MARCH 1988, VOLUME 35, NUMBER 3 Notices of the American Mathematical Society 0821824414

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OT ICE S OF THE

AMERICAN MATHEMA TICAL SOCIETY

Elliott H. Lieb Awarded 1988 Birkhoff Prize page 381

East Lansing Meeting (March 18-19) page 413 !"

Knoxville Meeting (March 25-26) Las Cruces Meeting (April 8-9)

page 42'2 page 430

MARCH 1988, VOLUME 35, NUMBER 3 Providence, Rhode Island, USA ISSN 0002-9920

Calendar of AMS Meetings and Conferences This calendar lists all meetings which have been approved prior to the date this issue of Notices was sent to the press. The summer

and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have been assigned. Programs of the meetings will appear in the issues indicated below. First and supplementary announcements of the meetings will have appeared in earlier issues. Abstracts of papers presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American

Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meeting. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the headquarters office of the Society. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for abstracts for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information, consult the meeting announcements and the list of organizers of special sessions.

Meetings Date

Meeting # 840 841 842 843 844

March 18-19, 1988 March 25-26, 1988 April 8-9, 1988 * April 23-24, 1988 August8-12, 1988 (AMS Centennial Celebration) October 28-30, 1988 January 11-14, 1989 (95th Annual Meeting) January 17-20, 1990 (96th Annual Meeting) January 16-19, 1991 (97th Annual Meeting)

Place

Abstract Deadline

Program Issue

East Lansing, Michigan Knoxville, Tennessee Las Cruces, New Mexico College Park, Maryland Providence, Rhode Island

Expired Expired Expired Expired May 19

March March March April July I August

Lawrence, Kansas Phoenix, Arizona

August 24 October 12

October December

Louisville, Kentucky San Francisco, California

* Please refer to page 441 for listing of special sessions.

Conferences April 21-23, 1988: Symposium on the Interface of Computing Science and Statistics, Reston, Virginia (see news item, page 42, January issue) May 4, 1988: Symposium on Some Mathematical Questions in Biology: The Dynamics of Excitable Media, Las Vegas, Nevada May 29-June 4, 1988: Symposium on The Legacy of John von Neumann, Hofstra University, Hempstead, New York June 4-August 11 , 1988: Joint Summer Research Conferences in the Mathematical Sciences, Bowdoin College, Brunswick, Maine

July 3-23, 1988: Summer Research Institute on Operator Theory /Operator Algebras and Applications, University of New Hampshire, Durham, New Hampshire July 18-29, 1988: AMS-SIAM Summer Seminar on Computational Solution of Nonlinear Systems Equations, Colorado State University, Fort Collins, Colorado August 6-7, 1988: AMS Short Course: Chaos and Fractals: The mathematics behind the computer graphics September 6-10, 1988: International Neural Network Society, 1988 Annual Meeting, Boston, Massachusetts (see news item, page 269, February issue)

Deadlines Classified Ads* News Items Meeting Announcements**

May 1June Issue

July I August Issue

September Issue

October Issue

Apr 18, 1988 Apr 22, 1988 Apr 14, 1988

May 30, 1988 Jun 10, 1988 Jun 3, 1988

Aug 1, 1988 Aug 5, 1988 Jul 28, 1988

Aug 31, 1988 Sept 6, 1988 Aug 24, 1988

* Please contact AMS Advertising Department for an Advertising Rate Card for display advertising deadlines.

** For material to appear in the Mathematical Sciences Meetings and Conferences section.

OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

ARTICLES

DEPARTMENTS

381 Elliott H. Lieb Awarded 1988 Birkhoff Prize

379 399 405 407

The Birkhoff Prize, awarded every five years for outstanding contributions to applied mathematics, was given to Elliott Lieb for his profound work in nonlinear differential equations and classical inequalities of analysis.

383 Atlanta Meeting Kicks Off AMS Centennial An excellent scientific program and a festive social atmosphere at the Annual Meeting keynoted the centennial year for American mathematics.

409 411

457

FEATURE COLUMNS

467 471

387 Inside the AMS: Report from the Executive Director William J. LeVeque reviews the activities of the Society for the past year and describes several projects that are exciting new ventures for the AMS.

391 Mathematical Text Processing RichardS. Palais Richard Palais' last official article in this column compares WYSIWYG mathematical word processing with TeX, and reviews the state of TWP software for the Macintosh.

397 Washington Outlook Kenneth M. Hoffman Kenneth M. Hoffman, in his regular column, describes the upbeat feeling that surrounded the banquet in Atlanta, but contrasts that event with the gloomy picture for research funding that is coming from Washington.

473

475 479 483 499

Letters to the Editor News and Announcements NSF News and Reports 1988 AMS Elections (Nominations by Petition) For Your Information Gina Kolata Leaves Science Meetings and Conferences of the AMS (Listing) Programs for three sectional meetings Mathematical Sciences Meetings and Conferences New AMS Publications AMS Reports and Communications Recent Appointments, 471 Reports of Past Meetings, 471 Election Results of 1987, 472 Miscellaneous Personal Items, 473 Deaths, 473 Backlog of Mathematics Research Journals New Members of the AMS Classified Advertising Forms

Mathematics Awareness Week AMERICAN MATHEMATICAL SOCIETY

EDITORIAL COMMITTEE

Robert J. Blattner, Ralph P. Boas Lucy J. Garnett, Mary Ellen Rudin Nancy K. Stanton, Steven H. Weintraub Everett Pitcher (Chairman) MANAGING EDITOR

James A. Voytuk ASSOCIATE EDITORS

Ronald L. Graham, Special Articles Jeffrey C. Lagarias, Special Articles SUBSCRIPTION INFORMATION

April 24-30, 1988 Mathematics Awareness Week was initiated in 1986 with the passage of legislation by the U.S. Congress. The idea for this national event developed in the office of Senator Pete Domenici (R-N.Mex.) as the brainchild of Congressional Fellow James R. Murphy, and a very active public information campaign on the part of the mathematical community led to the actual passage of the bill. The first Mathematics Awareness Week (April14-20, 1986) was highlighted by many special events including the airing of a public service announcement on over 200 television stations across the country. Since 1986, the U.S. mathematical community, under the leadership of the Joint Policy Board for Mathematics, has recognized a week during April as National Mathematics Awareness Week. Last year the week's activities focused on regionally developed projects and local efforts appeared across the country. Symposia were organized, state proclamations were issued, bumper stickers were distributed, local television spots were prepared and numerous other events took place (see Notices, June 1987). All this was developed around the theme "The Beauty and Challenge of Mathematics."

Subscription prices for Volume 35 (1988) are $1051ist; $84 institutional member; $63 individual member. (The subscription price for members is included in the annual dues.) A late charge of 10% of the subscription price will be imposed upon orders received from nonmembers after January 1 of the subscription year. Add for postage: Surface delivery outside the United States and lndia-$10; to lndia-$20; expedited delivery to destinations in North America-$15; elsewhere-$38. Subscriptions and orders for AMS publications should be addressed to the American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901-9930. All orders must be prepaid.

In 1988 the focus will again emphasize local events. The theme for Mathematics Awareness Week 1988 is 100 YEARS OF AMERICAN MATHEMATICS. In particular, descriptive material covering four major areas of mathematical endeavor during our first century in America

ADVERTISING

• Symmetry

Notices publishes situations wanted and classified advertising, and display advertising for publishers and academic or scientific organizations. Copyright@ 1988 by the American Mathematical Society. All rights reserved. Printed in the United States of America.

The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and durability. § [Notices of the American Mathematical Society is published ten times a year (January, February, March, April, May/June, July/August, September, October, November, December) by the American Mathematical Society at 201 Charles Street, Providence, Rl 02904. Second class postage paid at Providence, Rl and additional mailing offices. POSTMASTER: Send address change notices to Notices of the American Mathematical Society, Membership and Sales Department, American Mathematical Society, P. 0. Box 6248, Providence, Rl 02940.] Publication here of the Society's street address, and the other information in brackets above, is a technical requirement of the U. S. Postal Service. All correspondence should be mailed to the Post Office Box, NOT the street address.

378

• From Finite Differences to Parallel Processing • The Nature of Space-Time • Technology's Cutting Edge are being developed. This material is being sent to Department Chairs along with other information and a sample news release. Individuals are encouraged to obtain copies of this material through their departments or directly from the Joint Policy Board for Mathematics. Using this material and the experience of the 1987 events, it is hoped that groups will join together to make Mathematics Awareness Week a major event of this centennial year. The general public's impression of mathematics and mathematicians has, for many years, been clouded by the lack of information. This has changed over the past few years; mathematical events are being reported in the media, articles are appearing in national publications about mathematicians and there is a growing awareness that mathematics stands at the base of technological development. It is through vehicles like Mathematics Awareness Week that this trend will continue.

