b. 1809). 1908 - Birthdate of Sergei Sobolev, a Soviet mathematician (d. 1989). 1918 - Birthdate of Abraham Robinson, a Jewish mathematician (d. 1974). 1921 - Birthdate of Evgenii Landis, a Soviet mathematician and theorist (d. 1997). 1936 - Birthdate of Robert Phelan Langlands, a Canadian mathematician. 1942 - Birthdate of Hellmuth Stachel, an Austrian mathematician. 1968 - Day of death of Phyllis Nicolson, an English mathematician and physicist (b. 1917). 1979 - Day of death of Dudley Ernest Littlewood, a British mathematician (b. 1903). 1986 - Day of death of Alexander Kronrod, a Soviet mathematician and computer scientist (b. 1921). 1994 - Andrew Wiles sent the new proof of Fermat's Last Theorem to three colleagues, including Faltings. The new proof was published and, despite its size, widely accepted as likely correct in its major components.

October, 7 1601 - Birthdate of Florimond de Beaune, a French mathematician (d. 1652). 1719 - Day of death of Pierre Remond de Montmort, a French mathematician (b. 1678). 1796 - Day of death of Thomas Reid, a Scottish mathematician, and philosopher (b. 1710). 1854 - In an addendum to his paper "An Introductory Memoir upon Quantics," Arthur Cayley would add a second differential equation and state that "a covariant is an expression which, if it satisfies one of these equations, it satisfies the other." This would be the backbone of his

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new formulation of covariants in his next paper, "A second Memoire upon Quantics." 1864 - The mathematical seminar at Berlin began. 1875 - Birthdate of Raymond Clare Archibald, an American mathematician (d. 1955). 1893 - Khayyam's tree was transplanted. When the poet and mathematician Omar Khayyam died in 1123, he was buried in a spot where the north wind would scatter rose petals over his grave. On this date, a rose tree started from those on Khayyam's grave was transplanted to the grave of Edward Fitzgerald (1809-1883), the Irish translator who made Khayyam's poetry so famous in modern times. 1899 - Birthdate of Øystein Ore, a Norwegian mathematician (d. 1968). 1903 - Day of death of Rudolf Lipschitz, a German mathematician (b. 1832). 1905 - Birthdate of Wilhelm Ljunggren, a Norwegian mathematician (d. 1973). 1913 - Danish physicist Niels Bohr proposed a new model for the atom. 1920 - Day of death of Achille Marie Gaston Floquet, a French mathematician (b. 1847). 1965 - Day of death of Jesse Douglas, an American mathematician (b. 1897). 1992 - Day of death of Martin Eichler, a German mathematician (b. 1912). 1994 - Day of death of Brian Hartley, a British mathematician (b. 1939). 1995 - Day of death of Olga Taussky-Todd, an Austrian-Czech-American mathematician and attendant of the Vienna Circle (b. 1906). 2014 - Day of death of Volodymyr Sharko, a Ukrainian mathematician (b. 1949).

October, 8 1561 - Birthdate of Edward Wright, an English mathematician, and cartographer (d. 1615). 1647 - Day of death of Christen Sorensen Longomontanus, a Danish astronomer, and mathematician (b. 1562). 1652 - Day of death of John Greaves, an English mathematician, and astronomer (b. 1602). 1850 - Birthdate of Peter Redford Scott Lang, a Scottish mathematician (d. 1926). 1883 - Day of death of Enoch Beery Seitz, an American mathematician (b. 1846).

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1908 - Birthdate of Hans Arnold Heilbronn, a German-Jewish mathematician (d. 1975). 1922 - O. Heaviside wrote to the parents of William Gordon Brown (who was killed at age 20): "For a youth of 20, he was surprisingly advanced. Why, at his age, I didn't know anything at all of Analysis, nor about Electricity, though I had made several inventions (telegraphic) at that time, and was trying to see my way." [121] 1924 - Birthdate of John Nelder, an English mathematician and statistician (d. 2010). 1932 - Birthdate of Kenneth Ira Appel, an American mathematician (d. 2013). 1940 - Day of death of Robert Emden, a Swiss astrophysicist, and mathematician (b. 1862). 1942 - Day of death of Sergey Chaplygin, a Soviet physicist, mathematician, and engineer (b. 1869). 1973 - Day of death of Evan Tom Davies, a British mathematician (b. 1904). 1985 - Day of death of Gordon Welchman, an English-American mathematician (b. 1906). 2005 - Day of death of Alfred Goldie, an English mathematician (b. 1920).

October, 9 1253 - Day of death of Robert Grosseteste, an English bishop who worked on geometry, optics, and astronomy (b. 1168). 1581 - Birthdate of Claude Gaspard Bachet de Meziriac, a French mathematician, and poet (d. 1638). 1701 - Yale College founded. 1704 - Birthdate of Johann Andreas Segner, a German mathematician, physicist, and physician (d. 1777). 1730 - Goldbach studies sums of three and four squares. [104] 1775 - A paper by Euler titled "Speculationes circa quasdam insignes proprietates numerorum" was presented at the Saint-Petersburg Academy. In this paper, he revisits the idea that has come to be called Euler's Phi function. 1807 - Day of death of Gianfrancesco Malfatti, an Italian mathematician (b. 1731). 1901 - Birthdate of Winifred Deans, a British mathematician (d. 1990). 1907 - Minkowski had written to Einstein asking for a reprint of his 1905 paper, in order to discuss it in his seminar with Hilbert on the electrodynamics of moving bodies.

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1909 - Day of death of Bailie Hugh Blackburn, a Scottish mathematician (b. 1823). 1911 - Birthdate of Luis Antoni Santalo Sors, a Spanish mathematician (d. 2001). 1941 - Birthdate of Richard Alan Day, a Canadian mathematician (d. 1990). 1948 - Day of death of Joseph Henry Maclagen Wedderburn, a ScottishAmerican mathematician (b. 1882). 1949 - Birthdate of Fan-Rong King Chung Graham (known professionally as Fan Chung), a Taiwanese-born American mathematician. 1990 - Day of death of Georges de Rham, a Swiss mathematician (b. 1903). 2014 - The post office of Macao in the People's Republic of China issued a series of stamps based on magic squares.

October, 10 1629 - Day of death of Richard Towneley, an English mathematician and astronomer (b. 1707). 1641 - Torricelli arrives in Arcetri to study with Galileo. 1708 - Day of death of David Gregory, a Scottish mathematician, and astronomer (b. 1659). 1844 - Grassmann asked Möbius to write a review of his book Ausdehnungslehre. [36]

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1861 - Birthdate of Heinrich Friedrich Karl Ludwig Burkhardt, a German mathematician (d. 1914). 1919 - Birthdate of William Kruskal, an American mathematician, and statistician (d. 2005). 1944 - Birthdate of Melvyn Bernard Nathanson, an American mathematician. 1946 - Day of death of Georgii Pfeifer, a Ukrainian-Soviet mathematician (b. 1872). 1975 - Day of death of Norman Levinson, an American mathematician (b. 1912). 2007 - Day of death of Karl Walter Gruenberg, a British mathematician (b. 1928).

October, 11 1595 - Birthdate of Albert Girard, a French-Dutch mathematician (d. 1632). 1638 - Descartes wrote to Mersenne: "Reverend Father, I shall begin this letter with my observations on the book of Galileo. In general, I find him to philosophize much better than the common man in as far as he avoids as much as possible the errors of the School and tries to examine physical matters by means of mathematical reasoning. In this, I am in complete agreement with him, and I maintain that there is no other method for finding the truth... He also assumes that the velocity of the same body on different planes is equal when the elevations of these planes are equal. But he does not prove this, and it is not absolutely true. And as far as everything else which follows depends on these two suppositions, one can say that he built entirely on a foundation of sand..." [40] 1697 - Day of death of Stephano Angeli, an Italian mathematician (b. 1623). 1708 - Day of death of Ehrenfried Walther von Tschirnhaus, a German mathematician, physicist, physician, and philosopher (b. 1651). 1731 - Day of death of John Craig, a Scottish mathematician (b. 1663). 1791 - Day of death of Johann Castillon, an Italian mathematician (b. 1704). 1822 - Birthdate of John Daniel Runkle, an American educator and mathematician (d. 1902). 1852 - Day of death of Gotthold Eisenstein, a German mathematician (b. 1823). 1881 - Birthdate of Lewis Fry Richardson, an English mathematician, physicist, meteorologist, psychologist, and pacifist (d. 1953).

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1885 - Birthdate of Alfred Haar, a Hungarian mathematician (d. 1933). 1910 - Birthdate of Cahit Arf, a Turkish mathematician (d. 1997). 1923 - Birthdate of Harish-Chandra, an Indian mathematician (d. 1983). 1940 - Day of death of Vito Volterra, an Italian mathematician and physicist (b. 1860). 1943 - Day of death of Geoffrey Thomas Bennett, an English mathematician (b. 1868). 1979 - Day of death of Franciszek Leja, a Polish mathematician (b. 1885). 1988 - A 109-digit number, 11104 + 1, was factored by Mark Manasse and Arjen Lenstra using a quadratic sieve and a network of hundreds of computers in the US, Europe, and Australia. 1994 - John Forbes Nash, Jr. won the Nobel Prize for pioneering work in game theory. 1996 - Day of death of Lars Valerian Ahlfors, a Finnish mathematician (b. 1907). 1996 - Day of death of Edwin Henry Spanier, an American mathematician (b. 1921).

October, 12 1492 - Day of death of Piero della Francesca, an Italian mathematician, and painter (b. 1415). 1919 - Day of death of Georgii Dmitrievic Suvorov, a Soviet mathematician (b. 1919). 1926 - Day of death of Edwin Abbott, an English schoolmaster, and theologian, author of "Flatland" (b. 1838). 1931 - Gödel appeals to the undefinability of truth within a formal system of arithmetic in his letter to Zermelo. [110] 1934 - Birthdate of Albert Shiryaev, a Russian mathematician. 1944 - Kondo's History of Geometry was completed. 1952 - Birthdate of Roger Heath-Brown, an English mathematician. 1970 - Day of death of Andreas Speiser, a Swiss mathematician (b. 1885).

October, 13 1597 - Kepler replied to Galileo's letter of 4 August 1597, urging him to be bold and proceed openly in his advocacy of Copernicanism. 1729 - Euler mentioned the gamma function in a letter to Goldbach. Legendre gave the function its symbol and name in 1826. 1734 - Birthdate of William Small, a British mathematician (d. 1775).

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1776 - Birthdate of Peter Barlow, an English mathematician and engineer (d. 1862). 1793 - Day of death of William Hopkins, an English mathematician and geologist (b. 1793). 1852 - Thomas Hirst wrote in his diary about a meeting with Dirichlet: “[Dirichlet] is a rather tall, lanky-looking man, with a mustache and beard about to turn gray, with a somewhat harsh voice and rather deaf. It was early, he was unwashed and unshaven (what of him required shaving), with his 'Schlafrock,' slippers, a cup of coffee, and a cigar… If all be well, we will smoke our friendly cigar together many a time yet, good-natured Lejeune-Dirichlet." [116] 1866 - Day of death of William Hopkins, an English mathematician and geologist (b. 1793). 1885 - Birthdate of Viggo Brun, a Norwegian mathematician (d. 1978). 1890 - Birthdate of Georg Feigl, a German mathematician (d. 1945). 1893 - Birthdate of Kurt Reidemeister, a German mathematician connected to the Vienna Circle (d. 1971). 1893 - The term "Diophantine equation" appears in English in 1893 in Eliakim Hastings Moore's "A Doubly-Infinite System of Simple Groups," Bulletin of the New York Mathematical Society. [118] 1913 - Day of death of Gyula Valyi, a Hungarian mathematician and theoretical physicist (b. 1855). 1915 - Alexandrov gave a talk at a student seminar at Moscow University on his theorem on B-sets. [58] 1932 - Birthdate of John Griggs Thompson, an American mathematician. 1990 - Day of death of Hans Freudenthal, a Dutch mathematician (b. 1905). 2001 - Day of death of Olga Arsenevna Oleinik, a Soviet-Russian mathematician (b. 1925). 2007 - Day of death of Olexandr Stepanets, a Soviet-Ukrainian mathematician (b. 1942).

October, 14 1687 - Birthdate of Robert Simson, a Scottish mathematician (d. 1768). 1868 - Birthdate of Alessandro Padoa, an Italian mathematician (d. 1937). 1956 - Day of death of Jules Antoine Richard, a French mathematician (b. 1862). 1982 - Day of death of Edward Hubert Linfoot, an English mathematician (b. 1905).

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1982 - Day of death of Clifford Hugh Dowker, a Canadian-British mathematician (b. 1912). 2010 - Day of death of Benoit Mandelbrot, a Polish-American mathematician and economist (b. 1924). 2010 - Day of death of Wilhelm Paul Albert Klingenberg, a German mathematician (b. 1924).

October, 15 1608 - Birthdate of Evangelista Torricelli, an Italian physicist and mathematician (d. 1647). 1715 - Day of death of Humphry Ditton, an English mathematician and philosopher (b. 1675). 1743 - Euler claims that if a number is a sum of two (three, four) rational squares, then it is a sum of two (three, four) integral squares. [104] 1745 - Birthdate of George Atwood, an English mathematician (d. 1807). 1759 - Euler's paper "An arithmetic theorem proved by a new method" was presented at the Saint-Petersburg Academy. In this paper, he introduces the idea that has come to be called Euler's Phi function. 1776 - Birthdate of Peter Barlow, an English mathematician (d. 1862). 1810 - The University of Berlin opened by Wilhelm von Humboldt. 1837 - Birthdate of Leo Konigsberger, a German mathematician (d. 1921). 1875 - Birthdate of Andre-Louis Cholesky, a French military officer and mathematician (d. 1918). 1909 - Birthdate of Bernhard Hermann Neumann, a German mathematician (d. 2002). 1921 - Birthdate of Lillian Katie Bradley, an American mathematician. 1944 - Birthdate of Yuri Drozd, a Ukrainian mathematician. 1959 - Day of death of Lipot Fejer, a Hungarian mathematician (b. 1880). 1965 - Day of death of Abraham Fraenkel, a German-Israeli mathematician (b. 1891). 1980 - Day of death of Mikhail Lavrentyev, a Soviet physicist and mathematician (b. 1900). 1990 - Day of death of Wilhelm Magnus, a German-American mathematician (b. 1907). 2016 - Day of death of Marcel Berger, a French mathematician (b. 1927).

October, 16 1655 - Day of death of Joseph Solomon Delmedigo, an Italian physician and mathematician (b. 1591).

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1689 - Birthdate of Robert Smith, an English mathematician (d. 1768). 1736 - Mathematician William Whiston wrongly predicted that a comet would strike the Earth. [169] 1797 - Gauss recorded in his diary that he had discovered a new proof of the Pythagorean Theorem. [27] 1843 - Sir William Rowan Hamilton discovered quaternions while walking with his wife one evening along the Royal Canal in Dublin. On the very same day, he presented his breakthrough to the Royal Irish Academy. 1865 - Cayley's first paper for the London Mathematical Society on "Transformation of Plane Curves" was read. 1882 - Birthdate of Ernst Erich Jacobsthal, a German mathematician (d. 1965). 1918 - Birthdate of Abraham Nemeth, an American mathematician (d. 2013). 1937 - Day of death of William Sealy Gosset, an English mathematician (b. 1876). 1959 - Birthdate of Philip Maini, a Northern Irish mathematician. 1983 - Day of death of Harish-Chandra, an Indian mathematician (b. 1923).

October, 17 1730 - Euler mentions another theorem by Fermat: “Any number is the sum of three triangular numbers." [104] 1759 - Birthdate of Jakob II Bernoulli, Swiss-Russian mathematician (d. 1789). 1776 - Euler read a paper to the St. Petersburg Academy of Science entitled “De quadratis magicis," in which he gave a method of constructing magic squares by means of two orthogonal Latin squares. [170] 1788 - Birthdate of Paul Isaak Bernays, Swiss mathematician (d. 1977). 1817 - Day of death of John West, Scottish mathematician (b. 1756). 1843 - Hamilton Writes to his friend, John Graves, with a description of Quaternions: “Observatory, October 17, 1843 My dear Graves, A very curious train of mathematical speculation occurred to me yesterday, which I cannot but hope will prove of interest to you. You know that I have long wished, and I believe that you have felt the same desire, to possess a Theory of Triplets, analogous to my published Theory of Couplets, and also to Mr.

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Warren's geometrical representation of imaginary quantities. Now I think that I discovered yesterday a theory of quaternions which includes such a theory of triplets." (See [69] for the whole letter) 1858 - DeMorgan writes a letter about Euler's prodigious output. 1927 - Birthdate of Friedrich Ernst Peter Hirzebruch, a German mathematician (d. 2012). 1933 - Albert Einstein seeks asylum in the US. 1937 - Day of death of Frank Morley, a British mathematician (b. 1860). 1952 - Day of death of Ernest Vessiot, a French mathematician (b. 1865). 1952 - D. H. Lehmer announced that 22203 - 1 and 22281 - 1 are Mersenne primes. 1963 - Day of death of Jacques Hadamard, a French mathematician (b. 1865). 1976 - Day of death of Edward Marczewski, a Polish mathematician (b. 1907). 1978 - Day of death of Gertrude Cox, an American statistician (b. 1900). 1989 - Day of death of Mark Grigorievich Krein, a Soviet mathematician (b. 1907). 1999 - Day of death of Nicholas Metropolis, a Greek-American mathematician and physicist (b. 1915). 2008 - Day of death of Andrew Mattei Gleason, an American mathematician (b. 1921).

October, 18 1564 - Day of death of Johannes Acronius Frisius, a Dutch physician, and mathematician (b. 1520). 1640 - Fermat, in a letter to Frenicle de Bessy, presented a generalization of results from an earlier letter, which is now known as Fermat's Little Theorem. It demonstrates that for any prime number p and an integer a that is not divisible by p, ap-1 - 1 is divisible by p. [126] 1740 - In a letter to Johann Bernoulli, Euler employed imaginaries in the exponent exi + e-xi = 2 cos x. It's worth noting that Euler used the square root of -1 rather than 'i.' Euler would later become the first to use 'i' for the imaginary constant, but not until a paper he presented in St. Petersburg in 1777. [27] 1786 - Day of death of Alexander Wilson, a Scottish surgeon, typefounder, astronomer, mathematician, and meteorologist (b. 1714). 1793 - Day of death of John Wilson, an English lawyer, and mathematician (b. 1741).