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

A Request to Support a Polish Mathematician

The Blending of Pure and Applied Mathematics Is it too late to help to "blur" further the "commonly recognized distinction between" pure and applied mathematics referred to by S. H. Cullinane, Notices 34 page 924 [October 1987]? I do not regard applied mathematics as being by definition useful. Apart from the fact that I believe that some mathematics done under the name applied mathematics has in fact no clear application, that done for application to fundamental scientific work probably has no immediate usefulness. The great scientific discoveries are useful, but surely often in ways quite unconnected with the original object of the work which was not useful. One eminent scientist who applied mathematics to many scientific problems wrote (according to my recollection) that heregarded "Applied Mathematics as a term of abuse." It was in the 1930s, and I think he meant that if the mathematics was applied to physics, engineering, biology, climatology or what have you, it became part of that subject, but if it was good enough to stand alone it was a piece of pure mathematics. As regards "the trickle-down theorists," I should like Mr. Cullinane to consider how the Whitehead-Russell formal logic through Turing's work became useful in computer software. I myself found inspiration for my work with Littlewood on experimental work on thermionic valves. Our work was no use for that and I believe that thermionic valves are obsolete. We worked as pure mathematicians. However, I have been told that our work was of interest to control engineers and I was invited several times to address engineers. I have also been told that some of our work is relevant to mathematics connected with biology. However, the overwhelming case for encouraging pure mathematics seems to me to be that the difficulty of its problems forces an intense mental effort and a clarity of expression far beyond that involved in any application. In fact I strongly suspect that it is just those apparently abstract parts

Letters to the Editor

of pure mathematics that will eventually "trickle-down" possibly into the schools, provided ofcourse that pure and applied are not segregated. Dame Mary L. Cartwright, F.R.S. (aged nearly 87) Cambridge, England (Received December 17, 1987)

Policy on Letters to the Editor Letters submitted for publication in Notices are reviewed by the Editorial Committee, whose task is to determine which ones are suitable for publication. The publication schedule requires from two to four months between receipt of the letter in Providence and publication of the earliest issue of Notices in which it could appear. Publication decisions are ultimately made by majority vote of the Editorial Committee, with ample provision for prior discussion by committee members, by mail or at meetings. Because of this discussion period, some letters may require as much as seven months before a final decision is made. Letters which have been, or may be, published elsewhere will be considered, but the Managing Editor of Notices should be informed of this fact when the letter is submitted. The committee reserves the right to edit letters. Notices does not ordinarily publish complaints about reviews of books or articles, although rebuttals and correspondence concerning reviews in Bulletin of the American Mathematical Society will be considered for publication. Letters should be typed and in legible form or they will be returned to the sender, possibly resulting in a delay of publication. Letters should be mailed to the Editor of Notices, American Mathematical Society, P.O. Box 6248, Providence, RI 02940, and will be acknowledged on receipt.

MARCH 1988, VOLUME 35, NUMBER 3

EDITOR's NoTE: The following letter was signed by 132 persons. It was submitted for publication by three former students of Dr. Morawiecki: Ewa Kubicka, Grzegorz Kubicki, and Dorota Baran (Western Michigan University). On November 9th of this year, the Polish communist government captured and immediately incarcerated the leader of the Polish opposition group-underground Solidarity-'Solidamosc Walczaca' Dr. Kornel Morawiecki. Kornel Morawiecki was a professor of mathematics at The Technical University of Wroclaw until the martial law was imposed in Poland in December, 1981. Until his arrest, he was the last remaining Solidarity founder to retain his freedom, he had become a symbol to all Poles concerned with Polish freedom and dignity. It was through him that the Underground Solidarity movement gained the legitimacy and strength it has today. There exists a high probability that especially cruel retribution will be taken against this man since the Polish secret police have been searching for him for over six years. The goals of the underground Solidarity movement are democracy, freedom for Poland, and respect for human rights and dignity. These are the only acts he can be charged with. We believe that only through the common action of people who are his academic colleagues in universities and academic and professional organizations as well as human rights groups can sufficient pressure be brought to the Polish government to persuade it to treat this man in a fair, just and humane manner. Thus we ask that The American Mathematical Society do all it can to promote a sense of fairness and justice in the case of the plight of Dr. Kornel Morawiecki. The matter is very urgent since his health and even his life are at risk.

379

Letters to the Editor

Comments on a Commentary Letter In the November 1987 Notices, you published a letter on the five referendum motions from a person in Providence whose name is not on the Combined Membership List. This letter contained an alleged quotation by D. Z. Manuilsky, taken from a publication Countdown which sounds suspiciously as if it emanated from a rightwing extremist source. I was amazed to see this "quote" rising again to the surface. It is a fake. It was used widely in the early 60s by John Birch Society sympathizers. In the 50s and 60s there was a cottage industry for inventing such quotations and attributing them to Lenin, Stalin, Khruschev and others. Even Senator Strom Thurmond was taken in by a Khruschev "quote." If one needs a conspiracy scenario, how about this one: The Soviets are secretly convinced that the Star Wars program will drive the United States into bankruptcy. Hence, in order to ensure that it goes ahead, they publicly denounce it and threaten to pull out of arms control negotiations. The right response for mathematicians on these issues is not irrational panic but the sort of rational analysis that appeared in the letter of Chandler Davis in the same Notices. David Merriell Vassar College (Received November 10, 1987)

One can sympathise with your correspondent's distrust of soviet intentions but one cannot surrender to paralysis of the will. Jf we disarm now we do indeed run the risk of being overrun. If we do not, we face the asymptotic certainty of nuclear destruction in the long run. Which do we prefer? The choice is not a hard one to understand: bridge players cope with it routinely. If you have not got enough tricks on top you take the finesse. Maybe you go down but then you would have gone down anyway: if you are serious about making the contract you simply have no choice. As a foreigner the internal policies of the U.S. and the Soviet Union are no concern of mine, and it does not seem to me that such differences as they exhibit in their attitudes to the rest of the world justify frying the entire planet. Indeed is there anything that justifies frying the entire planet? Thomas Edward Forster University of Cambridge, England (Received December 15, 1987)

N. Ghoussoub, G. Godefroy, B. Maurey, and W. Schachermayer In the last twenty years, several remarkable results have been established in the context of infinite-dimensional Banach space theory. Most of the results emphasize the interplay between topological, geometrical, and measure theoretical structures of a Banach ~pace. ~his book examines this interplay m certrun classes of Banach spaces. The authors focus in particular on those spaces whose bounded subsets have arbitrarily norm-small convex combinations of slices. This class contains spaces with the Radon-Nikodym property as well as B-convex Banach spaces. The topological analysis of these spaces leads to the concept of "first class functions around sets," an extension of the classical notion of Baire-1 functions. Stemming from the study of bounded linear operators from L 1 into these spaces, the measure-theoretical analysis of those subsets of L 00 with "small" or "regular oscillation" is carried out. Various geometrical properties of these spaces are established, including a result analogous to the Krein-Milman theorem ~d. the .existence of some geometrically d1stmgu1shed points. The authors also consider the special cases of Banach lattices and C* -algebras. Contents: First class functions around a subset of a Polish space; Affine and first class functions around a subset of a convex compact; Dentability and related notions in Banach spaces; Operators from £1 (0, 1) intc Banach spaces; A characterization of strong! regular Banach spaces; On w•-regular sets in dual Banach spaces; On regular Banach spaces and the Radon-Nikodym property; Examples and remarks.

There are many objectionable features in your correspondent Sbardella' s letter in the last [November 1987] issue of the Notices. For one thing the AMS has members of many widely different persuasions, communist and reaganite, and it is not the function of the AMS to air their differences. For another it is hardly helpful to judge current soviet foreign policy by remarks made more than fifty years ago. In any case there are some recent remarks made by senior Americans that make pretty unsavoury reading too. It is best not to embark on such a discussion if the AMS is to continue to serve its wider role.

380

SOME TOPOLOGICAL AND GEOMETRICAL STRUCTURES IN BANACH SPACES

1980 Mathematics Subject Classification: 46 ' ISBN 0-8218-2441-4, LC 87-19556 ISSN 0065-9266 124 pages (softcover), October 1987 List price $15, Institutional member $12 Individual member $9 ' To order, please specify MEM0/ 378 NA

Shipping/Handling: 1st book $2, each add'l Sl, S25 max. By air, let book $5, each add'l $3, $100 max. Prepayment required. Order from AMS, P.O. Box 1571, Annex Station, Providence, RI 02901-9930 or call 800-556-7774 to use VISA or MasterCard:

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NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

ELLIOTT H. LmB AWARDED 1988 BIRKHOFF PRIZE

The George David Birkhoff Prize is awarded every five years to a recipient selected, by a joint committee of the American Mathematical Society and the Society for Industrial and Applied Mathematics, for outstanding contributions to "applied mathematics in the highest and broadest sense." The 1988 recipient is ELLIOTT H. LIEB of Princeton University. The Birkhoff Prize Fund was originally created by the Birkhoff family in 1967. The awards are currently augmented by monies from the AMS Leroy P. Steele Fund (presented to the Society for prizes in honor of George David Birkhoff, William Fogg Osgood, and William Caspar Graustein). In 1988 the award is $4000. Previous recipients of Birkhoff prizes are Jurgen K. Moser (1968), Fritz John (1973), James B. Serrin (1973), Garrett Birkhoff ( 1978), Mark Kac ( 1978), Clifford A. Truesdell III (1978), and Paul R. Garabedian (1983). The Birkhoff Prize is awarded by action of the Councils of the AMS and SIAM on the recommendation of the joint AMS-SIAM Committee to Select the Winner of the Birkhoff Prize for 1988, whose members are Wendell H. Fleming, W. Gilbert Strang, and Hans F. Weinberger (chairman). The material which follows consists of the selection committee's citation, the remarks of Professor Lieb at the Prize Session in Atlanta on the presentation of the award, and a brief biographical sketch of Lieb. Citation The Birkhoff prize is awarded to Elliott Lieb of Princeton University for his profound analysis of problems arising in mathematical physics. In nonlinear differential equations and in the classical inequalities of analysis, Lieb has resolved the cases of greatest importance to physics-exactly the cases in which simplified hypotheses and general compactness arguments did not apply, and the analysis was most delicate. In the Schrodinger equation his work went beyond short range interactions, to allow the slow decay of Coulomb potentials. The LiebThirring inequality connects the stability of matter to a new estimate, independent of N, for the norm of an antisymmetric N-fold tensor product. His sharp bounds in

the Hardy-Littlewood-Sobolev inequalities have opened new approaches to nonlinear equations. Lieb's influence on mathematical physics-the Thomas-Fermi problem, the theory of liquid crystals, harmonic maps, the Ising model, and much more-has reached so far because it has remained so deep.