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1845 - Day of death of Dominique Cassini, a French mathematician, and surveyor (b. 1748). 1871 - Day of death of Charles Babbage, an English mathematician, and engineer who invented the mechanical computer (b. 1791). 1921 - Day of death of Paul Rudolf Eugen Jahnke, a German mathematician (b. 1861). 1938 - Birthdate of Phillip Griffiths, an American mathematician. 1974 - Day of death of Charles Weatherburn, an Australian mathematician (b. 1884).

October, 19 1759 - Gauss wrote in a letter to his former teacher, E. A. W. von Zimmermann, expressing his disappointment that many of his discoveries in indefinite analysis were not original. He mentioned that he had found more general and natural viewpoints compared to Euler's discoveries. 1871 - Birthdate of John Miller, a Scottish mathematician (d. 1956). 1890 - Day of death of Emile Leonard Mathieu, a French mathematician (b. 1835). 1903 - Birthdate of Jean Frederic Auguste Delsarte, a French mathematician (d. 1968). 1910 - Birthdate of Subrahmanyan Chandrasekhar, an Indian-American astrophysicist, astronomer, and mathematician who later became a Nobel Prize laureate (d. 1995). 1917 - Birthdate of Sharadchandra Shankar Shrikhande, an Indian mathematician. 1944 - Day of death of Denes Konig, a Hungarian mathematician (b. 1884). 1951 - Birthdate of Demetrios Christodoulou, a Greek mathematician and physicist. 1965 - The London Times reported that an archaeologist had located what he believed to be the tomb of Archimedes. 1979 - Day of death of Marjorie Lee Browne, an American mathematician (b. 1914). 2007 - Day of death of Winifred Asprey, an American mathematician and computer scientist (b. 1917).

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October, 20 1616 - Birthdate of Thomas Bartholin, Danish physician, mathematician, and theologian (d. 1680). 1631 - Day of death of Michael Maestlin, German astronomer, and mathematician (b. 1550). 1632 - Birthdate of Christopher Wren, English physicist, mathematician, and architect, known for designing St. Paul's Cathedral (d. 1723). 1735 - Benjamin Franklin's paper titled "On the Usefulness of Mathematics" appeared in the Pennsylvania Gazette. 1744 - Euler announced the discovery of a simple curve that exhibited a cusp of the second kind, also known as a ramphoid. [150] 1863 - Birthdate of William Henry Young, English mathematician (d. 1942). 1865 - Birthdate of Aleksandr Petrovich Kotelnikov, Soviet mathematician (d. 1944). 1904 - Birthdate of Hans Lewy, American mathematician (d. 1988). 1914 - Birthdate of R.H. Bing, American mathematician (d. 1986). 1958 - Italy issued a stamp to celebrate the 350th anniversary of the birth of Evangelista Torricelli, a mathematician, and physicist.

1974 - Day of death of Harold Stanley Ruse, British mathematician (b. 1905). 1984 - Day of death of Paul Dirac, English-American physicist and mathematician, Nobel Prize laureate (b. 1902). 1987 - Day of death of Andrey Kolmogorov, Soviet mathematician (b. 1903).

October, 21 1505 - Day of death of Paul Scriptoris, German mathematician, and educator (b. 1460). 1687 - Birthdate of Nicolaus I Bernoulli, Swiss mathematician (d. 1759).

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1796 - Entry 43 of Gauss's scientific diary states “Vicimus GEGAN" (We have conquered GEGAN). The meaning of this was a mystery for many years. Biermann (1997) found a manuscript by Gauss suggesting that GEGAN is a reversal of the acronym NAGEG standing for Nexum medii Arithmetico-Geometricum Expectationibus Generalibus and refers to the connection between the arithmetic geometric mean and elliptic functions.

1823 - Birthdate of Enrico Betti, Italian mathematician (d. 1892). 1872 - Day of death of Jacques Babinet, French physicist, mathematician, and astronomer (b. 1794). 1881 - Day of death of Heinrich Eduard Heine, German mathematician (b. 1821). 1882 - Birthdate of Harry Schultz Vandiver, American mathematician (d. 1973). 1855 - Birthdate of Giovanni Battista Guccia, Italian mathematician (d. 1914). 1914 - Birthdate of Martin Gardner, American mathematician, and writer (d. 2010). 1925 - Birthdate of Boris I. Plotkin, Soviet-Israeli mathematician. 1935 - Birthdate of Evgeny S. Golod, Soviet-Russian mathematician (d. 2018). 1965 - Greece issued a postage stamp picturing Hipparchus and an astrolabe to commemorate the opening of the Evghenides Planetarium in Athens.

1969 - Day of death of Waclaw Sierpinski, Polish mathematician (b. 1882). 1988 - Science (pp. 374-375) reported that the 100-digit number 11104 +1 was factored by using computers working in parallel using a quadratic sieve method.

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2000 - Day of death of Dirk Jan Struik, Dutch mathematician (b. 1894). 2002 - Day of death of Bernhard Hermann Neumann, German mathematician (b. 1909).

October, 22 1511 - Birthdate of Erasmus Reinhold, German astronomer, and mathematician (d. 1553). 1587 - Birthdate of Joachim Jungius, German mathematician, and philosopher (d. 1657). 1668 - Leibniz writes to the German emperor to request permission to publish a “Nucleus Libareaus." This was the beginnings of the foundation of Acta Eruditorium, the first German scientific journal. 1745 - Day of death of Isaac Greenwood, American mathematician (b. 1702). 1746 - Princeton University is chartered as the “College of New Jersey." It moved to Princeton in 1756 and changed its name to Princeton University in 1896. 1843 - Birthdate of John S. Mackay, Scottish mathematician (d. 1914). 1850 - Weber-Fechner law introduced. Describing the relationship between physical stimuli and human perception as logarithmic, it was one of the first mathematical models in the field of human cognition. 1895 - Birthdate of Rolf Herman Nevanlinna, Finnish mathematician (d. 1980). 1906 - Birthdate of Aurelio Baldor, Cuban mathematician, and lawyer (d. 1978). 1907 - Birthdate of Sarvadaman D. S. Chowla, Indian mathematician (d. 1995). 1916 - Birthdate of Nathan Jacob Fine, American mathematician (d. 994). 1921 - Birthdate of Alexander Kronrod, Soviet mathematician, and computer scientist (d. 1986). 1927 - Birthdate of Alexander Ivanovich Skopin, Soviet mathematician (d. 2003). 1950 - Day of death of Ada Isabel Maddison, British mathematician (b. 1869). 1977 - Day of death of Beniamino Segre, Italian mathematician (b. 1903). 1979 - Day of death of Reinhold Baer, German mathematician (b. 1902).

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October, 23 1581 - Day of death of Michael Neander, German mathematician, and astronomer (b. 1529). 1613 - Kepler, in a letter to an unknown recipient, goes into great detail concerning his attempts over the preceding two years to find a wife. [32] 1813 - Gauss found a complete proof for the reciprocity law to powers greater than two, and in particular to the law of biquadratic reciprocity (published in his book Disquisitiones Arithmeticae in 1801). [52] 1821 - Birthdate of Philipp Ludwig von Seidel (d. 1896). 1832 - Galois was sentenced to six months in prison for illegally wearing a uniform. 1852 - De Morgan conveyed the Four-Color Problem to Hamilton, writing, “A student of mine asked me today to give him a reason for a fact which I did not know was a fact – and do not yet. He says that if a figure is anyhow divided and the compartments differently colored so that the figures with any portion of a common boundary line are differently colored – four colors may be wanted, but not more… Query cannot a necessity for five or more be invented." [182] 1865 - Birthdate of Piers Bohl, Latvian mathematician (d. 1921). 1913 - The “Declaration of the Professors of the German Reich," stating that the German Army nurtured scholarship and shared its values, was signed by over 3100 professors, including Klein, Hilbert, Moritz Cantor, and Max Noether. [7] 1930 - Gödel sent the incompleteness article for publication. [110] 1948 - Birthdate of Akihiro Kanamori, Japanese-born American mathematician. 1973 - Day of death of Maurice Princet, French mathematician, and actuary (b. 1875). 985 - Day of death of John Semple, Irish-English mathematician (b. 1904). 2011 - Day of death of Herbert A. Hauptman, American chemist, and mathematician, Nobel Prize laureate (b. 1917).

October, 24 1601 - Day of death of Tycho Brahe, Danish astronomer and mathematician (b. 1546). 1676 - Newton, at the request of Oldenburg and Collins, wrote to the former a letter where he just mentioned explains the way in which he found the Binomial Theorem, and also communicates his method of

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uxions and uents in form of an anagram in which all the letters in the sentence communicated were placed in alphabetical order. Thus Newton says that his method of drawing tangents was 6a cc d æ 13 e ff 7 i 3 l 9 n 4 o 4 q rr 4 s 9 t 12 v x. The sentence was, “Data æquatione quotcunque uentes quantitates involvente uxiones invenire, et vice versa." (“Having any given equation involving never so many owing quantities, to find the uxions, and vice versa.") [27] 1729 - The young L. Euler sent his first letter to Ch. Goldbach. (Their correspondence would continue until Goldbach's death in 1764. Almost 200 of their letters survive. Goldbach served as a kind of mentor for Euler, and it was he who introduced Euler to number theory through the works of Fermat.) The letter goes on to discuss Euler's first definition of what we now call the gamma function writing . In passing, Euler mentions a fact that depends on knowing that eʌi = -1. He then uses a process similar to the interpolation of the factorial progression that led to the gamma function to give the partial sums of the harmonic series. [151] 1655 - Day of death of Pierre Gassendi, French priest, astronomer, and mathematician (b. 1592). 1826 - Abel wrote Holmboe his impressions of continental mathematics and mathematicians. Upon reaching Paris from Berlin, he worked on what would be called the Paris Treatise that he submitted to the Academy in October 1826. In this memoir, Abel obtained among other things, an important addition theorem for algebraic integrals. It is also in this treatise that we see the first occurrence of the concept of the genus of an algebraic function. Cauchy and Legendre were appointed referees of this memoir. In Paris, Abel was disappointed to find little interest in his work, which he had saved for the Academy. He wrote to Holmboe, “I showed the treatise to Mr. Cauchy, but he scarcely deigned to glance at it." [3] He also noticed that he had met “Herr Lejeune Dirichlet, a Prussian, who visited me the other day, since he considered me as a compatriot. He is a very sagacious mathematician. Simultaneously with Legendre he proved the insolubility of the equation x5 + y5 = z5 in integers and other nice things" [43] 1853 - Birthdate of Heinrich Maschke, German mathematician (d. 1908). 1872 - Birthdate of Georgii Pfeiffer, Ukrainian-Soviet mathematician (d. 1946). 1873 - Birthdate of Edmund Taylor Whittaker, English mathematician (d. 1956). 1902 - In Science, George Bruce Halsted wrote that his student R. L. Moore, who had proved that one of Hilbert's betweenness axioms was

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redundant, “was displaced in favor of a local schoolmarm," Miss Mary E. Decherd. 1904 - Emmy Noether matriculated at the University of Erlangen as number 468. At that time, she only listed mathematics as her course of study. [38] 1906 - Birthdate of Alexander Gelfond, Soviet mathematician, and cryptographer (d. 1968). 1920 - Birthdate of Marcel-Paul Schutzenberger, French mathematician (d. 1996). 1927 - From the 24th to 29th of October 1927 in Brussels, the fifth Solvay Conference took place, perhaps the most famous science conference in history. 17 of the 29 attendees were or became Nobel Prize winners. It is also famously remembered for it was at this conference that Einstein, who liked to invent catchy phrases, uttered his, “God does not play dice." Bohr replied, “Einstein, stop telling God what to do." 1930 - Birthdate of Johan Galtung, Norwegian sociologist, and mathematician. 930 - Day of death of Paul Emile Appell, French mathematician (b. 1855). 1933 - In a letter to Springer, the German Mathematical Society (DMV) demanded the closing of Zentralblatt in favor of the Jahrbuch. 1953 - Birthdate of Charles Colbourn, Canadian computer scientist, and mathematician. 1966 - Day of death of Sofya Yanovskaya, Russian mathematician, and historian (b. 1896).

October, 25 1647 - Day of death of Evangelista Torricelli, Italian physicist, and mathematician (b. 1608). 1713 - Gottfried Leibniz, in a letter to Johann Bernoulli, observed that an alternating series whose terms monotonically decrease to zero in absolute value is convergent. 1733 - Day of death of Giovanni Girolamo Saccheri, Italian priest, mathematician, and philosopher (b. 1667). 1811 - Birthdate of Evariste Galois, French mathematician (d. 1832). 1884 - Day of death of Carlo Alberto Castigliano, Italian mathematician, and physicist (b. 1847). 1886 - Birthdate of Lester Randolph Ford, American mathematician (d. 1967). 1905 - Day of death of Otto Stolz, Austrian mathematician (b. 1842).

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1915 - Birthdate of Ivan M. Niven, Canadian-American mathematician (d. 1999). 1926 - Birthdate of James Eells, American-British mathematician (d. 2007). 1933 - Day of death of Friedrich Heinrich Albert Wangerin, German mathematician (b. 1844). 1944 Max Planck writes to Hitler to plead for the life of his son, Erwin. In the note, the discoverer of the energy quantum pleads for the life of his son, who was involved in the attempted to kill Hitler three months before. Max Planck had already lost his eldest son, who was killed in the Battle of Verdun, during World War I. Planck writes in his letter that he is `confident' that the Fohrer will lend his ear to `an imploring 87-year-old'. This plea, apparently written from the Planck family's bombed-out home in a suburb of Berlin, was ignored by the authorities. Erwin was executed on 23 January 1945, and his death certificate recorded: `parents unknown' [46]. 1952 - Birthdate of Wendy Hall, English computer scientist, and mathematician. 1994 - Karl Rubin announced two papers: one by R. Taylor and A. Wiles and another by A. Wiles, completing Wiles' proof of Fermat's last theorem. 1996 - Day of death of Ennio de Giorgi, Italian mathematician (b. 1928). 1997 - Day of death of Mina Spiegel Rees, American mathematician (b. 1902). 2002 - Day of death of Jean Estelle Hirsh Rubin, American mathematician (b. 1926). 2002 - Day of death of Rene Thom, French mathematician, and biologist (b. 1923).

October, 26 1675 - Leibniz first used a calculus symbol in a letter on this date. He wrote that he would use 'w' as the differential of the variable 'y'. 1676 - Newton, through the intermediary of Oldenburg, wrote to Leibniz concerning his work on calculus. 1773 - Day of death of Amedee-Francois Frezier, French mathematician, engineer, and explorer (b. 1682). 1802 - Gauss, in a letter to Heinrich Olbers, wrote: "I have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science… And with this thankless work, the professor loses his noble time."

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1817 - Day of death of Aida Yasuaki, also known as Aida Ammei, Japanese mathematician (b. 1747). 1818 Thomas Jefferson writes Nathaniel Bowditch to offer him the Math Professorship at the newly forming University of Virginia: “I have stated that where men of the 1st order of science in their line can be found in our country, we shall give them a willing preference. We are satisfied that we can get from no country a professor of higher qualifications than yourself for our Mathematical department, and we entertain the hope and with great anxiety that you will accept of it. The house for that Professorship will be ready at midsummer next or soon after, when we should wish that school to be opened. I know the prejudices of every state against the climates of all those South of itself: but I know also that the candid traveller advancing Southwardly, to a certain degree at least, sees that they are more prejudices, and that the real advantages of climate are in the middle & temperate states, and especially when above their tide waters." [87] 1843 - John T. Graves replied to Hamilton about the invention of Quaternions: "There is something in the system which gravels me. I have not yet any clear views as to the extent to which we are at liberty to arbitrarily create imaginaries and to endow them with supernatural properties… If with your alchemy you can create three pounds of gold, why should you stop there?" 1849 - Birthdate of Ferdinand Georg Frobenius, German mathematician (d. 1917). 1885 - Birthdate of Niels Erik Norlund, Danish mathematician (d. 1981). 1893 - Karl Pearson's first statistical publication was the first in a series of 18 papers titled "Mathematical Contributions to the Theory of Evolution." 1911 - Birthdate of Shiing-shen Chern, Chinese-American mathematician, and educator (d. 2004). 1930 - Birthdate of Walter Feit, Austrian mathematician (d. 2004). 1935 - Birthdate of Gloria Conyers Hewitt, American mathematician. 1945 - Day of death of Aleksey Krylov, Soviet mathematician, and engineer (b. 1863). 1968 - Day of death of Sergei Natanovich Bernstein, Soviet mathematician (b. 1880). 1983 - Day of death of Alfred Tarski, Polish-American mathematician, and logician (b. 1901). 1984 - Day of death of Mark Kac, Polish mathematician (b. 1914). 1998 - Day of death of Kenkichi Iwasawa, Japanese mathematician (b. 1917).

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October, 27 1449 - Day of death of Ulugh Beg, Persian astronomer, mathematician, and sultan (b. 1394). 1616 - Day of death of Johann Richter or Johannes Praetorius, Bohemian German mathematician, and astronomer (b. 1537). 1654 - Blaise Pascal wrote to Pierre de Fermat, praising him for his solution to the Problem of the Points, about which they had exchanged seven previous letters. 1675 - Day of death of Gilles de Roberval, French mathematician (b. 1602). 1678 - Birthdate of Pierre Remond de Montmort, French mathematician (d. 1719). 1798 - Birthdate of Heinrich Ferdinand Scherk, German mathematician (d. 1885). 1856 - Birthdate of Ernest William Hobson, English mathematician (d. 1933). 1890 - Birthdate of Olive Clio Hazlett, American mathematician (d. 1974). 1915 - Birthdate of Robert Alexander Rankin, Scottish mathematician (d. 2001). 1930 - Day of death of Ellen Hayes, American mathematician, and astronomer (b. 1851). 1974 - Day of death of C. P. Ramanujam, Indian mathematician (b. 1938). 1980 - Day of death of John Hasbrouck Van Vleck, American physicist, and mathematician, Nobel Prize laureate (b. 1899).

October, 28 1386 - University of Heidelberg opened. 1636 - Harvard College founded. 1703 - Birthdate of Antoine Deparcieux, French mathematician, and engineer (d. 1768). 1703 - Day of death of John Wallis, English mathematician, and cryptographer (b. 1616). 1718 - Birthdate of Ignacije Szentmartony, Croatian priest, mathematician, astronomer, and explorer (d. 1793). 1752 - Euler published a paper listing the 161 numbers less than 15,000 for which n2 + 1 is a prime. He also listed eight numbers for which n4 + 1 is a prime (they are 1, 2, 4, 6, 16, 20, 24, and 34). 1804 - Birthdate of Pierre Francois Verhulst, Belgian mathematician (d. 1849).