Elliott H. Lieb

Response Naturally, I am very happy to receive the Birkhoff prize of the American Mathematical Society and the Society for Industrial and Applied Mathematics. My pleasure stems not only from the generous citation of my own work but also from the fact that a certain tradition in mathematical physics is being honored. The tradition I have in mind is that mathematical physics

MARCH 1988, VOLUME 35, NUMBER 3

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1988 Birkhoff Prize

does not simply borrow from mathematics but that there is also some feedback. From time to time problems in physics can generate mathematical questions whose answers have some intrinsic mathematical value. In other words, good mathematical physics can aspire to be both good mathematics and good physics, and both fields can benefit from the interaction. This is the view shared by most of my coworkers in mathematical physics. In the nineteenth century this attitude was not uncommon but, unfortunately, in about the first half of the twentieth century there was a tendency on both sides to disparage it. Happily, the interdependence of the two fields is now being increasingly appreciated by both mathematicians and physicists. Biographical Sketch Elliott H. Lieb was born July 31, 1932, in Boston, Massachusetts. He received his B.Sc. degree from the Massachusetts Institute of Technology in 1953 and his Ph.D. degree in mathematical physics from the University of Birmingham, England, in 1956. He also received an honorary D.Sc. degree from the University of Copenhagen in 1979. Professor Lieb was a Fulbright Fellow at Kyoto University (1956-1957). He was a research associate at the University of Illinois ( 1957-1958) and at the Laboratory for Nuclear Studies at Cornell University (1958-1960). Between 1960-1963, he worked as a staff physicist at the T. J. Watson Research Center of the IBM Corporation. He was associate professor of physics at Belfer Graduate School of Science, Yeshiva University (1963-1966); professor of physics at Northeastern University ( 19661968); and professor of mathematics at Massachusetts Institute of Technology ( 1968-197 5). Since 197 5, he has been a professor of mathematics and physics at Princeton University.

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Professor Lieb has held numerous concurrent positions. For a year (1961-1962) he was a visiting Senior Lecturer in mathematics at Fourah Bay College, The University of Sierra Leone. He was a visiting professor at the Institut des Hautes Etudes Scientifiques, France ( 1972-1973 and 1986); at the Research Institute of Mathematical Sciences of Kyoto University (1978-1979); and at the Institute of Advanced Study, Princeton ( 1982). In both 1972 and 1978 he was awarded a Guggenheim Fellowship. For five years he was an editor for Communications in Mathematical Physics and is currently an editor for Advances in Applied Mathematics, Studies in Applied Mathematics, Letters in Mathematical Physics and Reviews of Modern Physics. He was a member of the board of governors of the Institute for Mathematics and its Applications ( 1983-1986) and has been a member of the board of trustees of the Mathematical Sciences Research Institute since 1985. Professor Lieb received the Boris Pregel Award for Research in Chemical Physics from the New York Academy of Sciences in 1970; the Dannie Heineman Prize for Mathematical Physics from the American Physical Society and the American Institute of Physics in 1978; and the Science Prize from UAP in France 1985. He is a member of the American Mathematical Society, the Mathematical Association of America, and is a fellow of the American Physical Society. He is a member of the U.S. National Academy of Sciences and the Austrian Academy of Sciences. Professor Lieb is a member of the International Association of Mathematical Physics and served on its executive committee from 1979 to 1981 and as its president from 1982 to 1984. Professor Lieb's primary areas of research interest are harmonic analysis, combinatorics, statistical mechanics, solid state physics and atomic physics.

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

ATLANTA MEETING KICKS OFF AMS CENTENNIAL

About thirty one hundred people attended the Joint Mathematics Meetings January 6-9 in Atlanta, Georgia. In the last 10 years, only one meeting was comparable in attendance. An excellent scientific program and a festive social agenda helped to make the Atlanta meeting a success. The high point of the meeting was a special banquet to inaugurate "100 Years of American Mathematics," a year-long expansion of the Centennial of the AMS. Two thousand mathematicians dined on caesar salad, supreme de volaille, and fettucine alfredo, while the Atlanta String Quintet tried to make itself heard in a room that was the size of a football field. The dessert, peach jubilee flambe, made possible a spectacular pyrotechnic display. With their number reduced by a snowstorm, the serving staff nonetheless did an excellent job. "Watching them solve the operations research problem ·Of serving 2000 people was worth the money," quipped one attendee. "It was mathematics in action."

Among those speaking at the banquet were Alfred B. Willcox, Executive Director of the Mathematical Association of America (MAA); Leonard Gillman, President of the MAA; and George Daniel Mostow, President of the AMS. Some of the attendees later confessed to feeling a little silly singing "Happy Birthday" to the AMS at Gillman's behest, but most participated in good humor. After dessert, over 1300 HP-28S calculators were distributed to those participants who had paid $60 in addition to the $30 banquet ticket. The calculator boasts a 32K memory and has graphing and symbolic manipulation capabilities. Hewlett-Packard offered the calculator to the banquet attendees at a considerable discount off the list price of $235. Many noted that this calculator has profound implications in mathematics education and exposing the mathematical community to this new technology is essential. "It could have been much more commercial," remarked one attendee. "[HewlettPackard] could have passed out color leaflets promoting

"100 Years of American Mathematics" Banquet

MARCH 1988, VOLUME 35, NUMBER 3

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Atlanta Meeting

other products, but they didn't." He also noted the company had sent the "right person" to speak at the banquet-William Wickes, an engineer who managed the research for the calculator. Wickes asked the banquet attendees to send him their comments on the calculator. The banquet set a congenial mood that continued throughout the meeting. "AMS meetings have tended to be impersonal," noted one participant. "There are not many occasions when everyone gets together." While a 2000-person banquet can hardly be considered personal, there was a clear sense of camaraderie.

Hour Talks Praised Many participants praised the hour talks sponsored by the AMS, the MAA, the Association for Women in Mathematics, and other organizations. There were four expository AMS-MAA Joint Invited Addresses. John G. Kemeny of Dartmouth College spoke on the ways in which computers have changed his teaching methods. His sincere concern for students and education came forth as he described his extensive experience in developing educational software and in using computers in teaching mathematics. David Mumford of Harvard University gave a personal view of his thesis adviser, colleague, and friend, Oscar Zariski. After a brief sketch of Zariski's life, Mumford used original papers to give a flavor of the field of algebraic geometry as Zariski practiced it. Joseph W. Dauben of Herbert Lehman College, City University of New York and the Graduate Center, CUNY, spoke on Georg Cantor and the development of transfinite set theory. This fascinating psychological portrait outlined Cantor's struggle to have his ideas accepted in the face of stubborn opposition. While all of the Joint Invited Addresses were wellattended and well-received, perhaps the warmest reception was given to Lipman Bers of Columbia University. Bers' poignant story focused on mathematicians who had emigrated from Europe to the United States. As one such mathematician himself, Bers expressed his gratitude at the warmth and openness with which he was greeted by Americans. The audience responded to his insightful and sincere observations with a standing ovation. Some noted that Bers' talk had a particular relevance now, when the increasing number of foreign PhDs in mathematics has been a subject of concern.

discussion. A referendum on the issue has been formulated, and the ballots have been mailed to members, who must return them by mid-March. While other issues are included, the most controversial portions of the referendum concern the articulatiptfof:ap, AMS position on the Strategic Defense Initiative (SDI) )and military funding of mathematics. [' In Atlanta, there seemed--to be less discussion of these issues than in San Antonjo; people may simply be waiting to see the outcome of the vote. However, the issues may have seemed mor¢ visible because of a "Yes on the Referendum" table set up in the headquarters hotel and because some of the participants were wearing "Vote Yes" buttons. At the business meeting in San Antonio, there was considerable discussion about the military funding issue. But in Atlanta, the highlight of the business meeting was the awarding of the Birkhoff prize to Elliott Lieb, and the military issue was not discussed. The Science Policy Committee sponsored a talk entitled "Why the SDI Software Could Never be Trusted," by David Parnas of Queen's University. A computer scientist, Parnas~A"esigned in 1985 from a Strategic Defense Initiative 1(SDI) Organization Panel on Computing in Support of BattJe Management. Since then, he has been a vocal and/ steadfast opponent of SOL In his talk, Parnas explained how there are fundamental reasons why the software would keep the SDI-antiballistic missile system from being trustworthy. Many praised the lecture as a knowledgeable presentation of the facts of the software issues surrounding SDI. Another attendee noted that Parnas not only gave arguments against SDI, but also surveyed and responded to the various opinions defending it.

Military Funding Motions At the Joint Mathematics Meetings in San Antonio in 1987, there was a special Science Policy Committee session devoted to discussion of military funding of mathematics. After that, a temporary Notices column, Commentary on Defense Funding, ran from June 1987 to January 1988 in order to provide a forum for public

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A busy registration area testifies to the success of the meeting.

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

Atlanta Meeting

Educational Issues An important focus of the meeting was mathematic s education. In addition to various educational sessions and MAA Minicourses, there was a special event entitled "Forces for Change in Mathematic s Education." After an exhibitor-sponsored reception, there were two concurrent sessions-on e on calculus reform and one on fractals (the third one, entitled "Who Will Teach Mathematics?", was cancelled because inclement weather prevented the arrival of the main speaker). The session on fractals became so crowded that the organizers had to move a wall to allow the crowd to spill over into an adjoining room. With what one attendee termed "a fireworks display" of graphics, Heinz-Otto Peitgen provided an excellent and accessible explanation of the Julia set and Mandelbrot set of a simple polynomial. He further enlivened the proceedings with a movie which brought out some interesting relationships between these two sets and which showed the seemingly infinite complexity of the Mandelbrot set. In his address upon his retirement as President of the MAA, Lynn Arthur Steen spoke on "Celebrating Mathematics." The title refers to the year-long celebration, "1 00 Years of American Mathematic s," a series of events that grew out of the AMS Centennial Celebration. In his talk, -Steen pointed to several areas of mathemati cscomputation al statistics, mathematic al biology, geometrical mathematics, and nonlinear dynamics- that have recently seen substantial theoretical developments and important applications. These areas can be used to convey to students and the general public the excitement of mathematic s and the crucial role it plays in science and technology. Saying that "we are not publicists, but we are teachers," Steen called on the mathematic s community to "educate the attentive public" about mathematics. He also stated various goals for improving mathematic s

education, including using computers, involving students in the practice and invention of mathematics, and emphasizing logical reasoning and communica tion skills. Saying that education is not an alternative to research but a way of renewing the research community, he spoke of closing the "gap" between research mathematic ians and mathematic s educators. Allyn Jackson Staff Writer

Lynn Arthur Steen, John W. Kenelly, and Marcia P. Sward try out the new calculators.

MARCH 1988, VOLUME 35, NUMBER 3

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AMERICAN MATHEMATICAL SOCIETY 1888-1988 100 YEARS OF AMERICAN MATHEMATICS

THEAMS CENTENNIAL This year the American Mathematical Society is celebrating its lOOth Anniversary. It is a time to look back with pride to our historic past and to look forward to a future of growth and increased service to the mathematical community.