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1880 - Birthdate of Michele Cipolla, Italian mathematician (d. 1947). 1905 - Birthdate of Tatyana Pavlovna Ehrenfest, Dutch mathematician (d. 1984). 1918 - Day of death of Ulisse Dini, Italian mathematician, and politician (b. 1845). 1960 - Birthdate of Landon Curt Noll, American computer scientist, and mathematician. 1965 - Day of death of Luther Pfahler Eisenhart, American mathematician (b. 1876). 1986 - Day of death of Irving Reiner, American mathematician (b. 1924).

October, 29 1669 - Newton appointed as Lucasian professor. 1675 - Leibniz first introduces a new notation for integral as well as the “d" for differential. He also constructed what he called the “triangulum characteristicum," which had been used before him by Pascal and Barrow. [27]

1690 - Birthdate of Martin Folkes, English mathematician, and astronomer (d. 1754). 1783 - Day of death of Jean le Rond d'Alembert, French mathematician, physicist, and philosopher (b. 1717). 1784 - Birthdate of Pierre Charles Francois Dupin, French mathematician (d. 1873). 1856 - William Rowan Hamilton submits a paper on “New Roots of Unity," which will be the foundation of his Icosian Calculus. 1897 - Birthdate of Edwin James George Pitman, Australian mathematician (d. 1993). 1912 - Einstein wrote to Sommerfeld: “I am now occupied exclusively with the gravitational problem, and believe that I can overcome all difficulties with the help of a local mathematician friend [Marcel

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Grossmann]. But one thing is certain, never before in my life have I troubled myself over anything so much, and that I have gained great respect for mathematics, whose more subtle parts I considered until now, in my ignorance, as pure luxury! Compared with this problem, the original theory of relativity is childish" [179]. 1917 - Day of death of Giovanni Battista Guccia, Italian mathematician (b. 1855). 1921 - Day of death of Konstantin Alekseevich Andreev, Russian mathematician (b. 1848). 1925 - Birthdate of Klaus Roth, British mathematician (d. 2015). 1926 - Birthdate of Jean Estelle Hirsh Rubin, American mathematician (d. 2002). 1931 - Day of death of Gabriel Xavier Paul Koenigs, French mathematician (b. 1858). 1933 - Day of death of Paul Painleve, French mathematician, and politician, 84th Prime Minister of France (b. 1853). 1971 - Birthdate of Daniel J. Bernstein, American mathematician, cryptologist. 1993 - Day of death of Lipman Bers, Latvian-American mathematician (b. 1914). 1993 - Day of death of Robert Palmer Dilworth, American mathematician (b. 1914). 2004 - Day of death of Peter Twinn, English mathematician, and entomologist (b. 1916). 2009 - Day of death of Shaun Wylie, British mathematician (b. 1913).

October, 30 1626 - Day of death of Willebrord Snell, Dutch astronomer, and mathematician (b. 1580). 1632 - Birthdate of Christopher Wren, English physicist, mathematician, and architect, who designed St Paul's Cathedral (d. 1723). 1710 - William Whiston, whom Newton had arranged to succeed him as Lucasian Professor at Cambridge in 1701, was deprived of the chair and driven from Cambridge for his unorthodox religious views. 1735 - Benjamin Franklin published “On the Usefulness of Mathematics," his only published article on mathematics, in the Pennsylvania Gazette. 1739 - Day of death of Leonty Filippovich Magnitsky, Russian mathematician, and educator (b. 1669). 1810 - Day of death of Francois Joseph Francais, French mathematician (b. 1768).

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1826 - Niels Abel presented a paper to the French Academy of Sciences that was ignored by Cauchy, who was to serve as referee. The paper was published some twenty years later, well after Abel's death. 1840 - Birthdate of Joseph Jean Baptiste Neuberg, Belgian mathematician (d. 1926). 1844 - Birthdate of George Henri Halphen, French mathematician (d. 1889). 1863 - Birthdate of Stanislaw Zaremba, Polish mathematician (d. 1942). 1906 - Birthdate of Andrei Nikolaevich Tikhonov, Soviet mathematician (d. 1993). 1907 - Birthdate of Harold Davenport, English mathematician (d. 1969). 1946 - Birthdate of William Paul Thurston, American mathematician (d. 2012). 1978 - Laura Nickel and Curt Noll, eighteen-year-old students at California State at Hayward, showed that 221.701 - 1 is prime. This was the largest prime known at that time. 1991 - Day of death of Ellis Robert Kolchin, American mathematician (b. 1916). 2007 - Day of death of Juha Heinonen, Finnish-American mathematician (b. 1960).

October, 31 1815 - Birthdate of Karl Weierstrass, German mathematician (d. 1897). 1840 - Day of death of Charles Bonnycastle, American mathematician (b. 1796). 1852 - An entry in Hirst's diary: “Dirichlet cannot be surpassed for richness of material and clear insight into it: as a speaker he has no advantages – there is nothing like fluency about him, and yet a clear eye and understanding make it dispensable: without an effort you would not notice his hesitating speech. What is peculiar in him, he never sees his audience – when he does not use the blackboard at which time his back is turned to us, he sits at the high desk facing us, puts his spectacles up on his forehead, leans his head on both hands, and keeps his eyes, when not covered with his hands, mostly shut. He uses no notes, inside his hands he sees an imaginary calculation, and reads it out to us – that we understand it as well as if we too saw it. I like that kind of lecturing." 1890 - Birthdate of Joseph Jean Camille Peres, French mathematician (d. 1962).

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1902 - Birthdate of Abraham Wald, Romanian mathematician and economist (d. 1950). 1903 - Frank N. Cole, at a New York meeting of the American Mathematical Society, presented a paper “On the factoring of large numbers." He spoke not a word, but carefully raised 2 to the 67th power, then subtracted one. Moving over, he computed 193,707,721 times 761,838,257,287. The calculations agreed, showing that this number is not a Mersenne prime. In 1911, E. T. Bell asked Cole how long it had taken him to find this factorization. He replied, “Three years of Sundays." 1915 - Closing date for a prize consisting of a gold medal bearing a portrait of Weierstrass and 3000 Swedish crowns, for the best essay on the theory of analytic functions. King Gustav V of Sweden founded the prize to commemorate the centenary of the birth of Weierstrass. 1919 - Birthdate of Magnus Wenninger, American mathematician (d. 2017). 1925 - Birthdate of John A. Pople, British mathematician and chemist (d. 2004). 1935 - Birthdate of Ronald Graham, American mathematician (d. 2020). 1983 - Day of death of Lu Jiaxi, Chinese self-taught mathematician (b. 1935). 1992 - The Vatican admitted erring for over 359 years in formally condemning Galileo Galilei for entertaining scientific truths such as the Earth revolves around the sun it, which the Roman Catholic Church long denounced as anti-scriptural heresy. After 13 years of inquiry, the Pope's commission of historic, scientific and theological scholars brought the pope a "not guilty" finding for Galileo. 2006 - Day of death of George Brinton Thomas Jr., American mathematician (b. 1914).

CHAPTER ELEVEN NOVEMBER

November, 1 1585 - Birthdate of Jan Brozek, Polish mathematician, physician, and astronomer (d. 1652). 1809 - Louis Poinsot (1777-1859) named assistant professor of analysis and mechanics at the Ecole Polytechnique. 1818 - William Whewell wrote John Herschel that he "would not be surprised if in a short time we were only to read a few propositions of Newton, as a matter of curiosity." [8] 1826 - John Boole, an amateur mathematician of some ability, would pencil into the cover of the sixth book of Leslie's Geometry, "George Boole finished this book on 1 Nov. 1826." The following day would be George's eleventh birthdate. 1828 - Birthdate of William Henry Besant, British mathematician (d. 1917). 1844 - Gauss in a letter to Schumacher, "I am rather surprised that you expect clarity from a professional philosopher. Muddled concepts and definitions are nowhere more at home than among philosophers who are not mathematicians… Just look around at today's philosophers, Schelling, Hegel, Nees von Esenbeck and Co. Don't their definitions make your hair stand on end? Or, in classical philosophy, read the kinds of things which “stars" like Plato and others (I except Aristotle) gave as explanations. Even Kant is often not much better: his distinction between analytic and synthetic propositions is, I believe, one of those which either turns on a triviality or is false." 1864 - Birthdate of Ludwig Schlesinger, German mathematician (d. 1933). 1913 - Birthdate of Andrzej Mostowski, Polish mathematician (d. 1975). 1919 - Birthdate of Hermann Bondi, English-Austrian mathematician and cosmologist (d. 2005). 1920 - Birthdate of Claude Ambrose Rogers, English mathematician (d. 2005). 1926 - Birthdate of James B. Serrin, American mathematician (d. 2012). 1927 - Germany issued a stamp featuring Leibniz.

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1951 - Birthdate of Andrei Polyanin, Russian mathematician. 1951 - Cuba commemorated the 30th anniversary of the winning of the World Chess title by Jose Raul Capablanca by issuing a stamp picturing the resignation play of Dr. Emanuel Lasker (1868-1941).

1962 - Day of death of Thomas Murray MacRobert, Scottish mathematician (b. 1884). 1971 - Day of death of Leonard Jimmie Savage, American mathematician, and statistician (b. 1917). 1989 - Day of death of Gerrit Bol, Dutch mathematician (b. 1906). 1996 - Day of death of Max Erich (Eric) Reissner, German-American civil engineer, and mathematician (b. 1913).

November, 2 1815 - Birthdate of George Boole, English mathematician, and philosopher (d. 1864). 1826 - Birthdate of Henry John Stephen Smith, Irish mathematician (d. 1883). 1838 - In a letter to Dirichlet, Gauss deeply regretted that unfortunate circumstances had not allowed him to elaborate on his theory of class numbers of quadratic forms which he possessed as early as 1801. 1871 - Birthdate of Poul Heegaard, Danish mathematician (d. 1948).

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1911 - Birthdate of Raphael M. Robinson, American mathematician, and philosopher (d. 1995). 1914 - Day of death of Heinrich Friedrich Karl Ludwig Burkhardt, German mathematician (b. 1861). 1970 - Day of death of Abram Samoilovitch Besicovitch, Russian-British mathematician (b. 1891). 1979 - Leonid Khachiyan's ellipse algorithm for linear programming is announced in Science. 1993 - Day of death of Duro Kurepa, Yugoslav mathematician (b. 1907). 2012 - Day of death of Shreeram Shankar Abhyankar, Indian-American mathematician (b. 1930).

November, 3 1643 - Day of death of Paul Guldin, Swiss astronomer, and mathematician (b. 1577). 1664 - Robert Hooke showed an advanced copy of his work titled "Micrographia, or some Physiological Descriptions of minute bodies made by magnifying glasses with observations and inquiries thereupon" to the Royal Society in London. [83]

1832 - Day of death of John Leslie, Scottish physicist, and mathematician (b. 1766).

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1832 - Janos Bolyai wrote a letter to his father Farkas telling him of his work on non-Euclidean geometry, expressing his intent to publish a work on the theory of parallels. 1863 - Arthur Cayley gave his Inaugural lecture at Cambridge. 1867 - Birthdate of Wilhelm Kutta, German mathematician (d. 1944). 1878 - Birthdate of Arthur Byron Coble, American mathematician (d. 1966). 1896 - Birthdate of Raymond Louis Wilder, American mathematician (d. 1982). 1906 - Birthdate of Carl Benjamin Boyer, American historian of sciences, especially mathematics (d. 1976). 1911 - Day of death of George Chrystal, Scottish mathematician (b. 1851). 1918 - Day of death of Aleksandr Lyapunov, Russian mathematician, and physicist (b. 1857). 1938 - Birthdate of Martin Dunwoody, English mathematician. 1967 - Day of death of Alexander Craig Aitken, New-Zealand mathematician (b. 1895).

November, 4 1652 - Day of death of Jean-Charles della Faille, Flemish priest, and mathematician (b. 1597). 1698 - Day of death of Rasmus Bartholin, Danish physician, and mathematician (b. 1625). 1744 - Birthdate of Johann (III) Bernoulli, Swiss mathematician (d. 1807). 1765 - Birthdate of Pierre-Simon Girard, French mathematician, and engineer (d. 1836). 1833 - R.W. Hamilton presents a paper to the Irish Academy on the representation of complex numbers as ordered pairs of real numbers. 1908 - Birthdate of Viktor Vladimirovich Wagner (Vagner), Soviet mathematician (d. 1981). 1912 - Day of death of John Monroe Van Vleck, American mathematician, and astronomer (b. 1833). 1915 - Einstein presented to the Prussian Academy of Berlin the first from a series of four papers (each separated from the other by a week: the 4th, 11th, 18th, and 25th of November) in which he expounded his final version of the theory of general relativity. [146] 1921 - Birthdate of Andrew Mattei Gleason, American mathematician (d. 2008). 1929 - Birthdate of Shakuntala Devi, Indian mathematician, and astrologer (d. 2013).

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1954 - Day of death of Archibald Read Richardson, British mathematician (b. 1881). 1959 - Day of death of Friedrich Waismann, Austrian mathematician, physicist, and philosopher from the Vienna Circle (b. 1896). 1986 - Day of death of Kurt Hirsch, German-English mathematician (b. 1906). 2019 - The Breakthrough Prize Foundation announced that the Maryam Mirzakhani New Frontiers Prize has been created to be awarded to outstanding women in the field of mathematics each year. The $50,000 award will be presented to early-career mathematicians who have completed their PhDs within the past two years.

November, 5 1526 - Day of death of Scipione del Ferro, Italian mathematician (b. 1465). 1662 - Robert Hooke was appointed Curator of Experiments to the Royal Society in London. 1666 - Leibniz received his doctor's degree at the age of 20 for his essay on a new, historical method of teaching law for the University of Altdorf in Nuremberg. 1688 - Birthdate of Louis Bertrand Castel, French mathematician, and philosopher (d. 1757). 1804 - Founding of the Universities of Moscow and Kasan. 1828 - Augustus De Morgan, at the age of 22, gave his introductory lecture, “On the study of mathematics," at London University (UCL). It described the position which mathematics held in a person’s education. 1848 - Birthdate of James Whitbread Lee Glaisher, English mathematician (d. 1928). 1866 - Birthdate of Alfred Tauber, Hungarian-born Austrian mathematician (d. 1942). 1879 - Day of death of James Clerk Maxwell, Scottish physicist, and mathematician (b. 1831). 1891 - Marie Curie enrolled in the Sorbonne, two days before her 24th birthday. 1906 - Marie Curie gave her inaugural lecture as the first woman lecturer at the Sorbonne. She explained the theory of ions in gases and her treatise on radioactivity to 120 students, the public, and the press.

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1907 - Minkowski gave a lecture about Space and Time, under the title “The Relativity Principle" in the Göttingen Mathematical society. [178] 1930 - Birthdate of John Frank Adams, English mathematician (d. 1989). 1934 - Day of death of Walther von Dyck, German mathematician (b. 1856). 1952 - Birthdate of Robert Wayne Thomason, American mathematician (d. 1995). 1981 - Day of death of Stanislaw Mazur, Polish mathematician (b. 1905).

November, 6 1638 - Birthdate of James Gregory, Scottish mathematician, astronomer, and inventor of a type of reflecting telescope (d. 1675). 1656 - Day of death of Jean-Baptiste Morin, French mathematician, astrologer, and astronomer (b. 1583). 1766 - Lagrange welcomed, at age 30, to the Berlin Academy by Frederick the Great. 1781 - Birthdate of Giovanni Antonio Amedeo Plana, Italian astronomer and mathematician (d. 1864). 1880 - Day of death of Giusto Bellavitis, Italian mathematician, senator, and municipal councilor (b. 1803). 1886 - Birthdate of Ida Barney, American astronomer and mathematician (d. 1982). 1906 - Birthdate of Emma Markovna Lehmer, Russian-American mathematician (d. 2007). 1910 - In a letter to a colleague, Markov explained his motivations for changing the area of research: “The unique service of P. A. Nekrasov, in my opinion, is namely this: he brings out sharply his delusion, shared, I believe, by many, that independence is a necessary condition for the law of large numbers. This circumstance prompted me to explain, in a series of articles, that the law of large numbers… can apply also to dependent variables. In this way a construction of a highly general character was arrived at, which P. A. Nekrasov cannot even dream about. I considered variables connected in a simple chain, and from this came the idea of the possibility of extending the limit theorems of the calculus of probability also to a complex chain." Thus, “Markov chains" were born. [58] 1946 - Day of death of Dunham Jackson, American mathematician (b. 1888).

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1950 - Birthdate of Amir Aczel, Israeli-American mathematician and historian (d. 2015). 1960 - Birthdate of Amir D. Aczel, Israeli-born American mathematician (d. 2015). 1966 - Birthdate of Laurent Lafforgue, French mathematician. 1966 - Day of death of Frieda Nugel, German mathematician (b. 1884). 1979 - Day of death of Alexander Weinstein, Russian-American mathematician (b. 1897). 2013 - Item number MR3000000 was added to MathSciNet.

November, 7 1660 - Birthdate of Thomas Fantet de Lagny, French mathematician (d. 1734). 1725 - Nicolaus II and Daniel Bernoulli arrived in St. Petersburg. 1799 - Birthdate of Karl Heinrich Graffe, German mathematician (d. 1873). 1872 - Day of death of Alfred Clebsch, German mathematician (b. 1833). 1898 - Birthdate of Raphael Salem, Greek-French mathematician (d. 1963). 1906 - Birthdate of Jean Leray, French mathematician (d. 1998). 1915 - Einstein wrote David Hilbert and sent him the proofs of the November 4 paper: “I am sending you the correction to a paper in which I changed the gravitation equations". [178] 1918 - Day of death of Artemas Martin, American mathematician (b. 1835). 1936 - Day of death of Gury Vasilievich Kolosov, Russian-Soviet mathematician (b. 1867). 1968 - Day of death of Alexander Gelfond, Soviet mathematician, cryptographer (b. 1906).

November, 8 1633 - Day of death of Xu Guang-qi, Chinese mathematician (b. 1562). 1656 - Birthdate of Edmond Halley, English astronomer, and mathematician (d. 1742). 1703 - Day of death of John Wallis, English mathematician (b. 1616). 1719 - Day of death of Michel Rolle, French mathematician (b. 1652). 1843 - Birthdate of Moritz Pasch, German mathematician (d. 1930). 1846 - Birthdate of Eugenio Bertini, Italian mathematician (d. 1933).