• ~~~~'/c:Eb. 0 UNDED \'B"

American Mathematical Society Centennial Celebration- August 8-12, 1988 Providence, Rhode Island

Inside the AMS Report of The Executive Director

William J. LeVeque 1987 stands out in my mind as a year of important decisions for the Society-decisions that will affect both the Society and the mathematical community for the better, I believe. Some were made by the Executive Committee and Board of Trustees (ECBT) or the Council, and some by other organizations; the consequences of some have already become visible, of others not. But this was also a year of solid accomplishment, both in pushing forward with our regular activities and in realizing the fruits of earlier decisions. As I write this, my final annual report, I am happy to say that I think the Society is in excellent shape as we start our second hundred years: with our second consecutive substantial surplus we seem to be rather secure financially, we have a strong ongoing program and the promise of even better things to come, and we have both the superb staff and the facilities needed to do the job capably and efficiently. With the continuing enormously important contributions from so many mathematicians who give their time and effort generously, the future looks rosy indeed.

Publications A major effort was required of the staff to change the format of the Notices to that which you are now reading. Many new TEX header files had to be created, new fonts brought into use, design experts consulted, and a Macintosh microcomputer (to assist in complicated page layout) purchased and assimilated. I was impressed that all this was accomplished in only about four months, while those involved continued with the production of all our many other journals and books, as well as the planning for the new Journal of the AMS, of which I trust you have seen a copy by now. The ECBT authorized the staff to begin work on two more new journals and to plan toward a third. The journal Sugaku (the word means 'mathematics'), published by the Mathematical Society of Japan, is approximately the equivalent of the Bulletin of the

AMS; each issue contains several expository articles which are said by Japanese-reading mathematicians to be highly informative accounts of current areas of research. The AMS will begin to publish translations of these articles during 1988 in a new journal entitled SugakujMathematics. The ECBT also authorized me to sign a contract with the Soviet copyright agency to publish a translation of the Journal of Theoretical and Applied Mathematics of the Leningrad branch of the Steklov Institute, which will commence publishing in 1989. Finally, the AMS and the MAA are joining forces to seek startup funding for a newsletter concerned with developments in collegiate mathematics education. You may be surprised that the Society is formally involving itself with mathematics education. In fact, the Society is broadening its interests in other ways as well, as is partially evidenced by the volumes that will soon begin to appear in three new book series: • During the centennial year and the few months thereafter, several volumes will be produced in the History of Mathematics Series, each consisting of reprints or new articles concerned with American mathematics during the past century. The series will continue after that, probably with an emphasis on areas still of interest to research mathematicians. Appropriate manuscripts will be welcome; To assist in providing the AMS membership and the general mathematical community with information relative to Society activities, this new column, '"Inside the AMS"', will appear on a regular basis in Notices. It is very appropriate that the first contribution to this column is William J. LeVeque's Report of the Executive Director. He describes many of the projects initiated last year and examines their impact on future activities of the Society. This is the type of article that will appear in this column and, as time passes, the membership will look to this column for information. This column will, in upcoming issues of Notices, contain the Report of the Secretary and the Report of the Treasurer.

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please communicate with this office or with Peter Duren, chairman of the editorial committee. • As its name implies, the University Lecture Series will preserve lecture series given by outstanding mathematicians at various universities. An early volume, by Michael Freedman on low-dimensional topology and its applications, sterns from the Russell Marker Lectures in the Mathematical Sciences, given at Pennsylvania State University. If your institution has such a lecture series (not a series of one-hour colloquium talks by different speakers) you may wish to suggest publication of the lectures in this form. • A number of excellent books have been allowed to go out of print (OP, in the trade jargon), and the Society has had many requests for help in obtaining copies of such books. Some had been in print for many years, but others have been allowed to go OP rather quickly because of new tax regulations. We will now be including some of these books in the AMS Reprint Series, as a service to the community. If you have any favorites to suggest (graduate level textbooks, monographs, 'special' books), please send information about them to Mary Lane, our director of publication in this office. Two new subseries will also be started, as parts of the series Translations of Mathematical Monographs. Historically this series consists primarily of translations from Russian; the new subseries will instead contain translations from Japanese.and Chinese. The Society received a sizeable grant to produce an expanded and updated version of A. J. Lohwater's Russian-Eng/ish Dictionary of the Mathematical Sciences. Work is now underway on this, under the able direction of Ralph Boas. The final product will probably be available on floppy disks as well as on paper, with occasional updates. In support of the Society's efforts to make it easy for mathematicians to use TE){, we have begun to sell software (commercial versions of TEX for microcomputers, and fonts and drivers) as well as related manuals. During the year, Mike Spivak's Joy of TE;X, the users' manual for AMS-TE){, became the Society's best seller ever. So this kind of service is apparently useful to members. One of my interests over the years has been in making the Society's books better known to mathematicians abroad. We have had an agent in Japan (Maruzen International) for many years, and in 1987 the ECBT agreed to an arrangement with Clarke Associates-Europe, Ltd., for warehousing, promoting, and selling our books in Europe, Africa and the Mid-

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dle East. Members in these regions, of which there are several thousand, will continue to be able to buy books at members' discount, from Providence or England. The warehouse in England will be able to provide faster service, but there will be a slight surcharge. Nonmember customers must order through Clarke.

Mathematical Reviews and Related Products This part of the report deals with activities at Mathematical Reviews during 1987, and was prepared principally by R. G. Bartle, the Executive Editor. For the past several years MR has published approximately 40,000 reviews per year; however, in 1987 we reviewed 51,853 items. (This is slightly less than the all-time maximum number of 52,812 reviews, which was attained in 1979.) The increase in size was partly due to the increase in the volume of the mathematical literature, but mostly to an attempt by the editors and staff at MR to publish reviews more expeditiously. It is estimated that approximately 45,000 reviews will be published in 1988. For many years we have reviewed the articles appearing in many journals from page proof. The editors now hope to expedite the reviewing process further by having many articles reviewed directly from manuscript, after they have been accepted for publication. This should make it possible to publish many reviews immediately after the actual publication of the article. MR will initiate this procedure with all AMS journals and add SIAM journals as soon as possible. It is hoped that other journals may be added later. These articles will also be announced in Current Mathematical Publications (CMP) soon after they are accepted for publication. In this manner scholars will be alerted to their existence as soon as possible; this should further enhance the value of CMP to researchers. It is now possible for reviewers to submit their reviews to MR electronically, provided they are written in TEX. For the exact procedure to be followed, reviewers should consult the January 1988 issue of MR. Last year, an agreement was reached between the AMS and the Association for Computing Machinery to make Computing Reviews and the Guide to Computing Literature available on MathSci-the electronic version of MR. Thus they join MR, CMP, the Current Index to Statistics and the Tukey Statistics Index on MathSci, making it the leading electronic database in the mathematical sciences.

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Inside the AMS

Staff in both offices began considering the problems and opportunities associated with a new technology for dissemination of information, the CD-ROM. These are compact disks, like the popular CDs, but containing immense amounts (about 500 megabytes) of digitalized information rather than music. In our case, we would record MathSci, together with search software so that one could locate records by author, title, words or phrases in title or review, journal, date, or any combination of these. We hope to be able to sell them at an affordable price to individuals at institutions subscribing to MR. But that's for the future! Compilations of the subject indexes of all the items in probability theory and in statistics that were reviewed in MR from 1940-1984 were published early in 1987. Further volumes of this nature will be published in the future. A five-volume set of Reviews in Numerical Analysis, 1980-1986, has now appeared, and sets of Reviews in Partial Differential Equations, 1980-1986, and of Reviews in Global Analysis, 19801986, are in preparation. These collections contain the complete reviews of all items having either a primary or secondary classification in these areas and which were reviewed in MR during this seven year time span. They should be of considerable interest to researchers in these active fields. Additional review volumes are also planned for future publication.

Meetings and Conferences In response to the urgings of many members, the Joint Meetings Committee reduced the length of the Joint Annual Meetings from five days to four in 1987. The brisk schedule makes for extremely busy meetings for mathematicians serving on several committees, and sometimes forces participants to make difficult choices between overlapping sessions, but on the whole it seems to be viewed with favor by participants. The Executive Committee decided to move the Symposium on Questions in Mathematical Biology, which has been held for many years 'in conjunction with the annual meeting of the AAAS, to a different venue. Starting in 1988 the symposium will be sponsored by SIAM (as before) and the Society for Mathematical Biology, and will meet alternately with the Federation of American Societies for Experimental Biology and the American Institute of Biological Sciences. In 1987 SIAM decided not to continue its cosponsorship of the Applied Mathematics Symposia. These have usually been held in alternate years at sectional AMS spring meetings. The Executive Committee has

decided that in the future, conferences on applied subjects (other than the AMS-SIAM Summer Seminar and the AMS-IMS-SIAM Summer Research Conferences) should be held at meetings of other societies, as will be the case with mathematical biology. The Society hopes to initiate an annual series of one-day programs for talented high school students, in various metropolitan areas around the country. We will fund the first such program ourselves in Boston in 1988, with the collaboration of the Boston Museum of Science. The Meetings department added a person to the staff temporarily to be responsible for the logistics of the various special activities that will occur during the centennial year. Those functions the Society did or will help to organize include the special events at the Annual Meeting in Atlanta, the symposium American Mathematics Entering its Second Century at the AAAS meeting in February, the Symposium on the Legacy of John von Neumann in June, and of course the Centennial Meeting in Providence in August. (For a complete list of the ten '100 Years of American Mathematics' functions, see p. 62 of the January Notices.)

Activities and Changes in the AMS Offices In the Providence office there was, as usual, considerable activity in the computer services division. A VAX 8700 was installed, and it, together with the 8600 purchased in 1986, will replace the two obsolescent DEC 2060s that have served us during the Eighties. We now compose all books and journals in TEX and we bought a new and faster typesetter (an APS Micro-S) to handle all the work. To accommodate to the new hardware, several programmers were busy rewriting all the programs used to process orders for publications and the membership records, this being an activity that will extend into 1989. Also, the staff made a careful evaluation of several packages of programs to support the work of the fiscal department, and one was chosen, to be installed during 1988. The 'ultimate' version of the matching program used by the Employment Register was also completed in time to be used (very successfully) at the Atlanta meeting. The AMS relies on mainframes for the big computing jobs in both offices (the latter are connected by a direct multiplex line), but 1987 saw steadily more functions being moved to microcomputers and work stations. Although the computer services division continued to need new hardware and software, it is my perception

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that, with the completion of the tasks mentioned above, and the conversion during the next few years of the MR database from the DEC machines to the VAX, the very large-scale purchases and programs will be complete-until and unless a new generation of computers requires a whole new effort. The Society has spent several million dollars on computerization in the past decade, and has kept 10-15 programmers very busy; a diminution in this level of effort would free resources for other valuable purposes. Under the guidance of the Trustees' membership committee, vigorous efforts were made by the staff both to attract new members to the Society and to provide new and better services for present members. To assist us in these efforts, we sent a questionnaire to a portion of the membership to survey their impressions of various AMS services. In addition to providing free literature and coffee at the members' booth at national meetings, we are now holding a New Members' Reception to help newcomers feel more at home. Also, we have joined the MAA in sponsoring a Gold Visa card which is free to members the first year and provides several benefits. And I think that the broadened publication program I described earlier will provide an attractive benefit for AMS members. There are about 225 employees of the Society, approximately two-thirds of them in Providence and the remainder at the Mathematical Reviews editorial office in Ann Arbor. In 1987 two Providence employees, Josephine Faria and Barbara Beeton, became twentyfive year employees of the Society; each of them is known to many of you through their work on Abstracts and TEX, respectively. And with the addition of Marcia Almeida and Theresa Drennan to the list, the number of twenty-year employees in Providence grew to 25. Unfortunately for the Society, we lost four good people to retirement; you may not have known Lillian Barraza or Ernest Nordman because their duties did not give them much contact with mathematicians, but every habitual meetings-goer knew Mary Coccoli and

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Dottie Smith, who have both been at the registration desk for about the past 15 years, helping members straighten out every conceivable problem. Fortunately, we have also had some fine additions to the staff. Among the new senior staff in Providence, one you are likely to get to know if you publish books or journal articles with us is Beth Kiley, the new Head of the Editorial Department. Two other persons whom you may already know have been promoted: Taissa Kusma as Head of the Database Services Department, and Lenore Stanoch as Head of the Marketing Department. The MR office moved from Providence to Ann Arbor only in 1965 and there was then an almost complete turnover of MR staff, so the number of very senior employees is not very large. But most of the supervisors and many of the editors have been at MR for a number of years. The newest supervisors are Ella Ponomarenko, the Head Librarian since the end of 1986, and James A. Sundberg, the Director of System Development since June. Dr. Leszek S. Zaremba joined the editorial staff last summer. In both offices, the level of commitment to the Society and its purposes is, in my opinion, remarkable. I was struck by it eleven years ago when I became director, and I still am. They are unusually capable men and women, and they really care about what they do, and about doing it with excellence. In spite of the difficulties and mixups some of you have encountered on occasion, I may say that I have almost never seen a case of bureaucratic indifference to members' needs, at least on the part of staff members of more than a few years' standing, during my tenure. Many of you will be in Providence in August, for the Centennial meeting. At the cost of a half-mile walk or cab ride you can visit the AMS building, where we will be holding an open house throughout the meeting. I think you will be impressed by what you see and the people you meet. It's your Society-come see how it works!

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

Mathematical Text Processing

Richard S. Palais Introduction In this last article of my series on technical word processing (TWP) I will make some final comparisons between WYSIWYG (what you see is what you get) mathematical word processing and TEX. There has now been a lot more experience in using both, and I think it is possible to give better answers to the complex question of under what circumstances and for which purposes one or the other may prove a better choice. In addition I will update my earlier discussion of TWP software for the Macintosh family of computers (Notices October 1986). Whither WYSIWYG But first I would like to make some comments about the WYSIWYG preparation of long or complex mathematical documents. In this area I feel that recent progress has been distressingly slow, both for the Macintosh and for the IBM-PC compatibles. Don't get me wrong. There are WYSIWYG technical word processing systems for both families of machines that are reasonably easy to use and with which it is possible to get quite respectable results. In fact the results are far superior to the technical typing of only a few years ago, and for simple projects like an exercise set or short paper, they are perfectly adequate. But the consis-

tent high quality needed to prepare camera copy for a book, a thesis, a long paper, or other complex project has so far been unattainable by these methods, or attainable only approximately and with unreasonable effort. The past two years have seen the rapid development of many excellent WYSIWYG "desktop publishing" programs that have made the LaserWriter, coupled with either the Mac or a PC, an ideal system for the production of high quality complex non-technical documents. During those two years the appearance of TEX for both the Mac and the PC has demonstrated that with a markup language approach: mathematical book production of the highest quality is also possible with the same hardware. In principle it should be possible to create a WYSIWYG technical document preparation system that closely approximates this "book quality" available from TEX, and it should even be possible to add such high quality TWP facilities to some of the existing WYSIWYG word processors. But in fact no such word processor has yet come along, and I have become pessimistic about the prospects for seeing one any time soon. It would appear that none of the big software houses see enough of a potential market in such a project to allocate the resources necessary to get the job done. Let me review briefly the spe-

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cial problems that give mathematical document preparation and typesetting its extra difficulty, and explain why I feel existing WYSIWYG technical word processors still have a long way to go to live up to their ultimate potential. As has been emphasized repeatedly in this column, a piece of text is more than just a string of characters; it has in addition an internal logical structure that is reflected by its organization into words, clauses, sentences, paragraphs, sections, chapters, etc., each of which can come in many flavors. An individual word may deserve emphasizing, a phrase may be a title, a sentence could be a footnote, and a paragraph may be an introduction or summary of a section or chapter. Centuries of effort and experimentation have gone into the design of distinctive typefaces of high readability, and to developing the art and science of book design for their effective use. The basic principle of book design is that the speed and ease of comprehension of text can be greatly enhanced by carefully choosing the size, weight, style, and placement of the type used to reflect the different elements of logical structure. A welldesigned book or article is after all one that can be read rapidly and comprehended easily. Its quality is a natural outgrowth of these utilitarian considerations rather than of any conscious effort to make it pleasing to the eye. The extra

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difficulty inherent in mathematical document preparation comes from the far greater logical complexity of mathematical text and the correspondingly greater complexity of the above design considerations. And this complexity grows more than linearly with the size of a document due to interrelationships between the various parts. To begin with, in mathematics there is a much larger alphabet of basic symbols, and these must be designed to blend in gracefully with the text typefaces. And besides the usual categories of words of normal text, mathematics has many extra categories, such as variables, operators, and indices; as well as the usual clauses and sentences of normal text we have also formulas and equations. And finally, in addition to the usual kinds of paragraphs of text, we have definitions, theorems, proofs, remarks, etc., all of which have special conventional formats to set them apart, and special numbering systems to make them easier to cross-reference. While many of the formatting rules and stylistic choices for these mathematical elements are obvious and well known to all mathematicians, many others are more subtle and esoteric. For example, in high quality mathematical typesetting, variables are set in a so-called mathematical italic that is actually distinct from the text italic used for emphasis and in the statement of theorems. And second order subscripts and superscripts are set smaller than first order ones, but usually at the same point size as third order ones. Even though mathematicians are often unaware of such niceties at a conscious level, they will feel something is not right if these conventions are violated. It can be distracting and confusing if the variable "a" in the statement of a theorem is indistin-

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guishable from the article "a". In fact almost all mathematicians will imme_diately recognize and appreciate the quality and improved readability of excellent mathematical typesetting, even if very few have the time, patience, or inclination to learn the myriads of detailed stylistic choices that go into attaining that quality. After all, a mathematician's time is better spent proving theorems than learning the arcana of mathematical book design. This may explain why TEX has become so popular with mathematicians who prepare their own manuscripts, and why it gives such superior results with comparatively little effort. It is not simply that TEX has readily available nearly every mathematical symbol that one is likely to ever need. The feature of TEX that really sets it apart is that very complete expert knowledge about conventional mathematical style is built into TF){ and is applied automatically, almost without user intervention. All TEX asks is to be given some little clues, such as typing a dollar sign to signal that you are starting to type mathematical rather than ordinary text, or typing "\proclaim" to tell TEX that the next paragraph is the statement of a theorem. By contrast, if one tries to approximate standard mathematical typesetting conventions with available WYSIWYG systems, it is necessary not only to have a complete and conscious knowledge of all the rules of mathematical style, but in addition one must apply these rules in a consistent fashion through constant adjustments of the typeface and size of the current font. Another serious problem with attempting high quality WYSIWYG typesetting of mathematiCs is that the available high resolution symbol fonts are inadequate for all but the simplest

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mathematical applications. It is relatively easy to create low resolution (72 dpi) fonts using bitmap font editors, and so there are many good bitmap symbol fonts around. But creating a high resolution font (300 dpi or better) requires the use of an outline font editor, a great deal more skill, and a major investment of time. Let me give the specifications for what I feel would be a convenient and mathematically competent WYSIWYG document preparation system; one that would be able to produce book quality mathematical typesetting without unreasonable effort. Of course it should have all the standard features of a normal word processor; these are well enough known not to need repetition. In addition: • It should have built into it a complete set of mathematical symbol fonts, and also a "math italic" font for variables. These should have bitmap screen versions in standard point sizes, but more importantly they should have outline versions that the program would automatically download as needed when doing output to a PostScript printer. There is an obvious source for such fonts: the Metafont source code for Knuth's excellent Computer Modern fonts are in the public domain. What is needed is a program to translate between the Metafont and the PostScript descriptions of an outline font, a difficult but worthwhile task in itself. • It should have a built-in WYSIWYG formula editor. There are now many excellent "desk accessory" formula editors (MacEqn, Expressionist, MathType) and these are fine for preparing an occasional displayed formula. But mathematical writing frequently has four or five

Mathematical Text Processing

•

•

•

•

small inline formulas per line of text and it is completely impractical to switch to a DA to prepare each one and then cut and paste it back into the text. Ideally I would like to see the program have a tool palette with three ''tools": a text editing tool, an inline formula editing tool, and a displayed formula editing tool. Moreover it should be possible to switch tools with a single keystroke as well as by choosing them from the palette with a mouse. It would be nice if there were a few more tools on the palette for drawing simple diagrams, but I would settle for the ability to create all the arrows needed for commutative diagrams. Of course it should be possible to label these arrows in the normal way. It should support paragraph styles and style sheets. This means that one should be able to define and save named paragraph styles, such as "theorem", "definition", etc., and then, when appropriate, choose them from a style menu. Many of the high end word processors already have this capability, notably Microsoft Word v.3.0 and Icon Technology's MacAuthor (sold as Laser Author in the US). In addition it should come with professionally prepared default style sheets for exercise sets, articles, theses, lecture notes, and books. It should have optional facilities for the automatic numbering of equations, definitions, and theorems, with the ability to refer by symbolic name to automatically numbered items (including forward references). It should have facilities to help in the creation of a table of contents, index, and bibliography.