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1848 - Birthdate of Gottlob Frege, German mathematician, and philosopher (d. 1925). 1858 - Day of death of George Peacock, English mathematician (b. 1791). 1868 - Birthdate of Felix Hausdorff, German mathematician (d. 1942). 1904 - Birthdate of William Leonard Edge, British mathematician (d. 1997). 1914 - Birthdate of George Bernard Dantzig, American mathematician (d. 2005). 1915 - Birthdate of Dmitrii Alexeevich Suprunenko, Soviet mathematician (d. 1990). 1940 - Day of death of Andrei Petrovich Kiselyov, Russian, and Soviet mathematician (b. 1852). 1949 - Claude Shannon's paper “Programming a Computer for Playing Chess," seminal in the development of computer chess and introducing the Shannon number, is received by the Philosophical Magazine. 1952 - Day of death of Gino Fano, Italian mathematician (b. 1871). 1993 - Day of death of Andrei Nikolaevich Tikhonov, Soviet mathematician (b. 1906). 2001 - Day of death of Albrecht Fröhlich, German mathematician (b. 1916). 2013 - Day of death of William C. Davidon, American physicist, mathematician (b. 1927).

November, 9 1752 - William Braikenridge, a British mathematician and theologian, was elected to the Royal Society. 1830 - Day of death of Jan ĝniadecki, Polish mathematician, philosopher, and astronomer (b. 1756). 1847 - Birthdate of Carlo Alberto Castigliano, Italian mathematician and physicist (d. 1884). 1857 - Maxwell wrote to Faraday: “Now, as far as I know, you are the first person in whom the idea of bodies acting at a distance by throwing the surrounding medium into a state of constraint has arisen, as a principle to be actually believed in" [136]. 1869 - Birthdate of Virgil Snyder, American mathematician (d. 1950). 1885 - Birthdate of Theodor Kaluza, German mathematician and physicist (d. 1954). 1885 - Birthdate of Hermann Weyl, German mathematician, physicist, and philosopher (d. 1955).

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1905 - Birthdate of Abraham Adrian Albert, American mathematician (d. 1972). 1906 - Birthdate of Yaroslav Borisovich Lopatynsky (d. 1981). 1915 - In an effort to obtain Habilitation, Emmy Noether gave a lecture before the Mathematical Society in Göttingen entitled "Uber ganze transzendente Zahlen" (On transcendental integers). On this occasion, she commented to Fischer, “Even our geographer came to hear it and found it rather too abstract; the faculty wants to make sure it's not going to be duped at the meeting by the mathematicians." Duped or not, the deal was never made; Habilitation was declared impossible because of "unmet legal requirements"! According to the Privatdozentenverordnung (regulations concerning Privatdozenten) of 1908, Habilitation could only be granted to male candidates. An appeal to the Minister of Culture was rejected. Hilbert's objection (not positively authenticated but willingly repeated) – that he couldn't see why the gender of the candidate should be an argument against admission as a Privatdozent; after all, this was a university, not a bathing establishment – effected nothing [38]. 1916 - Birthdate of Howard Levi, American mathematician (d. 2002). 1922 - Birthdate of Imre Lakatos, Hungarian mathematician and philosopher (d. 1974). 1957 - France issued a postage stamp with a portrait of Newton.

1966 - Day of death of Dan Rutherford, Scottish mathematician (b. 1906). 1981 - Day of death of Lois Wilfred Griffiths, American mathematician (b. 1899). 2012 - Day of death of Sergey Nikolsky, Russian mathematician (b. 1905).

November, 10 1619 - Descartes found the cold so bad that he locked himself in a heated room and began his contemplations. He and others consider this the

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most significant date of his entire life and the birthdate of analytic geometry. 1683 - Day of death of John Collins, English mathematician (b. 1624). 1829 - Birthdate of Elwin Bruno Christoffel, German mathematician and physicist (d. 1900). 1896 - Birthdate of Ernst Paul Heinz Prufer, German mathematician (d. 1934). 1918 - A marble monument to Tartaglia (1499-1557) was unveiled at Brescia. 1939 - Martin Farber, editor of Philosophical Essays in Memory of Edmund Husserl, invited Klein to submit a paper to the volume [84]. 1951 - Several "largest" prime numbers were announced in Nature (p. 838). For the previous 75 years, 2127 – 1 was the largest known prime. Edouard Lucas discovered it. 1970 - Day of death of Heinz Rutishauser, Swiss mathematician (b. 1918). 1983 - Microsoft announces its new product, Windows. 1984 - France issued a postal stamp honoring Evariste Galois.

1998 - Day of death of Jean Leray, French mathematician (b. 1906). 2006 - Day of death of Fokko du Cloux, Dutch mathematician and computer scientist (b. 1954). 2008 - Day of death of Kiyosi Ito, Japanese mathematician (b. 1915). 2008 - Day of death of Dorothy Vaughan, American mathematician and computer programmer (b. 1910).

November, 11 1619 - During the night, while living in Neuberg on the Danube, Descartes had a dream in which he was visited by the Angel of Truth. The angel revealed to him that mathematics was the sole key needed to unlock the secrets of nature. [126] 1729 - Birth of Louis-Antoine de Bougainville, French soldier, explorer, and mathematician (d. 1811).

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1744 - Cramer gave Euler a complete description of his rule for solving systems of linear equations. This is noteworthy because Cramer's Rule would not appear in print until six years later, where it was an appendix in his influential book "Introduction to the analysis of algebraic curves." 1844 - The terms "vector" and "scalar" were introduced by William Rowan Hamilton. Both terms appear in "On quaternions," a paper presented by Hamilton at a meeting of the Royal Irish Academy. 1895 - Birthdate of Wealthy Babcock, American mathematician (d. 1990). 1904 - Birthdate of J. H. C. Whitehead, Indian-American mathematician (d. 1960). 1906 - Birthdate of Georg Aumann, German mathematician (d. 1980). 1930 - Birthdate of Hugh Everett III, American physicist, and mathematician (d. 1982). 1954 - Day of death of Horatio Carslaw, British-Australian mathematician (b. 1870). 1967 - Day of death of Lester Randolph Ford, American mathematician (b. 1886). 1997 - John Friedlander and Henryk Iwaniec submitted a proof to the Proceedings of the National Academy of Science, showing that there are infinitely many prime numbers of the form m² + nၪ, for positive integers m and n. 2003 - G. Perelman posted the first of a series of preprints to the arXiv, in which he outlined a proof of the Poincaré conjecture. [134]

November, 12 1746 - Jacques-Alexandre-Cesar Charles, French mathematician, physicist, and inventor, was born (d. 1823). 1733 - Abraham de Moivre privately presented the normal distribution curve to some friends. 1793 - Jean Sylvain Bailly, French astronomer, mathematician, and politician, and the 1st Mayor of Paris, passed away (b. 1736). 1825 - Birth of Mikhail Vashchenko-Zakharchenko, Ukrainian mathematician (d. 1912). 1835 - Birth of Hugues Charles Robert Meray, French mathematician (d. 1911). 1906 - William Thomson (Lord Kelvin) wrote, “The unique strength of Cambridge, as a place of experimental research and as a leader in the advancement of Science generally, has depended greatly on the

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mathematical foundations given a large portion of all the undergraduates by the mathematical Tripos." 1910 - Birthdate of Hua Luogeng, Chinese mathematician (d. 1985). 1916 - Percival Lowell, American astronomer and mathematician, passed away (b. 1855). 1923 - Birthdate of Irving Stoy Reed, American mathematician and engineer (d. 2012). 1927 - Birthdate of Yutaka Taniyama, Japanese mathematician (d. 1958). 1937 - Alan Turing's paper "On computable numbers," in which he introduced the "Turing machine," was published.

November, 13 1629 - Descartes wrote to Mersenne from Amsterdam about the curve called "quadratrix." [153] 1665 - Newton tried a new approach to finding tangents "to crooked lines, however they may be related to straight ones" and developed his "fluxions," although he would not use that term until 1671. He used a small letter "o" to represent a small change in time and used "p" and "q" for what we would now call dx/dt and dy/dt, respectively. He wrote, "What is x and y in one moment will be x + o and y + oq/p in the next."

1711 - Joseph Addison wrote in The Spectator (Issue #221): "Those who are versed in the Philosophy of Pythagoras, and swear by the Tetractys, that is, the number Four, will know very well that the number Ten, which is signified by the letter X (and which has so much perplexed the town) has in it many particular powers; that it is called by Platonic writers the complete number; that One, Two, Three, and Four put together make up the number Ten, and that Ten is all. But these are not mysteries for ordinary readers to be let into. A man must have spent many years in hard study before he can arrive at a knowledge of them."

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1843 - Hamilton presents a paper on Quaternions to the Royal Irish Academy. It was also the first time when the term "associative" is used. 1857 - Faraday wrote to Maxwell: "When a mathematician engaged in investigating physical actions and results has arrived at his own conclusions, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formulae? If so would it not be a great boon to such as I to express them so? – translating them out of their hieroglyphics, that we might also work upon them by experiment. I think it must be so because I have always found that you could convey to me a perfectly clear idea of your conclusions… so clear in character that I can think and work from them." 1876 - Birthdate of Ernest Julius Wilczynski, American mathematician (d. 1932). 1884 - The London Mathematical Society awarded its first De Morgan Medal to Arthur Cayley, who "has invented and worked out the theory of invariants and in steady life-long work connected it with nearly every branch of mathematics, enriching everything he touches, and everywhere throwing open new vistas of future work." 1878 - Birthdate of Max Dehn, German-American mathematician (d. 1952). 1920 - Birthdate of Kollagunta Gopalaiyer Ramanathan, Indian mathematician (d. 1992). 1927 - Birthdate of Albert Turner Bharucha-Reid, American mathematician (d. 1985). 2002 - Day of death of Frederick Valentine Atkinson, British mathematician (b. 1916). 2014 - Day of death of Alexander Grothendieck, German-French mathematician (b. 1928).

November, 14 1716 - Day of death of Gottfried Leibniz, German mathematician and philosopher (b. 1646). 1750 - Euler creates the term "edge" for polyhedra and describes it in a letter to Goldbach. 1761 - Day of death of Giovanni Poleni, Italian mathematician (b. 1683). 1798 - Day of death of Naonobu Ajima, Japanese mathematician and astronomer (b. 1732). 1845 - Birthdate of Ulisse Dini, Italian mathematician and politician (d. 1918).

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1882 - Birthdate of Robert Lee Moore, American mathematician (d. 1974). 1954 - Day of death of Ernst Fischer, Austrian mathematician (b. 1875). 1916 - Birthdate of Roger Apery, Greek-French mathematician (d. 1994). 1919 - Birthdate of Paulette Libermann, French mathematician (d. 2007). 1933 - Birthdate of Arkadiy Onishchik, Soviet-Russian mathematician (d. 2019). 1949 - France issued stamps honoring Voltaire and the Comte de Buffon (1707-1778).

1954 - Day of death of Ernst Fischer, Austrian mathematician (b. 1875). 1971 - Day of death of Johanna Neumann, German-born mathematician (b. 1914). 1997 - Day of death of Joel Lee Brenner, American mathematician (b. 1912). 2014 - Day of death of Eugene Dynkin, Soviet-American mathematician (b. 1924).

November, 15 1593 - Giovanni Antonio Magini responds to a claim by Thomas Fincke that he had made an error in his tables because they were not in agreement with the list by Ptolemy. Magini, one of the first to use decimals, challenges Fincke to find an error. 1630 - Day of death of Johannes Kepler, German astronomer and mathematician (b. 1571). 1638 - In a letter to Mersenne, Descartes announced that every odd perfect number must be of the form ps2, where p is a prime, and cited an example, although it relied on a pseudo-prime. 1688 - Birthdate of Louis Bertrand Castel, French Jesuit mathematician (d. 1757).

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1747 - Clairaut, at a public session of the French Academy, announced that the Newtonian Theory of gravity was false but later reversed his stance. 1761 - Day of death of Giovanni Poleni, Italian mathematician (b. 1683). 1783 - Etienne de Montgolfier discussed in mathematical terms the problem of navigating balloons at the Paris Academie des Sciences. 1793 - Birthdate of Michel Chasles, French mathematician (d. 1880). 1794 - Birthdate of Franz Taurinus, German mathematician (d. 1874). 1900 - Birthdate of Laszlo Redei, Hungarian mathematician (d. 1980). 1907 - Birthdate of Edward Marczewski, Polish mathematician (d. 1976). 1922 - Day of death of Petros Protopapadakis, Greek mathematician and politician, 107th Prime Minister of Greece (b. 1854). 1942 - Birthdate of David George Crighton, British mathematician and physicist (d. 2000). 1957 - Brazil issued a stamp commemorating the centenary of the death of Auguste Compte, French mathematician, and philosopher.

November, 16 1717 - Birthdate of Jean le Rond d'Alembert, French mathematician, physicist, and philosopher (d. 1793). 1786 - Day of death of Istvan Hatvani, Hungarian mathematician (b. 1718). 1823 - Birthdate of Jacob Amsler, Swiss mathematician (d. 1912). 1835 - Birthdate of Eugenio Beltrami, Italian mathematician (d. 1900). 1886 - Birthdate of Marcel Riesz, Hungarian mathematician (d. 1969). 1897 - Birthdate of Josif Zakharovich Shtokalo, Soviet mathematician and historian of mathematics (d. 1987). 1924 - Birthdate of Louis Leithold, American mathematician (d. 2005). 1945 - Day of death of Hans Blichfeldt, American mathematician (b. 1873).

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1954 - After a visit with Albert Einstein at Princeton on Nov. 16, 1954, Linus Pauling wrote in his diary about Einstein's thoughts on the atomic bomb. 1982 - Day of death of Pavel Alexandrov, Soviet mathematician (b. 1896). 2002 - Day of death of Frank Smithies, British mathematician (b. 1912). 2013 - Day of death of Oscar Lanford, American mathematician (b. 1940).

November, 17 1597 - Birthdate of Henry Gellibrand, English astronomer, and mathematician (d. 1636). 1704 - Day of death of Valentin Heins, German arithmetician (b. 1637). 1717 - An infant found on the steps of the Church of Saint Jean-le-Rond in Paris is christened Jean-le-Rond. He later added the surname d'Alembert. 1790 - Birthdate of August Ferdinand Möbius, German mathematician, and astronomer (d. 1868). 1837 - Heliotropes are mentioned as having been invented by K. F. Gauss. In a report to the Secretary of the Treasury on November 17, 1837, Hassler wrote about their use for surveying. 1854 - Ernst Julius Schering, one of the 14 attendees of Gauss' lecture "The Method of Least Squares," enrolled at Göttingen University to study mathematics. 1891 - Karl Pearson started his thirty-eight Gresham Lectures. 1902 - Birthdate of Eugene Wigner, Hungarian physicist, and mathematician, Nobel Prize laureate (d. 1995). 1917 - Birthdate of Ruth Aaronson Bari, American mathematician (d. 2005). 1921 - Fisher reads his famous Royal Society paper, "On the Mathematical Foundations of Theoretical Statistics." 1930 - Kurt Gödel’s “On formally undecidable propositions of Principia Mathematica and related systems" was received for publication. 1930 - Harvard mathematician Oliver D. Kellogg wrote to Richard Courant in Göttingen regarding mathematical reviews. 1953 - Day of death of Pierre Humbert, French mathematician (b. 1891). 1954 - Day of death of Tadeusz Banachiewicz, Polish astronomer, mathematician, and geodesist (b. 1882). 1958 - Day of death of Yutaka Taniyama, Japanese mathematician (b. 1927).

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November, 18 1676 - Newton observes, “I see I have made myself a slave to philosophy; but if I get rid of Mr. Linus's business, I will resolutely bid adieu to it eternally, excepting what I do for my private satisfaction, or leave to come out after me; for I see a man must either resolve to put out nothing new, or to become a slave to defend it." 1752 - Goldbach writes Euler with the conjecture that every odd number greater than 3 is the sum of an odd number and twice a square (he allowed 02). Euler would reply that it was true for the first 1000 odd numbers, and then later confirmed it for the first 2500. A hundred years later, German mathematician Moritz Stern found two contradictions, 5777 and 5993. 1812 - Jean Victor Poncelet (1788-1867), a military engineer, was captured while Napoleon's army was retreating from Moscow. He profited from this enforced leisure (until his release in June 1814) by resuming his study of mathematics. While in Russia, he did important work on projective geometry. 1816 - Birthdate of Ernst Reinhold Eduard Hoppe, German mathematician (d. 1900). 1844 - Birthdate of Friedrich Heinrich Albert Wangerin, German mathematician (d. 1933). 1872 - Birthdate of Giovanni Enrico Eugenio Vacca, Italian mathematician, and historian of science (d. 1953). 1879 - After the death of Maxwell, George Stokes writes to offer Lord Rayleigh the position of head of the Cavendish Laboratory in Cambridge. 1912 - Birthdate of Shigeo Sasaki, Japanese mathematician (d. 1987). 1916 - Birthdate of David Robert Bates, Irish mathematician, and physicist (d. 1994). 1919 - Day of death of Adolf Hurwitz, Jewish German-Swiss mathematician (b. 1859). 1927 - Birthdate of John Leslie Britton, English mathematician (d. 1994). 1928 - Day of death of Alexander Ziwet, German-American mathematician (b. 1853). 1930 - Birthdate of Alessandro Faedo, Italian mathematician, and politician (d. 2001). 1933 - Day of death of Robert Forsyth Scott, British mathematician (b. 1849). 1939 - Birthdate of John McKay, British-Canadian mathematician.

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1959 - Day of death of Aleksandr Yakovlevich Khinchin, Soviet mathematician (b. 1894). 1965 - Day of death of Frank Wilcoxon, American mathematician (b. 1892). 1994 - Day of death of Maurice Auslander, American mathematician (b. 1926). 1994 - Day of death of Nathan Jacob Fine, American mathematician (b. 1916).

November, 19 1672 - Day of death of John Wilkins, English mathematician (b. 1614). 1822 - Day of death of Johann Georg Tralles, German mathematician, and physicist (b. 1763). 1857 - Arthur Cayley opens a letter to J. J. Sylvester with, “I have just obtained a theorem that appears to be very remarkable." The theorem would be the centerpiece of his Memoire on the Theory of Matrices. The theorem showed that a matrix was the solution of its own characteristic equation. 1876 - Birthdate of Tatyana Afanasyeva, Russian-Dutch mathematician, and theorist (d. 1964). 1894 - Birthdate of Heinz Hopf, German mathematician (d. 1971). 1900 - Birthdate of Mikhail Lavrentyev, Soviet mathematician, and hydrodynamicist (d. 1980). 1901 - Birthdate of Nina Bari, Soviet mathematician (d. 1961). 1927 - MacMahon in a letter expresses the view that Redfield has made a valuable contribution to the solution to MacMahon's conjecture and goes on to mention a conjecture which he himself made in his recently delivered Rouse-Ball memorial lecture. He also says that it is probable that Redfield's work would lead to a proof of it. 1964 - Birthdate of Fred Diamond, American-English mathematician. 1982 - Friedman's version of Kruskal's Theorem appeared in Science. 2004 - Day of death of Filep Laszlo, Hungarian mathematician (b. 1941).

November, 20 1711 - Robert Simson passed a simple test of his mathematical knowledge and was duly admitted as professor of mathematics at the University of Glasgow, Scotland. 1764 - Day of death of Christian Goldbach, Prussian mathematician, and theorist (b. 1690).

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1778 - Day of death of Francesco Cetti, Italian priest, zoologist, and mathematician (b. 1726). 1841 - Birthdate of Victor D'Hondt, Belgian mathematician, lawyer, and jurist (d. 1901). 1843 - Sylvester departs the US for England and describes his life as “Pretty much a blank." 1856 - Day of death of Farkas Bolyai, Romanian-Hungarian mathematician (b. 1775). 1893 - Birthdate of Andre Bloch, French mathematician (d. 1948). 1908 - Day of death of Georgy Voronoy, Ukrainian mathematician (b. 1868). 1910 - Birthdate of Willem Jacob van Stockum, Dutch mathematician, pilot (d. 1944). 1915 - Hilbert delivered a talk in Göttingen presenting his new axiomatic derivation of the “basic equations of physics" (five days prior to Einstein). 1917 - Birthdate of Leonard Jimmie Savage, American mathematician (d. 1971). 1924 - Birthdate of Benoit Mandelbrot, Polish-American mathematician, and economist (d. 2010). 1934 - Day of death of Willem de Sitter, Dutch mathematician, physicist, and astronomer (b. 1872). 1960 - Day of death of Hidehiko Yamabe, Japanese mathematician (b. 1923). 1963 - Birthdate of Timothy Gowers, English mathematician. 1986 - Day of death of Arne Carl-August Beurling, Swedish mathematician (b. 1905). 2006 - Day of death of Zoia Ceausescu, Romanian mathematician (b. 1950).

November, 21 1652 - Day of death of Jan Brozek, Polish mathematician, physician, and astronomer (b. 1585). 1675 - Leibniz found the equation ydx = d(xy) - xdy, giving an expression for d(xy), which he observed to be true for all curves. 1811 - Gauss to Bessel: “One should never forget that the functions, like all mathematical constructions, are only our own constructions." 1866 - Day of death of Gustav Roch, German mathematician (b. 1839). 1867 - Birthdate of Dmitrii Matveevich Sintsov, Soviet mathematician (d. 1946).

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1913 - Birthdate of Gunnar Kangro, Estonian mathematician (d. 1975). 1933 - Birthdate of Etta Zuber Falconer, American educator, and mathematician (d. 2002). 1973 - Mexico issued a stamp portraying an Aztec calendar stone and another with the mathematician and astronomer Carlos de Siguenza y Gongora (1645-1700).

1978 - Day of death of Francesco Giacomo Tricomi, Italian mathematician (b. 1897). 1980 - Day of death of Laszlo Redei, Hungarian mathematician (b. 1900). 1991 - Day of death of Hans Zassenhaus, German-American mathematician (b. 1912).

November, 22 1784 - Day of death of Paolo Frisi, Italian mathematician, astronomer, and physicist (b. 1728). 1796 - Birthdate of Charles Bonnycastle, American mathematician (d. 1840). 1803 - Birthdate of Giusto Bellavitis, Italian mathematician, senator, and municipal councillor (d. 1880). 1840 - Birthdate of Emile Michel Hyacinthe Lemoine, French mathematician (d. 1912). 1850 - Sylvester was called to the Bar. Rather than practicing law, he gave private instruction in mathematics, and among his pupils was Florence Nightingale. 1930 - Day of death of Peter Pinkerton, Scottish mathematician (b. 1870). 1944 - Day of death of Arthur Stanley Eddington, English astrophysicist, and mathematician (b. 1882). 1986 - Day of death of Nikolai Grigor'evich Chudakov, Soviet mathematician (b. 1904). 1996 - Day of death of Garrett Birkhoff, American mathematician (b. 1911).

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2001 - Day of death of Luis Antonio Santaló Sors, Spanish mathematician (b. 1911). 2007 - Day of death of Andrew Ronald Mitchell, British mathematician (b. 1921).

November, 23 Fibonacci Day is an annual holiday celebrated on November 23rd (11/23 in the month/day date format). Here are the corrected historical events: 1604 - Day of death of Francesco Barozzi, Italian mathematician, astronomer, and humanist (b. 1537). 1616 - Birthdate of John Wallis, British mathematician (d. 1703). 1654 - From 10:30 to 12:30 in the evening, Pascal was driving a four-inhand when the horses ran away. The two leaders dashed over the parapet of the bridge at Neuilly, and Pascal was saved only by the traces breaking. He experienced a religious ecstasy that led him to give up his intermittent interest in mathematics and devote his time to religious contemplation.* 1670 - James Gregory writes to John Collins, introducing the first use of what will come to be called the Newton-Gregory interpolation formula [10]. 1820 - Birthdate of Isaac Todhunter, English mathematician (d. 1884). 1821 - Thomas Jefferson writes to West Point Instructor Claudius Crozet to thank him for the gift of a copy of his "A Treatise on Descriptive Geometry" and praises the book and the author. 1823 - Janos Bolyai wrote to his father, saying, "I have made such wonderful discoveries that I am myself lost in astonishment." He was referring to his discovery of non-Euclidean geometry, which was published in 1833. 1853 - Birthdate of George Bruce Halsted, American mathematician (d. 1922). 1882 - Birthdate of Arnold Dresden, Dutch-American mathematician (d. 1954). 1917 - Birthdate of Elizabeth Scott, American mathematician (d. 1988). 1942 - Day of death of Stanislaw Saks, Polish mathematician (b. 1897). 1942 - Day of death of Stanislaw Zaremba, Polish mathematician (b. 1863). 1982 - Poland issued stamps honoring the mathematicians Stanislaw Zaremba (1863-1942), Waclaw Sierpinski (1882-1969), Zygmunt Janiszewski (1888-1920), and Stefan Banach (1892-1945).

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* Pascal described it as (from an English translation given in Marvin O'Connell's book “Blaise Pascal, Reasons of the Heart")

The year of grace 1654. Monday, 23 November, feast of St. Clement, pope and martyr and others in the martyrology. The eve of Saint Chrysogonus martyr and others. From about half-past ten in the evening until about half-past midnight. Fire. The God of Abraham, the God of Isaac, the God of Jacob. Not of the philosophers and intellectuals. Certitude, certitude, feeling, joy, peace. The God of Jesus Christ. My God and your God [in Latin, accusative case]. Your God will be my God. Forgetfulness of the world and of everything except God. One finds oneself only by way of the directions taught in the gospel. The grandeur of the human soul. Oh just Father, the world has not known you, but I have known you. Joy, joy,,, joy, tears of joy. I have separated myself from him.______________ They have abandoned me, the fountain of living water [in Latin]. My God, will you leave me? May I not be separated from him eternally. This is eternal life, that they know you the one true God and J.C. whom you have sent. Jesus Christ.____________________ Jesus Christ.______________ I have separated myself from him. I have run away from him, renounced him, crucified him. May I never be separated from him._______________ One preserves oneself only by way of the lessons taught in the gospel. Renunciation total and sweet. And so forth. [80]

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November, 24 1759 - Lagrange wrote Euler that he believed that he had developed the true metaphysics of the calculus; at that time he seems to have been convinced that the use of infinitesimals was rigorous. Lagrange attempted to prove Taylor's Theorem, the power of which he was the first to observe, and then to develop the entire calculus from it. 1789 - Lagrange finished his Mecanique analytique.

1858 - Dedekind discovered his cuts, representing real numbers in terms of rationals, thereby providing the first correct definition of continuity. 1864 - George Boole walked three miles from his home in Ballintemple to Queen's College in Cork, Ireland, in a pouring rain so as not to miss a lecture. He lectured in wet clothes, caught a cold, and died two weeks later at the age of 49. [108] 1879 - Birthdate of Duncan MacLaren Young Sommerville, New Zealand mathematician (d. 1934). 1888 - On Thanksgiving Day, six members of the mathematics department at Columbia University met to form a society for the purpose of discussing mathematics and reading papers of mathematical interest. A month later, they christened it the New York Mathematical Society. By 1894, the society had attained a national character, so its name was changed to the American Mathematical Society. The six founding members were J. H. Van Amring (the first president), Thomas Scott Fiske, Rees (a professor), Jacoby, Stabler (fellow students with Fiske), and Maclay (a graduate student). [41] 1909 - Birthdate of Gerhard Gentzen, German mathematician (d. 1945). 1918 - Richard Courant signed a contract for the series of books now famous as the “Yellow Series" [139]. 1947 - C.P. Snow wrote to his brother Phillip, “Hardy is now dying (how long it will take no one knows, but he hopes it will be soon), and I have to spend most of my spare time at his bedside" [2].

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1948 - Birthdate of Lawrence F. Martinek, American mathematics educator. 1982 - Sweden issued five stamps honoring Nobel Prize winners Niels Bohr, Erwin Schrödinger, Louis de Broglie, Paul Dirac, and Werner Heisenberg. 1987 - Day of death of Hans Herbert Schubert, German mathematician (b. 1908). 2008 - Day of death of John Robert Stallings, American mathematician (b. 1935).

November, 25 1658 - The prize committee for Pascal's cycloid problems decided not to award the prize of sixty Spanish gold doubloons to anyone. The problems were announced on October 1, 1658. 1694 - Day of death of Ismael Bullialdus, French astronomer, and mathematician (b. 1605). 1730 - By studying prime divisors of numbers of the form 2p - 1, Euler discovered "Fermat's Little Theorem" [104]. 1731 - Euler introduced the letter e as the base for natural logarithms, writing in a letter, “e denotat numerum, cuius logarithmus hyperbolicus = 1," though he may have used the notation in his manuscripts as early as 1727. 1783 - Birthdate of Claude-Louis Mathieu, French astronomer, and mathematician (d. 1875). 1804 - Gauss, in a letter to his close friend Farkas Bolyai, explains that he does not agree with Bolyai's claim that he had put Euclidean Geometry on Solid Ground. He expresses his hope that Bolyai will succeed in his work. 1840 - The term "mean curvature" appears in 1840 in J. R. Young's "Mathematical Dissertations" (1841). (The preface is dated Nov. 25, 1840.) 1841 - Birthdate of Ernst Schroder, German mathematician (d. 1902). 1907 - The Warsaw Scientific Society held its first general meeting. 1915 - Einstein presented the final version of the field equations [146]. 1936 - Day of death of Edouard-Jean-Baptiste Goursat, French mathematician (b. 1858). 1937 - Day of death of Alessandro Padoa, Italian mathematician (b. 1868). 1943 - Birthdate of Evelyn Merle Nelson, Canadian mathematician (d. 1987).

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1952 - Day of death of Edward Vermilye Huntington, American mathematician (b. 1874). 1952 - Portugal issued two stamps commemorating the centenary of the birth of the mathematician Francisco Gomes Teixeira (1851-1932).

1978 - Day of death of Eduard L. Stiefel, Swiss mathematician (b. 1909). 1988 - Day of death of Dmitrii Evgenevich Menshov, Soviet mathematician (b. 1892). 1990 - Day of death of Ernest Roland Duncan, New Zealand-born mathematician, Australian headmaster, and American professor (b. 1916). 1993 - Day of death of Hans-Egon Richert, German mathematician (b. 1924). 2008 - Day of death of Beno Eckmann, Swiss mathematician (b. 1917). 2012 - Day of death of Lars Hörmander, Swedish mathematician, and educator (b. 1931).

November, 26 1750 - Euler presents his famous formula Vertices + Faces - 2 = Edges to the Berlin Academy. The proof is read to the Berlin Academy on September 9, 1751. 1864 - Charles Dodgson gives Alice Liddell a hand-printed copy of Alice's Adventures under Ground, a work he wrote for her. This was reproduced by Dover in 1965. (See 4 July 1862 entry). 1894 - Birthdate of Norbert Wiener, American-Swedish mathematician, and philosopher (d. 1964). 1915 - Einstein wrote his close friend Heinrich Zangger: "The general relativity problem is finally dealt with. The perihelion motion of Mercury is explained wonderfully by the theory… The theory has unique beauty. Only one colleague has understood it really, but he tries in a tricky way to 'nostrify' it (an expression due to Abraham). In my personal experience, I have not learned any better the wretchedness of

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the human species as on the occasion of this theory and everything related to it. However, that does not concern me in the slightest." 1916 - Day of death of Zoard Geocze de Szendro, Hungarian mathematician (b. 1873). 1936 - Day of death of Edouard(-Jean-Baptiste) Goursat, French mathematician (b. 1858). 1940 - Birthdate of Enrico Bombieri, Italian mathematician. 1949 - Albert Einstein published an essay in the Saturday Review of Literature in which he described the most pivotal moments in his childhood. The first involved a compass that his father showed him when he was four or five. Einstein recalled his sense of wonderment that the needle always pointed north, even though nothing appeared to be pulling it in that direction. He came to a conclusion, then and there, about the structure of the physical world: “Something deeply hidden had to be behind things." The second moment occurred soon after he turned twelve, when he was given “a little book dealing with Euclidean plane geometry." The book's “lucidity," he wrote – the idea that a mathematical assertion could “be proved with such certainty that any doubt appeared to be out of the question" – provoked “wonder of a totally different nature." Pure thought could be just as powerful as geomagnetism. 1965 - Day of death of Hilda Hudson, English mathematician (b. 1881). 1968 - Day of death of Georgii Nikolaevich Polozii, Soviet mathematician (b. 1914). 1977 - Day of death of Ruth Moufang, German mathematician (b. 1905). 1981 - Day of death of Max Euwe, Dutch chess player, and mathematician (b. 1901). 1990 - Day of death of Richard Alan Day, Canadian mathematician (b. 1941). 2015 - Day of death of Amir Aczel, Israeli-American mathematician, and historian (b. 1950).

November, 27 1701 - Birthdate of Anders Celsius, Swedish astronomer, physicist, and mathematician (d. 1744). 1727 - Isaac Greenwood began his "private" lectures as Hollis Professor of Mathematics and Natural Philosophy at Harvard. These lectures were given to selected students and required parental permission, probably to ensure payment of the attendance fee of forty shillings.

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1754 - Day of death of Abraham de Moivre, French-English mathematician (b. 1667). 1849 - Birthdate of Horace Lamb, English mathematician (d. 1934). 1852 - Day of death of Ada Lovelace, English mathematician, and computer scientist (b. 1815). 1867 - Birthdate of Arthur Lee Dixon, British mathematician (d. 1955). 1875 - Johns Hopkins University offered J. J. Sylvester $5000 a year plus moving expenses to assume the math professorship. He set three conditions under which he would accept: The sum be paid in gold, the university provides a residence, and that he be allowed to appropriate student fees. Only the first condition was acceptable to the university, but Sylvester agreed when the offer was increased to $6000 in gold. Shortly after arriving, he founded the American Journal of Mathematics. 1895 - Alfred Nobel had his will drawn up in Paris, then deposited it in a bank in Stockholm. 1904 - Day of death of Paul Tannery, French mathematician, and historian of mathematics (b. 1843). 1909 - Birthdate of Anatoly Maltsev, Soviet mathematician, and theorist (d. 1967). 1914 - Birthdate of Edward Griffith Begle, American mathematician (d. 1978). 1918 - Ukrainian Academy of Science is founded.

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1923 - Birthdate of J. Ernest Wilkins Jr., American nuclear scientist, mechanical engineer, and mathematician (d. 2011). 1934 - Birthdate of Gilbert Strang, American mathematician. 1979 - The New York Times, in an article entitled "Soviet mathematician is obscure no more," reported on Leonid Khachiyan, the 27-year-old discoverer of a polynomial-time algorithm for linear programming. 1998 - Day of death of Moshe Flato, Israeli-French mathematician, and theoretical physicist (b. 1937).

November, 28 1660 - The Royal Society of London is founded. 1679 - Newton writes to the Royal Society, suggesting that if falling objects were studied, they would find a consistent deviation east due to the rotation of the Earth. 1700 - Birthdate of Nathaniel Bliss, English astronomer, and mathematician (d. 1764). 1821 - Day of death of Samuel Vince, English clergyman, mathematician, and astronomer (b. 1749). 1898 - Birthdate of John Wishart, Scottish mathematician, and agricultural statistician (d. 1956). 1905 - Birthdate of Albert William Tucker, Canadian-American mathematician (d. 1995). 1915 - Birthdate of Wilfred Kaplan, American mathematician (d. 2007). 1943 - Day of death of Eduard Helly, Austrian mathematician (b. 1884). 1952 - Day of death of Fritz Carlson, Swedish mathematician (b. 1888). 1968 - Day of death of Jean Frederic Auguste Delsarte, French mathematician (b. 1903). 1968 - Day of death of Leonard Roth, British mathematician (b. 1904). 1969 - Day of death of Elbert Frank Cox, American mathematician (b. 1895).

November, 29 1692 - Huygens, in a letter to L'Hospital, gave the first complete sketch of the folium of Descartes. Although the curve was first discussed August 23, 1638, no complete sketch had previously been given due to a reluctance to use negative numbers as coordinates.