Perhaps the best hope for such a system lies with Steve Jobs' new company, NeXT Inc. NeXT has stated as a primary goal the development of high quality computer hardware and software for the university community, and one of their chief programmers, John Anderson (who programmed WriteNow for NeXT), is one of those rare people to have both the understanding of what is required and the high level of programming skill needed to implement the above specifications. The introduction this year of the NeXT workstation could be a real landmark for academic computing and is being eagerly anticipated. Of currently available programs, perhaps the one that comes closest is Icon Technology's MacAuthor, programmed by Mike Glover. He is in the process of adding an equation processor, and given the incentive to do so he could probably add most of the other features mentioned above.

Choosing Between and WYSIWYG

lEX

From the above discussion it might seem that the basic criterion for choosing between TEX and a WYSIWYG system for a given project should be its complexity. For a long, complex project, like a book or thesis, use TEX, while for a short preprint or an exercise set use a WYSIWYG system. That was pretty much the advice I was giving until recently, until feedback from others and my own observation indicated that this was too simplistic an answer and not always the best advice. Experience has shown that mathematicians who write their own manuscripts, once they make the decision to adopt TEX, usually learn it quickly, often in only a few days, and then find it so natural and easy to

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use that they subsequently use it for everything. On the other hand technical typists frequently dislike and resist TE)(, finding it difficult and unnatural to learn and use, and easy to forget. Given a choice they usually prefer a WYSIWYG system for everything. I suppose that in retrospect this is not really surprising. TEX was written by a mathematician for mathematicians. A mathematician seey'X dx thinks to himself ing "integral from a to b of the square root of x, dx", and this is almost precisely the TEX idiom for rendering it ($\int_a -b\, \sqrt{x}\, dx$). But technical typists are often unaware of this logical structure of a formula and tend to see formulas more as patterns of symbols that have to be laid out on the page. For them the TEX code seems illogical and arbitrary. So the answer to whether TEX or a WYSIWYG system should be used for a given project may really depend on who will do the keyboarding rather than on the nature of the project. This poses difficulties for mathematics departments that would like a uniform method for preparing manuscripts. Perhaps the gap can be bridged by Siebenmann's SweeTEX and similar programs being developed to permit the input of TEX with a WYSIWYG user interface.

J:

Macintosh

TWP

Since the appearance of my earlier review of technical word processing on the Macintosh, many users have written or called to ask questions or make comments about their experiences and problems using various TWP software packages, and I have myself at least experimented with most of the major systems. As best I can I will try to summarize what I have

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learned from this collective experience in the form of recommendations and warnings about what software seems most suitable or unsuitable for various purposes. I know from past such undertakings that this is bound to be controversial; in particular I am sure to omit many readers' favorit~ fonts, programs, or desk accessories. So let me emphasize that there are of course many more ways to skin the TWP cat than I will mention below. What I have tried to do is concentrate on common and standard systems that appear to work well and easily for many users. As in the previous article I will assume that the reader has gone through basic training on the Macintosh and understands the standard terminology (e.g., applications, desk accessories, fonts) and has used at least MacWrite and MacPaint. In addition to fonts, there are four basic types of software that are of interest to those wanting to do mathematical word processing on the Macintosh. These are: graphics programs, equation processors, WYSIWYG word processors, and finally, of course, TEX. Most mathematical exposition requires occasional diagrams, and whether one uses TEX or WYSIWYG, these are best handled by pasting them in from a specialized graphics program. A "paint" (or "bitmap") program can be used for this purpose, but most people find that the object oriented or "draw" programs are a better choice, and they give sharper results on high resolution output devices. The old standbys, MacPaint and MacDraw, are perfectly adequate, and the Apple spinoff, Claris, is about to reincarnate them in upgraded versions. My own favorites are MacDraft and SuperPaint. Not only is the latter inexpensive, but it also con-

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veniently combines paint and draw capabilities in two separate layers. One of the trickier parts of WYSIWYG mathematical word processing is, of course, entering the formulas. The problem is that, beyond simple subscripting and superscripting, standard text processors like MacWrite or WriteNow have no built·in facilities for making this convenient, and even creating a matrix or a complex fraction can be a real chore. MicroSoft Word 3.0 is almost always an exception; it does have a special mode for creating formulas, but it is TEX-like rather than fully WYSIWYG, and as reported in the article last month by Ted Wallstrom, it is still somewhat primitive, difficult to use, and often gives less than satisfactory results. There are now available a number of quite sophisticated, fully WYSIWYG formula processors (or "equation editors") that can make entering equations a lot less painful, if not exactly enjoyable. These are either desk accessories or applications (sometimes both) that have considerable built-in knowledge about formatting mathematical formulas. The idea is to create mathematical expressions in the formula processor and then electronically cut and paste them into the basic text processor via the Clipboard (using Switcher, Servant, or MultiFinder in the case of the applications). There are some problems with this approach. There are really two kinds of formulas. The bulk of mathematical text consists of many short "inline" expressions separated by normal text. A typical example is " ... if x E R and x > 0 then x has two square roots, .jX and -vlx in R". It is altogether too cumbersome to switch back and forth several times per line between the text processor and an external formula processor. As I

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pointed out in my October 1986 article, if one has available a good set of mathematical symbol fonts (e.g., the Maine family) and knows how to use it, it is really much easier to enter these short formulas directly in the text processor. Thus most people quickly get into the habit of using the formula processors only for complicated displays. But since the formula processors aim for high quality output by using LaserWriter fonts, this means that there will often be jarring inconsistencies between the inline and displayed formulas. For this reason I believe that the route taken by MicroSoft, namely integrating a formula processor with a word processor, is a logical evolutionary step, and I am looking forward to seeing smoother implementations of that approach as time goes on. But for now the formula processor is a useful tool. The main contenders in this field are MacEqn (the original), Expressionist (formerly Weinberg), MathWriter, and MathType. At first glance they look pretty much alike, but there are some important differences. MathWriter, which is perhaps the easiest to use, suffers from two drawbacks. The first is merely an inconvenience; it does not have a desk accessory version so it must be used with MultiFinder or Switcher. Much more serious, once an expression created in MathWriter is pasted into a word processor, it cannot be pasted back into MathWriter for editing. If you don't like it you have to start over from scratch. The publishers (Cooke Publications) recognize this problem, say that it is easy to fix, and promise to do so very soon. By the way, Math Writer pioneered a really neat trick: once an equation has been created, a remarkable desk accessory called MW2TEX will translate it instantly into TEX

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input! I originally suggested this to them, but only half seriously since I thought it would be too difficult to implement; nevertheless it has performed remarkably well with all the examples I've tried. MacEqn also lacks the ability to paste equations back into it for editing. In fact it is even awkward to edit an equation before pasting it into a word processor, and despite some recent improvements, MacEqn seems rough by comparison with the others. I guess my favorite is Expressionist. It is a desk accessory, very smooth and easy to use, and is able to edit its children. And so can MathType, which seems every bit as good. It can run as a desk accessory, is smart about choosing correct typefaces automatically and, like MathWriter, it can translate into TEX. However I have only seen it demonstrated and have not tried it out personally. I very recently received yet another equation editor, called Formulator, from Icon Technology. It is still in the Ptest stage but worked well for me in limited testing. It is highly automatic about making correct choices and can translate into TEX. What's more it came with one of the better HyperCard stacks I've seen. The stack is an introduction to Formulator, and is so well done that I could easily learn the features of the program in ten minutes. Formulator is designed as a small stand alone WYSIWYG word processor, with basic text editing· features, and I could not get its equations to paste into other word processors, except MacAuthor. The WYSIWYG word processors I would recommend for mathematics are WriteNow, for simple documents, and either MicroSoft Word v.3.0, or perhaps MacAuthor (aka LaserAuthor) if you are trying something more ambitious. MacWrite has two serious flaws:

it can open only one window at a time and it does not allow the pasting of a graphic (e.g., an expression from a formula editor) in the middle of a line. Perhaps the new version due soon from Claris will correct these misfeatures. If you can become comfortable and fluent with the formula-making mode in MS Word this is probably one of the fastest methods for doing medium quality mathematical word processing. As for MacAuthor, I do not now find it easy to use for mathematics, but if as I hope it can be well integrated with Formulator the combination could become the most satisfactory WYSIWYG technical word processor for the Mac. And finally there is TEX, which on the Mac comes in two flavors, Kellerman & Smith's TEXTURES (distributed by Addison-Wesley), and MacTEX from FTL Systems Inc. (distributed in the US by Personal TEX Inc.). MacTEX now has a lot more going for it than when I wrote a year and a half ago. First there is a so-called University Edition, available to members of non-profit educational institutions for $399 (comparable to the educational price for TEXTURES). Secondly FTL now has made the Computer Modem fonts available for MacTEX, and since they are even provided in PostScript outline form they are scaleable to any pointsize, whereas the TEXTURES version of the CM fonts are bitmapped, so that full LaserWriter quality is available for them only at their nominal sizes. Thirdly, MacTEX supplies font metrics for a very large selection of downloadable Adobe PostScript fonts, rather than for just the fonts built into the LaserWriter And· finally, the two products are now much closer together in raw speed. In a benchmark test I ran on my Macintosh II (consisting of ten

Plus.