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1759 - Day of death of Nicolaus I Bernoulli, Swiss mathematician (b. 1687). 1803 - Birthdate of Christian Doppler, Austrian mathematician, and physicist (d. 1853). 1847 - Birthdate of Alfred George Greenhill, English mathematician (d. 1927). 1849 - Birthdate of Horace Lamb, English applied mathematician (d. 1934). 1872 - Day of death of Mary Somerville, Scottish-Italian astronomer, and mathematician (b. 1780). 1873 - Birthdate of Suzan Rose Benedict, American mathematician (d. 1942). 1873 - Cantor first writes to Dedekind about the totality of positive rational numbers [135]. 1879 - Birthdate of Nikolai Mitrofanovich Krylov, Russian and Soviet mathematician (d. 1955). 1892 - Birthdate of Gustav Doetsch, German mathematician (d. 1977). 1935 - Day of death of Ivar Otto Bendixson, Swedish mathematician (b. 1861). 1952 - Birthdate of John David Barrow, English cosmologist, theoretical physicist, and mathematician. 1953 - Day of death of Ernest William Barnes, English mathematician, and theologian (b. 1874). 1959 - Birthdate of Richard Borcherds, South African-English mathematician. 1992 - Birthdate of Jean Dieudonné, French mathematician (b. 1906).

November, 30 1549 - Birthdate of Sir Henry Savile, English mathematician (d. 1622). 1647 - Day of death of Bonaventura Cavalieri, Italian mathematician, and astronomer (b. 1598).

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1703 - Isaac Newton was made president of the Royal Society, an office he held until his death in 1727. 1712 - William Jones was elected a fellow of the Royal Society. 1836 - Day of death of Pierre-Simon Girard, French mathematician, and engineer (b. 1765). 1841 - George Boole became involved in the Lincoln Topographical Society, serving as a member of the committee, and presenting a paper entitled, "On the origin, progress, and tendencies of Polytheism, especially amongst the ancient Egyptians and Persians, and in modern India." 1844 - Birthdate of Constantin Climescu, Romanian mathematician (d. 1926). 1852 - Birthdate of Andrei Petrovich Kiselyov, Russian and Soviet mathematician (d. 1940). 1861 - Birthdate of Paul Rudolf Eugen Jahnke, German mathematician (d. 1921). 1877 - Luigi Bianchi received his degree in mathematics. 1891 - Birthdate of Edward Lindsay Ince, British mathematician (d. 1941). 1910 - Birthdate of Franz Leopold Alt, Austrian-born American mathematician (d. 2011). 1921 - Day of death of Karl Hermann Amandus Schwarz, German mathematician (b. 1843). 1936 - Birthdate of Dmitri Anosov, Soviet-Russian mathematician (d. 2014). 1937 - Birthdate of Andrei Roiter, Soviet-Ukrainian mathematician (d. 2006). 2005 - Jason Doucette's algorithm and program (using Benjamin Despres' reversal-addition code) found that 1,186,060,307,891,929,990 takes 261 iterations to reach the 119-digit palindrome in the reverse-and-add process, and thus it is not a Lychrel number.

CHAPTER TWELVE DECEMBER

December, 1 1671 - Birthdate of John Keill, Scottish mathematician, and natural philosopher (d. 1721). 1729 - Day of death of Giacomo F. Maraldi, French-Italian astronomer, and mathematician (b. 1665). 1729 - Goldbach, in his first letter to Euler, asks whether Euler knows Fermat's claim that all numbers are prime [104]. 1750 - Day of death of Johann Gabriel Doppelmayr, German mathematician, astronomer, and cartographer (b. 1671). 1792 - Birthdate of Nikolai Lobachevsky, Russian geometer (d. 1856). 1890 - After regular competition, Peano was named an extraordinary professor of infinitesimal calculus at the University of Turin. 1892 - Birthdate of Krishnaswami Ayyangar, Indian mathematician (d. 1953). 1928 - Birthdate of Lee Albert Rubel, American mathematician (d. 1995). 1940 - Birthdate of Yuri Kozachenko, Soviet-Ukrainian mathematician (d. 2020). 1947 - Day of death of G. H. Hardy, English mathematician, and theorist (b. 1877). 1977 - Day of death of Kenneth O. May, American mathematician, and historian of mathematics (b. 1915). 1983 - Day of death of Leonid Mirsky, Russian-British mathematician (b. 1918).

December, 2 1594 - Day of death of Gerardus Mercator, Flemish mathematician, cartographer, and philosopher (b. 1512). 1831 - Birthdate of Paul David Gustav du Bois-Reymond, German mathematician (d. 1889). 1865 - Birthdate of Niels Nielsen, Danish mathematician (d. 1931).

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1873 - Day of death of Karl Heinrich Graffe, German mathematician (b. 1799). 1901 - Birthdate of Dom George Frederick James Temple, English mathematician (d. 1992). 1914 - Birthdate of Robert Palmer Dilworth, American mathematician (d. 1993). 1966 - Day of death of L. E. J. Brouwer, Dutch mathematician, and philosopher (b. 1881). 1978 - Science News reports that 221.701 - 1 is prime. 1982 - Day of death of Geoffrey Timms, British mathematician, and cryptoanalyst (b. 1903). 1984 - Birthdate of Maryna Sergiivna Viazovska, Ukrainian mathematician. 2006 - Day of death of Dikran Tahta, British-Armenian mathematician (b. 1928).

December, 3 1616 - Birthdate of John Wallis, English mathematician, and cryptographer (d. 1703). 1938 - Birthdate of Sally Shlaer, American mathematician, and engineer (d. 1998). 1956 - Day of death of Felix Bernstein, German mathematician (b. 1878). 1967 - Day of death of Marie Francoise Ouedraogo, Burkinabe mathematician. 1983 - Day of death of Elliott Waters Montroll, American mathematician (b. 1916). 1984 - Day of death of Vladimir Abramovich Rokhlin, Soviet mathematician (b. 1919). 2004 - Day of death of Shiing-Shen Chern, Chinese-American mathematician (b. 1911). 2010 - Day of death of Cora Susana Sadosky de Goldstein, ArgentinianAmerican mathematician (b. 1940). 2014 - Day of death of James Stewart, Canadian mathematician (b. 1941).

December, 4 1131 - Day of death of Omar Khayyam, Persian poet, astronomer, mathematician, and philosopher (b. 1048). 1409 - University of Leipzig established. 1574 - Day of death of Georg Joachim Rheticus, Austrian-Slovak mathematician, and cartographer (b. 1514).

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1679 - Day of death of Thomas Hobbes, English scholar, and amateur mathematician (b. 1588). 1680 - Day of death of Thomas Bartholin, Danish physician, mathematician, and theologian (b. 1616). 1806 - Birthdate of John Thomas Graves, Irish jurist, and mathematician (d. 1870). 1886 - Birthdate of Ludwig Georg Elias Moses Bieberbach, German mathematician (d. 1982). 1890 - Birthdate of Harry Clyde Carver, American mathematician (b. 1977). 1915 - Hilbert had presented to the Göttingen Academy of Science a “Second Communication" on the “Foundations of Physics" [146]. 1934 - Day of death of Horace Lamb, English mathematician (b. 1849). 1938 - Birthdate of George Eyre Andrews, American mathematician. 1980 - Ireland issued a stamp picturing Robert Boyle (1627-1691) and his 1659 Air Pump.

2015 - Day of death of Lajos Takacs, Hungarian mathematician (b. 1924). 2020 - Day of death of Anatoly Mykhailovych Samoilenko, Ukrainian mathematician (b. 1938).

December, 5 1708 - Day of death of Takakazu Seki Kawa, Japanese mathematician (b. 1642). 1735 - Euler presents his paper on “The sums of Series of reciprocals" to the St. Petersburg Academy. 1770 - Day of death of James Stirling, Scottish mathematician, and surveyor (b. 1692). 1859 - Day of death of Louis Poinsot, French mathematician, and physicist (b. 1777).

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1825 - Abel wrote how delighted he was that Crelle was starting a new mathematics journal, for this meant he would now have a place to publish his research. The first volume contained seven papers by Abel. 1863 - Birthdate of Paul Painleve, French mathematician, and politician, 84th Prime Minister of France (d. 1933). 1883 - J. J. Sylvester, in Baltimore, received a cable containing the single word, “Elected," informing him of his appointment as Savilian Professor of Geometry at Oxford. This ended his seven-year stay at Johns Hopkins University. 1895 - Birthdate of Elbert Frank Cox, American mathematician (d. 1969). 1901 - Birthdate of Werner Karl Heisenberg, German physicist, and philosopher (d. 1976). 1979 - Iran issued a stamp commemorating the 600th anniversary of the death of the mathematician Ghyath-al-din Jamshid Kashani.

1999 - Day of death of Nathan Jacobson, American mathematician (b. 1910). 2005 - Day of death of Claude Ambrose Rogers, English mathematician (b. 1920).

December, 6 1592 - Galileo delivered his inaugural lecture at the University of Padua, Republic of Venice, where he would teach geometry and astronomy for 18 years. 1616 - Day of death of Ahmad Ibn al-Qadi, Moroccan writer, judge, and mathematician (b. 1552). 1682 - Birthdate of Giulio Carlo Fagnano dei Toschi, Italian mathematician (d. 1766). 1788 - Day of death of Nicole-Reine Lepaute, French astronomer and mathematician (b. 1723). 1856 - Birthdate of Walther Franz Anton von Dyck, German mathematician (d. 1934).

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1880 - Birthdate of Pierre Leon Boutroux, French mathematician, and historian of science (d. 1922). 1908 - Birthdate of Herta Freitag, Austrian-American mathematician (d. 2000). 1917 - Kuratowski gave a talk, “On the definitions in mathematics," which became his first published paper. 1941 - Birthdate of Filep Laszlo, Hungarian mathematician (d. 2004). 1956 - The knapsack problem was first named and discussed by George B. Dantzig, the father of linear programming. 1959 - Day of death of Erhard Schmidt, German mathematician (b. 1876). 1963 - Day of death of Archibald Henderson, American mathematician and writer (b. 1877). 1963 - Time magazine published a copy of Salvador Dali's “Fifty abstract pictures which as seen from two yards change into three Lenines masquerading as Chinese and as seen from six yards appear as the head of a royal tiger." It is based on the semi-regular tessellation 4 - 3 - 4 - 3 - 3 made up of squares and triangles.

1973 - Day of death of Joseph Leonard Walsh, American mathematician (b. 1895). 1990 - Day of death of Lev Arkad'evich Kaluznin, Soviet mathematician (b. 1914). 1996 - Day of death of Stefan Schwarz, Slovakian mathematician (b. 1914).

December, 7 1637 - Birthdate of William Neile, English mathematician, and founder member of the Royal Society (d. 1670).

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1647 - Birthdate of Giovanni Ceva, Italian mathematician (d. 1734). 1676 - The first public release of Ole Romer's conjecture that the speed of light was finite is published in the Journal des savans. 1725 - The first meeting of the Petersburg Academy of Science was held in a meeting room of the palace of Baron Peter Pavlovich Sharov. The meeting featured discussion of the physics theories of Wolff and Leibniz. 1823 - Birthdate of Leopold Kronecker, Polish-German mathematician (d. 1891). 1826 - Birthdate of Ludwig Christian Wiener, German mathematician, physicist, and philosopher (d. 1896). 1830 - Birthdate of (Antonio) Luigi (Gaudenzio Giuseppe) Cremona, Italian mathematician (d. 1903). 1873 - Cantor wrote Dedekind that the real numbers are uncountable. Five days earlier he had written that he “had never seriously concerned himself with the problem since it seemed to have no practical value." 1903 - Birthdate of Danilo Blanusa, Croatian mathematician, and physicist (d. 1987). 1912 - Day of death of George Howard Darwin, mathematical astronomer, the fifth child of the evolutionist Charles Darwin (b. 1845). 1924 - Birthdate of Mary Ellen Rudin, American mathematician (d. 2013). 1928 - Day of death of James Whitbread Lee Glaisher, English mathematician (b. 1848). 1936 - Birthdate of Oleksandr Mikolaiovich Sharkovsky, Soviet Ukrainian mathematician. 1943 - Birthdate of Nicholas Katz, American mathematician. 1957 - Birthdate of Sergiy Kolyada, Ukrainian mathematician (d. 2018). 1967 - Gödel, discussing issues related to Skolem's work, wrote to Wang: “This blindness (or prejudice, or whatever you might call it) of logicians is indeed surprising. But I think the explanation is not hard to find. It lies in a widespread lack, at that time, of the required epistemological attitude towards metamathematics and towards nonfinitary reasoning… I might add that my objectivistic conception of mathematics and metamathematics in general, and of transfinite reasoning in particular, was fundamental also to my other work in logic." 2011 - Day of death of Tonny Albert Springer, Dutch mathematician (b. 1926).

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December, 8 1594 - Birthdate of Pierre Petit, French astronomer, physicist, mathematician, and instrument maker (d. 1677). 1632 - Day of death of Albert Girard, French-Dutch mathematician (b. 1595). 1632 - Day of death of Johan Philip Lansberge, Dutch Calvinist minister, astronomer, and mathematician (b. 1561). 1795 - Birthdate of Peter Andreas Hansen, Danish astronomer, and mathematician (d. 1874). 1864 - Day of death of George Boole, English mathematician, and philosopher (b. 1815). 1865 - Birthdate of Jacques Hadamard, French mathematician (d. 1963). 1883 - Birthdate of Ludwig Berwald, Czech mathematician (d. 1942). 1894 - Birthdate of Pafnuty Chebyshev, Russian mathematician, and theorist (b. 1821). 1919 - Birthdate of Julia Robinson, American mathematician (d. 1985). 1931 - Saunders MacLane, then a student at Göttingen, wrote his mother: “Prof. Noether's lectures (she is a woman – a member of a noted mathematical family) are also excellent… Prof. Noether thinks fast and talks faster. As one listens, one must also think fast – and that is always excellent training. Furthermore, thinking fast is one of the joys of mathematics." 1948 - Birthdate of Luis Caffarelli, Argentinian-American mathematician. 1955 - Day of death of Hermann Klaus Hugo Weyl, German mathematician, theoretical physicist, and philosopher (b. 1885). 1961 - Day of death of Francesco Severi, Italian mathematician (b. 1879). 1966 - Day of death of Arthur Byron Coble, American mathematician (b. 1878). 1973 - Day of death of Griffith Conrad Evans, American mathematician (b. 1887). 1969 - Birthdate of Kristin Lauter, American mathematician, and cryptographer.

December, 9 1048 - Day of death of Al-Biruni, Persian mathematician (b. 973). 1508 - Birthdate of Gemma Frisius, Dutch mathematician and cartographer (d. 1555). 1571 - Birthdate of Metius, Dutch mathematician and astronomer (d. 1635).

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1667 - Birthdate of William Whiston, English mathematician, historian, and theologian (d. 1752). 1675 - Newton writes to Leibniz to comment on the response to his theory that light was corpuscular, "I was so persecuted with discussions arising from the publication of my theory of light, that I blamed my own imprudence for parting with so substantial a blessing as my quiet, to run after a shadow." 1703 - Birthdate of Chester Moor Hall, English jurist, and mathematician (d. 1771). 1741 - Euler writes to Goldbach: "I have lately also found a remarkable paradox. Namely that the value of the expression (2i + 2-i)/2 is approximately equal to 10/13 and that this fraction differs only in parts per million from the truth. The true value of this expression, however, is the cosine of the arc .6931471805599 (ln(2)) or the arc of 39 degrees 42 min. 51 sec. 52 tenths of sec. and 9 hundredths of sec. in a circle of radius one." 1839 - Birthdate of Gustav Roch, German mathematician (d. 1866). 1866 - Day of death of James P. Pierpont, American mathematician (b. 1866). 1883 - Birthdate of Nikolai Luzin, Soviet mathematician, theorist (d. 1950). 1907 - Birthdate of Max Deuring, German mathematician (d. 1984). 1911 - Henri Poincare wrote the editor of a mathematical journal to ask if, contrary to custom, an unfinished piece of work could be published. He explained that at his age he may not be able to finish it, but that his work might provide ideas for another. The paper was published, and not long afterward, George David Birkhoff (1884-1944) completed the solution. 1917 - Birthdate of Sergei Vasilyevich Fomin, Soviet mathematician (d. 1975). 1939 - Day of death of James P. Pierpont, American mathematician (b. 1866). 1941 - Birthdate of Kirsti Muller Andersen (Kirsti Pedersen), Danish historian of mathematics. 1957 - Birthdate of Aleksandr Ivanovich Nekrasov, Soviet mathematician (d. 1957). 1958 - Day of death of John Jackson (b. 1887). 1968 - The first demonstration of the use of a computer mouse was given at the American Federation of Information Processing Societies' Fall Joint Computer Conference at Stanford University, California. 1969 - Birthdate of Raphael Rouquier, French mathematician.

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December, 10 1269 - The Flemish Dominican priest Willem van Moerbeke completed the first translation of the works of Archimedes into Latin. 1452 - Birthdate of Johannes Stoffler, German mathematician, and astronomer (d. 1531). 1478 - The Treviso Arithmetic, the first printed mathematics text, was published in Treviso, Italy, as Arte dell'Abbaco by an unknown author. 1626 - Day of death of Edmund Gunter, English mathematician (b. 1581). 1672 - In a letter to Collins, Newton describes a method of drawing tangents to curves given by f(x, y) = 0 whose equations are polynomials in x and y and says: "This is one particular, or rather corollary, of a general method, which extends itself, without any troublesome calculation, not only to the drawing of tangents to any curve lines, whether geometrical or mechanical, or anyhow respecting right lines or other curves, but also to the resolving other abstruser kinds of problems about the crookedness, areas, lengths, centers of gravity of curves, etc.; nor is it (as Hudden's method of Maximis and Minimis) limited to equations which are free from surd quantities. This method I have interwoven with that other of working in equations, by reducing them to infinite series." 1684 - Halley at Royal Society meetings reported that he'd seen Newton in Cambridge, who had "showed him a curious treatise, De Motu, [De motu corporum in gyrum] which, upon Mr Halley's desire, was, he said, promised to be sent to the Society to be entered upon their register." 1701 - Newton resigned his Lucasian professorship at Cambridge, having been at the mint since 1696. 1799 - Delambre and Mechain measured the meridian from Dunkirk to Barcelona, completing their work in 1799 and leading to the formal definition of the meter. 1804 - Birthdate of Carl Gustav Jacob Jacobi, German mathematician (d. 1851). 1815 - Birthdate of Ada Lovelace, English mathematician and computer scientist (d. 1852). 1858 - Arthur Cayley's A Memoir on the Theory of Matrices was received at the Royal Society. 1901 - The first Nobel Prizes were awarded. 1920 - Birthdate of Alfred Goldie, English mathematician (d. 2005). 1928 - The Netherlands issued a stamp with a portrait of Christiaan Huygens.