MARCH 1988, VOLUME 35, NUMBER 3

pages of 26 pica by 44 pica text set at 10 points) TEXTURES ran at 5 sec.jpage while MacTEX ran at 7.3 sec.jpage. Doing output to the LaserWriter, MacTEX was actually faster at 17 sec.jpage versus 20.4 sec.jpage for TEXTURES. If I were a publisher and had to choose one or the other I would quite possibly go with MacTEX. But for a mathematician or a mathematics department TEXTURES still seems to me to have the clear advantage. It is simpler to set up and is easier to learn and to use. In particular, putting graphics into MacTEX is quite awkward by comparison with TEXTURES. In fact I never get over just how simple, elegant and pleasant the operation of TEXTURES is. A point where TEXTURES has a particularly strong advantage is in its superb, fast screen previewer. The way I use TEX is as follows: I type about a half page of new material (even less if it is complicated mathematics) in a special window I call "current", and then correct this by running it through TEX and proofreading it in the preview window until I am satisfied, at which time I cut and paste it to the end of the document I am working on and start the cycle again. I ran a test, and with a full output page it took 1£XTURES eight seconds from the time I selected "Typeset" from the menu to the time I was proofing the output in the preview window. The corresponding time for MacTEX was twenty seconds. (These times should be multiplied by about 2.3 for a Mac Plus or SE.)

Signing Off Running this Technical Word Processing column the past two and one half years would have been impossible without a great deal of help. I would like first to thank all those who have contributed ar-

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tides. Special thanks go to the IBM-PC technical group of the Boston Computer Society for the immense effort they went to in preparing their definitive reviews of TWP software in the MS DOS world. But I would also like to thank all the readers who took the time to call or write in their comments, questions, and problems. The field of TWP is extensive and dynamic, and it is not easy to keep up with new developments. Without all the reader feedback, this column would have been not only much less accurate and useful, but also much less fun to write. This is not the end of coverage of computer-related matters in the Notices. Rather, it marks a change of emphasis and a broadening of that coverage. Just as the computer has become increasingly a part of modem everyday life, so also has it started to play an ever more

important role in the intellectual lives of mathematicians. This is not surprising. Despite its name, the "computer" is primarily a general information processor. And if you stop to think about what mathematicians (and other intellectuals) do, you will quickly realize that it is almost entirely concerned with the creation, transformation, communication, and storage of ideas and other information. Obviously we have much to gain from a technology that can help us automate the more routine aspects of our intellectual life, or that can otherwise amplify our abilities to deal with information. One of the first ways many mathematicians start using computers is to transform their mathematical ideas into readable form, so it was appropriate that initial coverage of computer-related questions in the Notices should con-

centrate on these uses. But that is rapidly changing. More and more, mathematicians are using personal computers at home as very intelligent terminals to attach themselves to various online databases or to exchange electronic mail and preprints with colleagues. Some mathematicians are using computers to create marvelous graphics that not only have an intrinsic beauty, but also the power to suggest new theorems or proofs of old conjectures. Others are using them to develop software to carry out old and new algorithms in combinatorics, algebra, or analysis. The other uses to which mathematicians will put computers in even the near future of course defies prediction. So too, the precise nature of the Notices coverage of these exciting developments will change with time, but you can be sure it will be here.

The first Ph.D. employed at the Society was Dr. Caroline E. Seeley. At first she was assistant to the secretary but later an editor of both the Bulletin and the Transactions.

AMERICAN MATHEMATICAL SOCIETY • PROVIDENCE • AUGUST 8-12, 1988

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NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

Washingt on Outlook

Kenneth M. Hoffman 1988: A Year for the Young at Heart Based on the first three months, it appears that 1988 will be very exciting, full of the sorts of highs and lows that characterize periods of change. The year we have billed as the centennial of American mathematics began on a marvelous note, with a rollicking banquet at Atlanta. Lured by the option to purchase for $60 Hewlett-Packard's HP 28S, the most powerful hand computer ever built, nearly 1,800 mathematicians accepted the January 7 dinner invitation issued by AMS President Dan Mostow and MAA President Len Gillman. They filled a room bigger than a football field to join in the kickoff of our year-long celebration '1 00 Years of American Mathematics' and the launch of Project MS 2000, the National Research Council's comprehensive review of the college-university mathematics enterprise. The mathematicians played, if that's the word, with their new calculators, and mused over what Euler, Newton or Gauss would have thought about holding such computing power in one's hand. But most of all, as Len Gillman had predicted, they enjoyed themselves among friends and colleagues. One suspects that those who attended the '100 Years' banquet will remember it for a long time.

It had an aura of a 'happening'. It was an unusual opportunity for mathematicians to feel good about themselves and their community. AI Willcox was a superb master of ceremonies - humorous and delightful. Dan Mostow said some profound things about changes in our community. Bill Wickes spoke well for HewlettPackard. Tom Tucker put the audience through its paces with the new calculators. And Phil Griffiths pointed to the future, setting the stage for Project MS 2000. Yet it was Len Gillman who best captured the spirit of the evening. The audience was somewhat incredulous when he announced that he planned to lead the assembled company in singing happy birthday to the American Mathematical Society. But he sounded his pitch pipe, stretched out his arms and led. And they sang - 1,800 of them, together and in tune. What's more, they loved it. It was a priceless way to start our special year. Meanwhile, back in Washington, the Congress of the United States was making sure that we didn't have too long to enjoy ourselves. First, the National Science Foundation (NSF) research budget was clobbered, ending up with only a 3.3% increase from last year to this. The NSF budget, along with many others, was caught in the squeeze of a last minute flurry of pre-Christmas appropriations

MARCH 1988, VOLUME 35, NUMBER 3

decisions, made in a backroom so quickly that smoke had no time to gather. Then an innocentlooking line was slipped into Department of Defense (DOD) appropriations language, requiring that, under DOD's University Research Initiative (URI), no more than 14% of the dollars can go to any one state. Its consequences were the .trimming of some URI grants, the principal means DOD research programs had for growing. This column went to press before the specific dollar implications of these actions for mathematics research were clear. At NSF, the high priority assigned to mathematics the last few years will undoubtedly be sustained. Yet this may mean that we stand still while the other sciences go backward. At DOD, upon which our support is so heavily dependent, the effect on mathematics is likely to be more severe than it is for the other sciences. We will know before too long. What lessons do we extract from events early in 1988? One is that the public life of mathematics has its ups and downs - more specifically, that we have much to celebrate yet much work to do. Another lesson is that life in the world of mathematics these days is pretty exciting. I sensed at the Atlanta banquet that we're young enough at heart to deal with whatever comes.

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AMERICAN MATHEMATICAL SOCIETY 1888-1988 100 YEARS OF AMERICAN MATHEMATICS

Celebrate theAMS Centennial!

Now you can have a remembrance of the American Mathematical Society's lOOth anniversary for your own -- a beautiful commemorative poster for your home, office, or department. This striking poster is a photographic reproduction of the sculpture "Torus with Cross-cap and Vector Field" by Helaman Rolfe Pratt Ferguson of Brigham Young University. The sculpture is a gift from the Mathematical Association of America to the American Mathematical Society on the occasion of its Centennial. The poster is printed on museum quality glossy paper. The sculpture is white and photographed on a rich blue background.

AMERICAN MATHE'MATICAL SOCIETY CENTENNIAL CELEBWION ·1888-1988 Torus with Cross-cap and Vector Field

To order, please specify POSTER/N List $10 each, plus $2 shipping and handling per order

To order your AMS anniversary remembrance, simply send a check or money order for $10 each (plus $2 shipping and handling per order) to: American Mathematical Society Annex Station, P. 0. Box 1571 Providence, RI 02901-9930 USA Send MasterCard or VISA orders to:

American Mathematical Society P. 0. Box 6248 Providence, RI 02940 or callS00-556-7774 to order by phone in the continental U.S. For your convenience, an order form is available at the back of this issue.

News and Announcements

Arne Beurling

1905-1986 Arne Beurling was born in Gothenburg, Sweden on February 3, 1905. He studied at the University of Uppsala, where he received his Ph.D. in 1933. He was appointed Professor of Mathematics at the same university in 1937 and worked there until 1952. He was a Visiting Professor at Harvard University (1948-1949) and moved permanently to the United States in 1952, where he was elected permanent member of the Institute for Advanced Study in Princeton in 1954. He was a member of many learned societies in Scandinavia and in 1963 received the Celsius Medal of the Uppsala Academy. He was a member of the American Academy of Arts and Sciences and he was honored by Yeshiva University in 1963. The Mittag-Leffler Institute in Stockholm organized a special year (1976-1977) devoted to his work. Beurling's mathematical work deals primarily with complex and harmonic analysis, and he · is regarded as one of the founders of modern analysis. His work is characterized by deep insight, beauty and fundamentally new ideas. In his thesis, written in 1933, the concepts of extremal and conformal invariance were introduced. They received their final form in collaboration with L. V. Ahlfors in the 1940s. Beurling realized very easily the connection between potential theory and harmonic analysis, and his paper on exceptional sets,

written in 1940, is the beginning of the modern theory of boundary behavior of holomorphic functions. His lecture in 19 38 at the Scandinavian Congress in Helsinki contains the first proof of the spectral radius formula for Fourier algebras. (Gelfand's paper was written in 1940). It also gives the first remainder formulas for Tauberian theorems, which are basic for eigen value distributions. One of Beurling's main interests was the general problem of recovering a function from its spectrum. In pursuit of this problem, he realized the importance of contractions and their relationship to potential theory. In collaboration with J. Deny, he later developed this concept into the theory of Dirichlet spaces, which is also now of basic importance in probability. His work also includes the extension of a quasi-conformal map from one to two dimensions (with L. Ahlfors), the closure length for general sets of exponentials (with P. Malliavin), and the characterization of the invariant subspaces for the .shift operator and the introduction of inner functions. Beurling was very generous with ideas to students and collaborators, but very restrictive in his publications. There is a plan to include his unpublished manuscripts in the collected volumes, which are expected to be published in 1988.