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1934 - Bourbaki began at 12 noon when H. Cartan, Chevalley, Delsarte, Dieudonné, René de Possel, and Weil met for lunch at the Café Capoulade. This group, with some variations, met regularly at the Café. The group was not named and officially announced until the following summer, so the earlier group has been called ProtoBourbaki. 1961 - Birthdate of Oded Schramm, Israeli-American mathematician (d. 2008). 1968 - Day of death of Clement Vavasor Durell, English mathematician and writer of mathematical books (b. 1882). 1995 - Day of death of Sarvadaman D. S. Chowla, Indian mathematician (b. 1907). 2016 - Day of death of Felix Browder, American mathematician (b. 1927).

December, 11 1610 - Galileo composed the cypher "The mother of love emulates the figures of Cynthia" to "copyright" his claim that Venus had phases like the moon. This idea, which may have been cribbed from a student, provided the first hard evidence that the Earth revolved around the Sun. 1781 - Birthdate of David Brewster, Scottish physicist, mathematician, and astronomer (d. 1868). 1740 - Birthdate of Anders Johan Lexell, Swedish-Russian astronomer, mathematician, and physicist (d. 1784). 1840 - Birthdate of Carl Johannes Thomae, German mathematician (d. 1921). 1845 - Birthdate of Vaclav Jerabek, Czech mathematician (d. 1931). 1867 - James Clerk Maxwell wrote to Peter Guthrie Tait with a thought experiment for violating the Second Law of Thermodynamics that came to be known as Maxwell's Demon. 1873 - Birthdate of Josip Plemelj, Slovenian mathematician (d. 1967).

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1882 - Birthdate of Max Born, German physicist and mathematician, Nobel Prize laureate (d. 1970). 1884 - Birthdate of Otto Szasz, Hungarian mathematician (d. 1952). 1884 - Hilbert defended his doctoral dissertation. 1906 - Birthdate of Samarendra Nath Roy, Indian-American mathematician and an applied statistician (d. 1964). 1906 - Day of death of Victor Mayer Amedee Mannheim, French mathematician (b. 1831). 1910 - Day of death of Jules Tannery, French mathematician (b. 1848). 1941 - Day of death of Émile Picard, French mathematician (b. 1856). 1954 - Birthdate of Guolaugur Kristinn Ottarsson, Icelandic guitarist, mathematician, and engineer. 1969 - Yuri Matiyasevich reads a journal article by Julia Robinson that will lead him to the proof of Hilbert's 10th problem. 1998 - Day of death of André Lichnerowicz, French physicist, and mathematician (b. 1915).

December, 12 1685 - Day of death of John Pell, English mathematician, and linguist (b. 1610). 1729 - Goldbach replies to the first letter of Euler with a letter in which he repeats Euler's form of the gamma function and mentions the sum of the series 1+1·2+1·2·3+1·2·3·4+…, and also admits that he doesn't know what “hyperbolic logarithms" are. As a final note, he writes “P.S. A note to you is that Fermat has observed that all numbers with the formula , that is 3, 5, 17, etc. are primes, but he himself was not able to prove this, and, as far as I know, nobody since him has proved it, either." [151] 1832 - Birthdate of Peter Ludwig Mejdell Sylow, Norwegian mathematician (d. 1918). 1885 - J. J. Sylvester, in the middle of his inaugural lecture as Savilian Professor of Geometry at Oxford University, “refreshed" the audience with his sonnet “To a missing member of a family group of terms in an algebraical formula."* 1889 - Day of death of Viktor Bunyakovsky, Ukrainian-Russian mathematician (b. 1804). 1919 - Day of death of Paul Gustav Samuel Stackel, German mathematician (b. 1862). 1962 - Birthdate of Ulrike Tillmann, German mathematician. 1965 - Day of death of Tibor Rado, Hungarian mathematician (b. 1895).

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1977 - Day of death of Arthur Erdelyi, Hungarian-born Scottish mathematician (b. 1908). 1994 - Day of death of Nicolaas Hendrik Kuiper, Dutch mathematician (b. 1920). 1997 - Day of death of Evgenii Landis, Soviet mathematician (b. 1921). 2014 - Day of death of Ivor Grattan-Guinness, English mathematician and historian of mathematics (b. 1941). * To a Missing Member of a Family Group of Terms in an Algebraical Formula, by James Joseph Sylvester Lone and discarded one! divorced by fate, From thy wished-for fellows – whither art flown? Where lingerest thou in thy bereaved estate, Like some lost star or buried meteor stone? Thou mindst me much of that presumptuous one Who loth, aught less than greatest, to be great, From Heaven's immensity fell headlong down To live forlorn, self-centred, desolate; Or who, new Heraclid, hard exile bore, Now buoyed by hope, now stretched on rack of fear Till throned Astraea, wafting to his ear Works of dim portent through the Atlantic roar, Bade him the sanctuary of the Muse revere And strew with flame the dust of Isis' shore.

December, 13 1048 - Day of death of Abu Arrayhan Muhammad ibn Ahmad al-Biruni, an Islamic mathematician (b. 973), known for his significant contributions to mathematics and other scientific fields. 1557 - Day of death of Niccolo Fontana Tartaglia, Italian mathematician, and engineer (b. 1499). Tartaglia is famous for his work on solving cubic equations. 1603 - Day of death of Seigneur (lord) De La Bigotiere Francois Viete, French mathematician (b. 1540). Viete made important contributions to algebra and trigonometry. 1866 - George Campbell De Morgan presented only one paper to the London Mathematical Society, titled "On the Development of a Certain Class of Functions," which he read on December 13, 1866.

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1883 - Felix Klein noted in his references that he received a call to go to Baltimore and had a great desire to go there, possibly for academic or research purposes. 1885 - Birthdate of Annie Dale Biddle Andrews, American mathematician (d. 1940). 1887 - Birthdate of George Polya, Hungarian-American mathematician (d. 1985), renowned for his work in problem-solving and mathematical pedagogy. 1904 - Birthdate of William Hunter McCrea, English astronomer, and mathematician (d. 1999). 1907 - Emmy Noether received her Ph.D. degree, summa cum laude, from the University of Erlangen for a dissertation on algebraic invariants directed by Paul Gordan. She is known for her groundbreaking work in abstract algebra and the development of Noether's theorem. 1908 - Birthdate of Leon Bankoff, American dentist, and mathematician (d. 1997). 1910 - Birthdate of Charles Alfred Coulson, British applied mathematician, theoretical chemist, and religious author (d. 1974). 1911 - Birthdate of Trygve Haavelmo, Norwegian economist, and mathematician, Nobel Prize laureate (d. 1999). 1921 - Birthdate of David Gale, American mathematician, and economist (d. 2008). 1921 - Day of death of Max Noether, German mathematician (b. 1844). 1927 - Day of death of Mehmet Nadir, Turkish mathematician (b. 1856). 1927 - J. Von Neumann's habilitation was completed. John von Neumann was a prolific mathematician and pioneer in computer science. 1928 - Birthdate of Solomon Feferman, American philosopher, and mathematician (d. 2016). 1943 - Croatia issued a pair of stamps to honor mathematician and physicist Fr. Rugjer Boscovich (1711-1787).

1950 - Day of death of Abraham Wald, Hungarian mathematician (b. 1902).

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1994 - Day of death of Nicolaas Hendrik Kuiper, Dutch mathematician (b. 1920).

December, 14 1498 - Luca Pacioli completed his "Divina Proportione" with illustrations by Leonardo da Vinci. This work explores the mathematics of proportionality and is notable for its artistic contributions by da Vinci. 1546 - Birthdate of Tycho Brahe, Danish astronomer, and mathematician (d. 1601). Brahe made significant contributions to the field of astronomy and is known for his precise astronomical observations. 1760 - Birthdate of James Wood, British mathematician (d. 1839). 1844 - Gauss wrote to Grassmann to thank him for sending a copy of his book "Ausdehnungslehre," which was a significant work in the field of mathematics. 1897 - Day of death of Francesco Brioschi, Italian mathematician (b. 1824), known for his contributions to the theory of elasticity. 1900 - Max Planck presented his ideas on quantum physics at a meeting of the German Physics Society. This marked a pivotal moment in the development of quantum theory. 1904 - Birthdate of Nikolai Grigor'evich Chudakov, Soviet mathematician (d. 1986). 1927 - Day of death of Julian Sochocki, Russian-Polish mathematician (b. 1842). 1936 - Birthdate of Charles Terence Clegg, British mathematician. 1946 - Denmark issued a stamp commemorating the 400th anniversary of the birth of the mathematician and astronomer Tycho Brahe.

1955 - Birthdate of Jill Pipher, American mathematician.

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December, 15 1732 - Birthdate of Wenceslaus Johann Gustav Karsten, German mathematician (d. 1787). 1742 - Euler gave the first clear statement of the Fundamental Theorem of Algebra: every algebraic equation of degree n has exactly n complex roots. 1802 - Birthdate of János Bolyai, Hungarian mathematician (d. 1860), known for his work in non-Euclidean geometry. 1827 - Day of death of Samuel Roberts, British mathematician (d. 1913). 1838 - Day of death of Émile Léger, French mathematician (b. 1795). 1847 - Birthdate of Achille Marie Gaston Floquet, French mathematician (d. 1920). 1855 - Day of death of Jacques Charles François Sturm, French mathematician (b. 1803), known for Sturm's theorem in real algebra. 1887 - Nature quoted J. J. Sylvester: “Perhaps I may, without immodesty, lay claim to the appellation of the mathematical Adam, as I believe I have given more names (passed into general circulation) to the creatures of the mathematical realm than all other mathematicians of the age combined." 1890 - Karl Pearson is appointed Gresham Professor of Geometry. 1897 - Birthdate of Myron Mathisson, Polish physicist, and mathematician (d. 1940). 1912 - Birthdate of Emil Grosswald, Romanian-American mathematician (d. 1989), known for his work in number theory. 1921 - Day of death of Leo Königsberg, German mathematician (b. 1837). 1923 - Birthdate of Freeman Dyson, English-American physicist, and mathematician (d. 2020). 1924 - Birthdate of Frank W. J. Olver, English-American mathematician (d. 2013). 1965 - Richard Feynman, having just won the Nobel Prize, makes a bet with CERN Director Viktor Weisskopf that he will not hold a “responsible" position within the next ten years. A wager he will win. 1970 - Day of death of Theodore Samuel Motzkin, Israeli-American mathematician (b. 1908). 1971 - Day of death of Paul Lévy, French mathematician (b. 1886), known for his contributions to probability theory and stochastic processes.

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December, 16 1474 - Day of death of Ali Qushji, Uzbek astronomer, mathematician, and physicist (b. 1403). 1625 - Birthdate of Erhard Weigel, German mathematician, astronomer, and philosopher (d. 1699). 1627 - Cavalieri announced to Galileo and Cardinal Borromeo that he had completed his Geometria, which contains his method of indivisibles, now known as Cavalieri's principle. 1799 - Gauss wrote to Farkas Bolyai, expressing regret that they hadn't discussed the theory of parallels during their student days together at Göttingen (1796-1798). 1804 - Birthdate of Viktor Bunyakovsky, Russian-Ukrainian mathematician (d. 1889). 1843 - John T. Graves announced the discovery of octonions, denoted with a boldface O, to his mathematician friend William Hamilton, who had discovered quaternions, in a letter on this date. 1849 - Birthdate of Julius König, Hungarian mathematician (d. 1913). 1861 - Weierstrass, who had endured painful attacks of vertigo for twelve years, experienced a complete collapse of his health due to overwork. He subsequently lectured while seated and delegated blackboard work to an advanced student. Nevertheless, he became a recognized master teacher. 1887 - Birthdate of Johann Radon, Austrian mathematician (d. 1956). 1905 - Birthdate of Piet Hein, Danish mathematician, and poet (d. 1996). 1932 - Birthdate of Grace Alele-Williams, Nigerian mathematician. 1933 - Day of death of Ludwig Schlesinger, German mathematician (b. 1864). 1934 - Day of death of Gustav de Vries, Dutch mathematician (b. 1866). 1968 - Birthdate of Valerie Berthe, French mathematician. 2014 - Day of death of Tim Cochran, American mathematician (b. 1955).

December, 17 1706 - Birthdate of Emilie du Châtelet, French mathematician, and physicist (d. 1749). 1750 - Mr. Theophilus Grew appointed the first Master in Mathematics at the Academy of Philadelphia (which later became the University of Pennsylvania). 1835 - Birthdate of Felice Casorati, Italian mathematician (d. 1890). 1842 - Birthdate of Sophus Lie, Norwegian mathematician (d. 1899).

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1851 - Day of death of Benjamin Olinde Rodrigues, French banker, mathematician, and social reformer (b. 1795). 1853 - Day of death of Robert R. Anstice, English mathematician (b. 1813). 1863 - Birthdate of Henri Padé, French mathematician (d. 1953). 1900 - Birthdate of Mary Cartwright, English mathematician (d. 1998). 1907 - Day of death of Lord Kelvin, born as William Thomson, ScottishIrish physicist, mathematician, and engineer (b. 1824). 1912 - Day of death of Spiru C. Haret, Romanian mathematician, astronomer, and politician (b. 1851). 1912 - Born presented Mie's theory for the first time at Göttingen during a meeting of the local Mathematical Society. 1940 - Day of death of Alicia Boole Stott, Anglo-Irish mathematician (b. 1860). 1941 - Birthdate of V. Frederick Rickey, American mathematical historian and author. 1999 - Day of death of Juergen Kurt Moser, German-American mathematician (b. 1928).

December, 18 1559 - Day of death of Cuthbert Tunstall, English Scholastic, church leader, diplomat, administrator, and royal adviser, author of the first arithmetic book printed in England (b. 1474). 1552 - Birthdate of Ahmad Ibn al-Qadi, Moroccan writer, judge, and mathematician (d. 1616). 1723 - Goldbach posed a Diophantine problem to Daniel Bernoulli: To find four numbers such that the pairwise product of any two, plus 1, was a square. 1799 - Day of death of Jean-Etienne Montucla, French mathematician, and historian (b. 1725). 1848 - Day of death of Bernard Bolzano, Bohemian priest, and mathematician (b. 1781). 1855 - Day of death of Jacques Charles-Francois Sturm, French mathematician (b. 1803). 1880 - Day of death of Michel Chasles, French mathematician (b. 1793). 1885 - The Ministry of Culture and Education in Dresden, which was the capital of Saxony, officially offers Sophus Lie the professorship. 1917 - Birthdate of Roger Conant Lyndon, American mathematician (d. 1988).

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1936 - Birthdate of Wilhelm Fushchych, Soviet-Ukrainian mathematical physicist (d. 1997). 1942 - Birthdate of Lenore Blum, American mathematician. 1970 - Day of death of Pao-Lu Hsu, Chinese mathematician (b. 1910). 1994 - Day of death of Roger Apery, Greek-French mathematician (b. 1916). 1998 - Day of death of Edwin Evariste Moise, American mathematician, and mathematics education reformer (b. 1918). 2007 - Day of death of Samuel Karlin, American mathematician (b. 1924). 2010 - Day of death of Rudolf F. Ahlswede, German mathematician (b. 1938).

December, 19 1615 - Birthdate of Charles Scarborough, English physician, and mathematician (d. 1693). 1714 - Birthdate of John Winthrop, American mathematician, physicist, and astronomer (d. 1779). 1765 - Joseph Priestley, visiting in London, is introduced to Benjamin Franklin and other members of the "Honest Whigs" by John Canton. 1783 - Birthdate of Charles-Julien Brianchon, French mathematician (d. 1864). 1875 - Birthdate of Grace Marie Bareis, American mathematician (d. 1962). 1894 - Karl Pearson introduced the Pearson family of densities. 1895 - Karl Pearson's "Contributions to the Mathematical Theory of Evolution II. Skew Variation in Homogeneous Material" received by the Royal Society of London. 1908 - Scientific American offered a $500 prize for "a simple explanation of the fourth dimension." 1910 - Birthdate of Helmut Wielandt, German mathematician (d. 2001). 1918 - Birthdate of Leonid Mirsky, Russian-British mathematician (d. 1983). 1932 - Birthdate of Crispin St. John Alvah Nash-Williams, BritishCanadian mathematician (d. 2001). 1937 - Birthdate of Barry Charles Mazur, American mathematician. 1939 - Day of death of Dmitry Aleksandrovich Grave, Russian and Soviet mathematician (b. 1863). 1943 - Birthdate of Victor G. Kac, Soviet-American mathematician. 1944 - Birthdate of Mitchell Feigenbaum, American physicist, and mathematician.

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1952 - Birthdate of David Harbater, American mathematician. 1952 - Day of death of Otto Szasz, Hungarian mathematician (b. 1884).

December, 20 1494 - Birthdate of Oronce Fine, French mathematician and cartographer (d. 1555). 1623 - Wilhelm Schickard described his calculating machine in a letter to Johannes Kepler. 1648 - Birthdate of Thommaso Ceva, Italian mathematician and poet (d. 1737). 1836 - Day of death of Johann Christian Martin Bartels, German mathematician (b. 1769). 1838 - Birthdate of Edwin Abbott, English schoolmaster and theologian, author of Flatland (d. 1926). 1843 - Birthdate of Paul Tannery, French mathematician and historian of mathematics (d. 1904). 1855 - Birthdate of Thomas Craig, American mathematician (d. 1900). 1875 - Birthdate of Francesco Cantelli, Italian mathematician (d. 1966). 1906 - Nature publishes a letter from Francis Galton on "Cutting a round cake on scientific principles." 1915 - Einstein wrote to Hilbert that “there has been certain resentment between us, the cause of which I do not want to analyze. I have fought against the associated feelings of bitterness with complete success. I think of you again with unmixed kindness, and ask you to try to do the same with me. It is objectively a shame when two real guys that have emerged from this shabby world do not give each other a little pleasure." [146]. 1931 - Day of death of Vaclav Jerabek, Czech mathematician (b. 1845). 1944 - Day of death of Peter Comrie, Scottish mathematician (b. 1868). 1962 - Day of death of Emil Artin, Austro-German mathematician (b. 1898). 1984 - Day of death of Max Deuring, German mathematician (b. 1907). 1988 - Day of death of Elizabeth Scott, American mathematician (b. 1917). 2005 - Day of death of Raoul Bott, Hungarian-American mathematician (b. 1923).

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December, 21 1542 - Birthdate of Thomas Allen, English mathematician and astrologer (d. 1632). 1671 - Newton proposed for membership in the Royal Society of London by Seth Ward. 1807 - Joseph Fourier announced to the French Academy of Science that an arbitrary function could be expanded as an infinite series of sines and cosines. 1877 - Birthdate of Jaan Sarv, Estonian mathematician (d. 1954). 1878 - Birthdate of Jan Lukasiewicz, Polish-Irish mathematician and philosopher (d. 1956). 1905 - Birthdate of Kate Fenchel, German mathematician (d. 1983). 1907 - Minkowski talked to the Göttingen scientific society on "The Basic Equations for Electromagnetic Processes in Moving Bodies" [179]. 1912 - Day of death of Paul Albert Gordan, German mathematician (b. 1837). 1917 - Lebesgue wrote his last letter to Borel: "I don't have the courage to rebuff your proposals. I told you, I don't have the same confidence in you as I used to. I don't believe in words anymore… For the moment any kind of relation going further than plain comradeship [la banalite de la camaraderie] would just be hypocrisy. I would not be having lunch with you but with some old memories. I think this letter will bring some sorrow to you and I keep too much hidden friendship for you not to be sorry myself." [58]. 1922 - Birthdate of Cecile DeWitt-Morette, French mathematician and physicist (d. 2017). 1946 - The Detroit News reported the Purdue University Engineer's yell: "E to the X, DY, DX; E to the X, DX; Cosine, Secant, Tangent, Sine; Three Point One Four One Five Nine; Square Root, Cube Root, BTU; Slipstick, Slide Rule, Yea Purdue." 1960 - Day of death of Eric Temple Bell, Scottish-American mathematician and writer (b. 1883). 1976 - Day of death of Vijay Kumar Patodi, Indian mathematician (b. 1945). 1980 - Day of death of Vladimir Petrovich Potapov, Soviet mathematician (b. 1914). 1987 - Day of death of Eugene Lukacs, Hungarian statistician (b. 1906).

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December, 22 National Mathematics Day (India) 1640 - Day of death of Jean Beaugrand, French mathematician (b. 1590). 1660 - Day of death of Andre Tacquet, Flemish priest, and mathematician (b. 1612). 1666 - Seven mathematicians and seven physicists met at the king's Library to inaugurate the French Academy of Sciences. They would not receive a formal decree of protection from Louis XIV until 1699. 1669 - John Wallis wrote: “In a dark night, in bed, without pen, ink, or paper, or anything equivalent, I did by memory extract the square root of 3,00000,00000,00000,00000,00000,00000,00000,00000, which I found to be 1,73205,08075,68077,29353,… and did the next day commit it to writing." 1765 - Birthdate of Johann Friedrich Pfaff, German mathematician (d. 1825). 1819 - Birthdate of Pierre Ossian Bonnet, French mathematician (d. 1892). 1824 - Birthdate of Francesco Brioschi, Italian mathematician (d. 1897). 1853 - Birthdate of Evgraf Fedorov, Russian mathematician, crystallographer, and mineralogist (d. 1919). 1859 - Birthdate of Otto Ludwig Holder, German mathematician (d. 1937). 1867 - Day of death of Jean-Victor Poncelet, French mathematician and engineer (b. 1788). 1869 - Birthdate of Dmitri Egorov, Russian mathematician (d. 1931). 1887 - Birthdate of Srinivasa Ramanujan, Indian mathematician (d. 1920). 1897 - Birthdate of Vojtech Jarnik, Czech mathematician (d. 1970). 1898 - Birthdate of Vladimir Fock, Soviet physicist, and mathematician (d. 1974). 1918 - Birthdate of Edwin Evariste Moise, American mathematician, and mathematics education reformer (d. 1998). 1928 - Day of death of Henry Burchard Fine, American mathematician (b. 1858). 1937 - Birthdate of Arthur Jaffe, American mathematical physicist. 1994 - Day of death of John Arthur Todd, British mathematician (b. 1908). 2006 - The journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific “Breakthrough of the Year," the first such recognition in the area of mathematics. 2010 - India issued a stamp featuring Srinivasa Ramanujan, who was born on this day, to celebrate their National Mathematics Day.

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December, 23 1693 - Birthdate of François Nicole, French mathematician (d. 1758). 1722 - Day of death of Pierre Varignon, French mathematician (b. 1654). 1751 - Jacobi called this the birthday of elliptic functions because on this day, a work by the Italian mathematician Fagnano, which had been sent to the Berlin Academy, was handed to Euler for review. The study of this work led Euler to his important investigations of elliptic integrals and to the discovery of the addition theorem. 1763 - Price read Bayes's “Essay towards solving a problem in the doctrine of chances" to the Royal Society. 1827 - Day of death of Robert Woodhouse, English mathematician (b. 1773). 1890 - Day of death of Edward Sang, Scottish mathematician (b. 1805). 1908 - Minkowski sent his manuscript "Raum und Zeit" (“Space and Time") to the editor of the Physikalisch Zeitschrift. Four days before his death, the editor of the Physikalisch Zeitschrift spoke with Minkowski about the contents of his talk. He did not say what Minkowski told him but mentioned that no one imagined that he would die suddenly [179]. 1909 - Birthdate of John Hamilton Curtiss, American mathematician (d. 1977). 1936 - Birthdate of Peter L. Hammer, Romanian-American mathematician (d. 2006). 1943 - Birthdate of Mikhail Leonidovich Gromov, Russian-French mathematician. 1987 - Egypt issued a stamp honoring the mathematician Ali Mustafa Mousharafa (1898-1950). 1989 - Day of death of Richard Rado, Jewish German mathematician (b. 1906). 2001 - Day of death of Donald Clayton Spencer, American mathematician (b. 1912).

December, 24 1740 - Birthdate of Anders Johan Lexell, Swedish-Russian astronomer, mathematician, and physicist (d. 1784). 1754 - Euler writes to Muller in St. Petersburg and describes d'Alembert as “the most argumentative man in the world," and calls him, “hated by everyone in Paris." [70].

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1819 - Bernard Bolzano was dismissed from his theological chair at the University of Prague and put under police supervision for his unorthodox religious views. 1822 - Birthdate of Charles Hermite, French mathematician (d. 1901). 1838 - Birthdate of Thorvald Nicolai Thiele, Danish astronomer, actuary, and mathematician (d. 1910). 1849 - Gauss writes to the Astronomer Johann Franz Encke in response to Encke's remarks about the Frequency of Primes: “Most Honored Friend! … The kind communication of your remarks on the frequency of prime numbers was interesting to me in more than one respect. You have reminded me of my own pursuit of the same subject, whose first beginnings occurred a very long time ago, in 1792 or 1793 when I had procured for myself Lambert's supplement to the table of logarithms. Before I had occupied myself with the finer investigations of higher arithmetic, one of my first projects was to direct my attention to the decreasing frequency of prime numbers, to which end I counted them up in several chiliads (sets of a thousand) and recorded the results on one of the affixed white sheets. I soon recognized that under all variations of this frequency, on average, it is nearly inversely proportional to the logarithm…" [37]. 1868 - Birthdate of Emanuel Lasker, German chess player, mathematician, and philosopher (d. 1941). 1880 - Hermite analyzed his own philosophical background in a letter to Gosta Mittag-Lefler: “Analysis is for me largely a science of observation. Analysts seem to me to be naturalists who, with the eyes of the mind, look at a world as real as that of nature, at beings outside of themselves, which they have by no means created, and whose existence is as much in the necessity of things as animals and vegetables. The study of the subjective world allows, therefore, an insight, a view of the real world." [58]. 1882 - Day of death of Johann Benedict Listing, German mathematician (b. 1808). 1882 - S. Lie wrote to Mittag-Lefler to say about the high level of French mathematicians at that time: “Overall, I am extremely satisfied with my stay in Paris, even if I (like Abel) associate on a much more intimate footing with the Germans. In Paris, as courteous as they are, one always has the impression that these gentlemen are extremely preoccupied. There is great mathematical life in Paris now for the time being. I have the feeling that the German's sovereignty in mathematics is beginning to weaken. And despite the good friendship I have with

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many Germans, this indeed is dear to my heart. For I certainly by far prefer to read French, as opposed to German Mathematics" [164]. 1962 - Day of death of Wilhelm Ackermann, German mathematician (b. 1896). 1994 - Day of death of Alfred Leon Foster, American mathematician (b. 1904). 2000 - Day of death of Laurence Chisholm Young, British mathematician (b. 1905).

December, 25 1597 - Ricci wrote a letter to Clavius in Rome from Nanjing, expressing his appreciation for having received Astrolabium from Clavius [153]. 1640 - Fermat wrote an elaborate version of Girard's theorem (in which he also provided the number of possible expressions of the powers of p of the form 4n + 1 as a sum of two squares) in a letter to Marin Mersenne. For this reason, this version of the theorem is sometimes called Fermat's Christmas theorem. 1642 - Birthdate of Isaac Newton, English physicist, and mathematician (d. 1726/1727). 1900 - Birthdate of Antoni Zygmund, Polish-American mathematician (d. 1992). 1905 - Birthdate of Gottfried Maria Hugo Kothe, Austrian mathematician (d. 1989). 1921 - Day of death of Piers Bohl, Latvian mathematician (b. 1865). 1929 - Day of death of Percy Alexander MacMahon, British mathematician (b. 1854). 1941 - Day of death of Theodor Molien, Baltic-German mathematician (b. 1861). 1944 - Day of death of Wilhelm Kutta, German mathematician (b. 1867). 1975 - Day of death of Gunnar Kangro, Estonian mathematician (b. 1913).

December, 26 1532 - Birthdate of Wilhelm Xylander, German classical scholar, and humanist, translator of Euclid and Diophantus (d. 1576). 1780 - Birthdate of Mary Somerville, Scottish mathematician, and astronomer (d. 1872). 1791 - Birthdate of Charles Babbage, English mathematician, and engineer (d. 1871). 1837 - Charles Babbage completed his "Calculating Engine" manuscript.

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1843 - John Graves writes to William Rowan Hamilton that he has invented an eight-dimensional normed division algebra he called "Octaves" [135]. 1861 - Birthdate of Friedrich Engel, German mathematician (d. 1941). 1903 - Birthdate of Lancelot Stephen Bosanquet, British mathematician (d. 1984). 1907 - Birthdate of Leonard Carlitz, American mathematician (d. 1999). 1927 - Redfield writes to MacMahon that he is able to solve MacMahon's conjecture. 1937 - Birthdate of John Horton Conway, English mathematician, known for Conway's Game of Life (d. 2020). 1951 - Kurt Gödel delivered the Gibbs Lecture, "Some Basic Theorems on the Foundations of Mathematics and their Philosophical Implications," at the annual AMS meeting at Brown University. 1960 - Birthdate of Keith Martin Ball, American mathematician. 1973 - Day of death of Harold Hotelling, American mathematician (b. 1895). 1992 - Day of death of John George Kemeny, Jewish-Hungarian American mathematician, computer scientist, and educator (b. 1926). 1997 - Day of death of Cahit Arf, Turkish mathematician (b. 1910). 2006 - Day of death of Martin David Kruskal, American mathematician, and physicist (b. 1925). 2007 - Day of death of Wilfred Kaplan, American mathematician (b. 1915).

December, 27 1571 - Birthdate of Johannes Kepler, German mathematician, astronomer, and astrologer (d. 1630). 1654 - Birthdate of Jacob Jacques Bernoulli, Swiss mathematician, and astronomer (d. 1705). 1915 - Birthdate of Jacob Lionel Bakst Cooper, South African mathematician (d. 1979). 1930 - Day of death of Gyula Farkas, Hungarian mathematician, and physicist (b. 1847). 1973 - Day of death of Raymond Woodard Brink, American mathematician (b. 1890). 1974 - Day of death of Vladimir Fock, Soviet physicist, and mathematician (b. 1898). 1992 - Day of death of Alfred Hoblitzelle Clifford, American mathematician (b. 1908).

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1995 - Day of death of Boris Vladimirovich Gnedenko, Soviet mathematician (b. 1912). 2006 - Day of death of Peter L. Hammer, Romanian-American mathematician (b. 1936).

December, 28 1663 - Day of death of Francesco Maria Grimaldi, Italian mathematician, and physicist (b. 1618). 1798 - Birthdate of Thomas Henderson, Scottish astronomer, and mathematician (d. 1844). 1808 - Birthdate of Victoire Louis Athanase Dupré, French mathematician, and physicist (d. 1869). 1828 - Crelle wrote to the Secretary of State for Education, expressing that he felt it was now necessary to act quickly before others also discovered Abel's remarkable talent and would offer him a position [165]. 1871 - Day of death of John Henry Pratt, British clergyman, and mathematician (b. 1809). 1882 - Birthdate of Arthur Eddington, English astronomer, physicist, and mathematician (d. 1944). 1893 - Simon Newcomb gave a speech to the New York Mathematical Society with comments on the fourth dimension: “It is a perfectly legitimate exercise… if we should not stop at three dimensions in geometry but construct one for space having four… and there is room for an indefinite number of universes." He also referred to his speculations on the fourth dimension as “the fairyland of geometry." [16]. 1903 - Birthdate of John von Neumann, Hungarian-American mathematician, and physicist (d. 1957). 1923 - George David Birkhoff of Harvard received the first Bocher Memorial Prize for his paper “Dynamical systems with two degrees of freedom." 1938 - Kurt Gödel lectured on the consistency of the axiom of choice and the generalized continuum hypothesis at the annual AMS meeting. 1950 - Birthdate of Clifford Cocks, English mathematician, and cryptographer.

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December, 29 1256 - Possible birthdate of Ibn Al-Banna, Moroccan-Berber mathematician, astronomer, Islamic scholar, Sufi, and one-time astrologer (d. 1321). 1692 - Huygens, in a letter to L'Hospital, provided the first complete sketch of the folium of Descartes. 1711 - As part of an ongoing argument with Newton, Leibniz wrote a letter to Hans Sloane stating, in particular, that he discovered calculus some years before he published it, possibly in 1675 or earlier [22]. 1731 - Day of death of Brook Taylor, English mathematician (b. 1685). 1737 - Day of death of Joseph Saurin, French minister, and mathematician (b. 1659). 1746 - Euler wrote to praise d'Alembert on his proof of the Fundamental Theorem of Algebra but disagreed with his idea that log(-x) = log(x). 1829 - Galois took the Baccalaureate examinations to enter the Ecole Normale. His mathematics examiner reported, “This pupil is occasionally unclear in expressing his ideas, but he is intelligent and displays a remarkable research spirit." [24]. 1856 - Birthdate of Thomas Joannes Stieltjes, Dutch-French mathematician (d. 1894). 1861 - Birthdate of Kurt Hensel, German mathematician (d. 1941). 1891 - Day of death of Leopold Kronecker, Polish-German mathematician (b. 1823). 1899 - Hilbert wrote to Frege about axiomatic analysis: "If we want to understand each other, we must not forget that our guiding intentions differ in kind. It was necessary for me to establish my axiomatic system: I aimed to facilitate the understanding of geometric propositions I deem the most significant outcomes of geometric inquiries: that the parallel axiom is not a consequence of other axioms, and similarly Archimedes' axiom, etc… I aimed to enable the understanding and addressing of questions like why the sum of angles in a triangle equals two right angles and how this is connected to the parallel axiom." [34]. 1923 - Birthdate of Yvonne Choquet-Bruhat, French mathematician, and physicist. 1939 - Day of death of Kelly Miller, American mathematician, the first black man to attend Johns Hopkins University (b. 1863). 1941 - Birthdate of Tullio Levi-Civita, Italian mathematician (b. 1873). 1941 - Day of death of William James Macdonald, Scottish mathematician (b. 1851).

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1947 - George Dantzig announced his discovery of the simplex method at the joint annual meeting of the American Statistical Association and the Institute of Mathematical Statistics. 1954 - Birthdate of Albrecht Böttcher, German mathematician. 1965 - Day of death of Tibor Radó, Hungarian mathematician (b. 1895). 1972 - Edward Lorenz presented a paper at the 139th Annual Meeting of the American Association for the Advancement of Science with the title, "Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?"

December, 30 1695 - Day of death of Samuel Morland, English mathematician, and inventor of mechanical calculators (b. 1625). 1881 - The "Four Fours" problem was first published in Knowledge. The problem is to express whole numbers using exactly four fours and various arithmetical signs. 1897 - Birthdate of Stanislaw Saks, Polish mathematician (d. 1942). 1932 - Day of death of Eliakim Hastings Moore, American mathematician (b. 1862). 1944 - Birthdate of Joseph Hilbe, American mathematician, and philosopher. 1947 - Day of death of Alfred North Whitehead, English-American mathematician, and philosopher (b. 1861). 1982 - Birthdate of Phillip Hall, British mathematician (b. 1904). 2013 - Day of death of Paul Sally, American mathematician (b. 1933).

December, 31 1610 - Day of death of Ludolph van Ceulen, German-Dutch mathematician (b. 1540). 1679 - Day of death of Giovanni Alfonso Borelli, Italian mathematician (b. 1608). 1714 - Birthdate of Arima Yoriyuki, Japanese mathematician and educator (d. 1783). 1831 - Gauss writes to Wilhelm Olbers regarding an essay published by Laplace, “The essay… is quite unworthy of this great geometer. I find two different, very gross blunders in it. I had always imagined that among geometers of the first rank, the calculation was always only the dress in which they present that which they created not by calculation, but by mediation about the subject itself." [175].

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1894 - Day of death of Thomas Joannes Stieltjes, Dutch mathematician (b. 1856). 1896 - Birthdate of Carl Ludwig Siegel, German mathematician (d. 1981). 1915 - The Mathematical Association of America was founded in Columbus, Ohio. 1916 - Birthdate of Douglas Geoffrey Northcott, British mathematician (d. 2005). 1930 - Birthdate of Jaime Alfonso Escalante Gutierrez, Bolivian educator and mathematician (d. 2010). 1944 - Day of death of Nikolai Evgrafovich Kochin, Soviet mathematician (b. 1901). 1952 - Birthdate of Vaughan Jones, New Zealand mathematician. 1982 - Day of death of Kurt Otto Friedrichs, German-American mathematician (b. 1901). 1999 - Andrew Wiles is knighted. 2004 - Day of death of Gerard Debreu, French economist and mathematician, Nobel Prize laureate (b. 1921).

CONCLUSIVE REMARKS

The dates (if different is not indicated) are from [79, 112, 166, 173] (see also Wikipedia). The data about stamps is taken from [119]. In the last stages of preparing this work, we found an excellent reference [142] (and one closely related to it, [133]), so some of the dates (that are included in these references as well) were double-checked with [133, 142].

REFERENCES

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