MARCH 1988, VOLUME 35, NUMBER 3

Mathematical Association of America Awards

The Mathematical Association of America (MAA) presented the Award for Distinguished Service to Mathematics and the Chauvenet Prize during its 7lst Annual Meeting on January 8 in Atlanta, Georgia. Murray S. Klamkin, emeritus professor of mathematics at the University of Alberta, Edmonton, Alberta, Canada, was presented with the MAA's Award for Distinguished Service to Mathematics. The award was presented to Klamkin for his outstanding service to mathematics which has significantly influenced the field of mathematics and mathematics education on a national scale. It consists of $1000 and a certificate that was presented to Klamkin during the annual meeting. A citation in honor of Klamkin will be published in the January 1988 issue of The American Mathematical Monthly. A life member of the MAA, Klamkin is recognized internationally for his contributions in the area of problem solving and his commitment to the U.S., Canadian, and International Mathematical Olympiads. Klamkin was a member of the USA Mathematical Olympiad Committee (1972-1985), chaired the committee (1975-1984), and served as the director of the U.S. International Olympiad Training Session (1983-1985). His recent books include International Mathematical Olympiads 1979-1985, which appears

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News and Announcements

as Volume 3 of the MAA's New Math Library Series, and Mathematical Modelling: Classroom Notes in Applied Mathematics. Klamkin is also planning a computation for the USA Mathematical Olympiads 1972-1986, which will soon appear in the New Math Library Series. Klamkin's honors include a Certificate of Merit from the MAA, election as a fellow to the American Association for the Advancement of Science, as well as the Doctor of Mathematics, honoris causa degree from the University of Waterloo. Steve Smale, professor of mathematics at the University of California, Berkeley, was awarded the Chauvenet Prize. This prize is awarded to the author of a noteworthy expository survey paper and includes a cash award of $1000. Smale received the award for "On the Efficiency of Algorithms of Analysis," which appeared in the Bulletin of the American Mathematical Society, Volume 13 (1985), pages 87121. The MAA Committee on the Chauvenet Prize said Smale's article "vibrates with the excitement of a current research frontier, of a fresh area of investigation, which is on the move. . . . The author has succeeded admirably in making his material accessible to the mathematical community." Smale was "very pleased" about being the recipient of the Chauvenet Prize, and said that he wrote his article in an effort "toward unifying numerical analysis and theoretical computer science." Smale received his B.S., M.S., and Ph.D. in mathematics from the University of Michigan. -MAA News Release Chernoff Awarded Wilks Medal

At the 1987 Annual Meeting of the American Statistical Association in San Francisco, Herman Chernoff received their Samuel S. Wilks Memorial Medal for his "outstanding research in large sample theory and

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sequential analysis, his extensive service to scholarly societies and on government panels, his effectiveness and popularity as a teacher, and his continuing impact on the theory of statistics and its applications in diverse disciplines." During his distinguished career, Chernoff has held faculty positions at the University of Illinois, at Stanford, and at the Massachusetts Institute of Technology. He is presently professor of statistics at Harvard. His publications include over 100 papers on theory and applications of statistics, and many results of his research are now considered classics. The Samuel S. Wilks Memorial Award, established in 1964, consists of a medal, a citation, and an honorarium, and is given to honor an individual for "contributions to statistical theory or practice, through publications or participation in programs of instruction on practical application, that directly or indirectly have benefited the U.S. Government or the country generally." -Amstat News

mer Research Conferences to be held June 11-August 5 at Bowdoin College, Brunswick, Maine; and the AMS Centennial Symposium to be held August 8-12 in Providence, Rhode Island. To be eligible for these grants the foreign student must be enrolled in full-time graduate studies at a U.S. institution of higher education. Students are ineligible if they are receiving any U.S. government funds for academic support or if they are on refugee, immigrant, or tourist visa status. Previous recipients of STEP awards are ineligible for a second grant. To apply, send a letter stating your name, home country, student status, the name of the institution at which you are enrolled, the name of an official at the institution who can verify your status and financial situation, and the name of the AMS conference you plan to attend to: Dr. James W. Maxwell, Associate Executive Director, American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02940.

Travel Support for Foreign Graduate Students

Japan-United States Mathematics Institute

The Society is pleased to announce that travel support for foreign graduate students attending 1988 AMS conferences is expected to be available again this year through a grant from the STEP program of the Institute of International Education. An application has been filed by the Society for foreign students attending the International Symposium on the Legacy of John von Neumann to be held May 29-June 4 at Hofstra University, Hempstead, New York; the Summer Institute on Operator Theory /Operator Algebras and Applications to be held July 3-23 at the University of New Hampshire; the Summer Seminar on Computational Solution of Nonlinear Systems of Equations to be held July 18-29 at Colorado State University, Fort Collins, Colorado; the Joint Sum-

The Johns Hopkins University is establishing the Japan-United States Mathematics Institute (JAMI). The primary aims of JAMI are to encourage mathematical exchanges and interaction between the two countries, and to further friendly relations. Junichi Igusa, J. J. Sylvester Professor of Mathematics at Johns Hopkins, is the director. Initially, each year approximately four outstanding young Japanese mathematicians will be selected to spend the year at Johns Hopkins. Areas of concentration for the first three years of operation will be algebraic analysis (1988-1989), algebraic K-theory and number theory (19891990), and algebraic geometry and complex analysis ( 1990-1991). In 1988-1989, the visitors will be M. Kashiwara, T. Oshima, T. Mat-

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

News and Announcements

suki, J. Sekiguchi, and Y. Shimizu. It is anticipated that funds will be

available to help support short-term visits to JAMI by interested U.S. mathematicians. An Inaugural Conference will be held at the Johns Hopkins University on May 16-19, 1988 to celebrate the founding of this institute. It will cover the areas mentioned above. The principal speakers will be J. G. Arthur, G. Faltings, D. Goldfeld, H. Hida, H. Hironaka, Y. Ihara, K. Kato, M. Kashiwara, G. Kempf, R. McPherson, J. Morava, S. Mori, T. Oshima, M. Sato, J. Shalika, G. Shimura, and S. Zucker. All interestedmathematicians are invited. For further information, please write to the Director, JAMI, Mathematics Department, The Johns Hopkins University, Baltimore, Maryland 21239. Workshop for Mathematics Educator Teams

The National Council of Teachers of Mathematics (NCTM) and the Mathematical Association of America (MAA) are sponsoring a workshop for educators interested in developing local mathematics teacher projects. The workshop, to be held October 21-23, 1988 at the Airlie Conference Center in Virginia, will acquaint participants with the directors of successful projects and provide an opportunity to discuss approaches to organizing and securing local support for their own projects. After the workshop, follow-up activities are planned over a period of two years. Teams of elementary, middle and high school teachers, college faculty, and mathematicians from business and industry are invited to apply. Participants will receive travel and subsistence expenses through a grant provided by the National Science Foundation. Application forms are due by March 15 and are available from Philip Daro, Executive Director, The

American Mathematics Project, University of California, Berkeley, 2199 Addison Street, Berkeley, California 94720. Telephone 415-643-7310. -Science Education News, AAAS

Centennial Celebration Travel and Subsistence Support It is anticipated that the Society will

receive funds from one or more federal agencies for travel and subsistence support for senior graduate students and young Ph.D.s to attend the AMS Centennial Celebration to be held in Providence, Rhode Island from August 8 through August 12, 19 88. The Centennial program, built around 21 Invited Addresses by an extraordinary group of U.S. mathematicians, is likely to influence the direction of mathematics research internationally for the next ten to fifteen years. Such a program will be particularly valuable to this new generation of mathematicians. Applicants eligible for support will include graduate students in the mathematical sciences at U.S. institutions of higher learning and Ph.D.s who are less than three years from their degrees. The selection committee will establish a selection criterion aiming at the broadest possible distribution of support. These selection requirements may undergo slight modification pending exact amount of awards. In order to apply for travel and subsistence support, graduate students must submit basic mathematical biographical data (school, degree program, major professor, expected graduation date, etc.,) plus two letters of recommendation (one from the major professor). Young Ph.D.s must submit a curriculum vitae, one letter of recommendation, and a list of current grant support. Applications and references must be received by Mrs. Tricia Cross, Centennial Coordinator, American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02940, no later than April 5, 1988. The selection panel will notify all applicants of its decision on May 15, 1988. Preregistration deadline is June 1, 1988.

MARCH 1988, VOLUME 35, NUMBER 3

NSA Sabbatical Program

The National Security Agency (NSA), one of the nation's largest employers of mathematicians, is making efforts to strengthen its ties with the academic mathematical community. One such effort is the NSA's new Mathematical Sabbatical Program. The sabbatical work primarily involves cryptanalysis, a mathematically based discipline. In addition, algebra, probability, statistics, number theory, and discrete mathematics are involved in the work. The sabbaticals run 9 to 24 months and have flexible starting dates. In addition to stipends at least equal the the participants' salaries, the NSA provides either an allowance for moving expenses or a housing supplement. The NSA offers in-house publications, summer workshop programs, continuing colloquia, cooperative education programs and occasional meetings that provide opportunities to interact with mathematicians both within and outside the agency. The deadline for applications is August 1, 1988. For more information, contact: S. Brent Morris, Director NSA Mathematical Sabbatical Program ATTN: RMA National Security Agency Fort George G. Meade, MD 207556000 Telephone: 301-859-6438 News from the Mathematical Sciences Institute Cornell University

The Mathematical Sciences Institute at Cornell University is sponsoring six workshops during the Spring Term of 1988. These workshops are open to all those interested in the topics. Travel assistance is available on a limited basis. Graduate students are invited to attend. Inquiries con-

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News and Announcements

cerning any of the workshops should be directed to: Mathematical Sciences Institute Cornell University 201 Caldwell Hall Ithaca, NY 14853 Telephone 607-255-805 Workshops Order and Disorder in Random Systems: April 17-19, 1988; Organized by R. Durrett Existence of Quantized Gauge Fields: May 30-June 4, 1988; Organized by L. Gross Gauge Theories of Continua: June 5-8, 1988; Organized by D.G.B. Edelen and D. C. Lagoudas Symmetry and Groups in Nonlinear Continuum Mechanics: June 9-14, 1988; Organized by T. J. Healey Mathematical Analysis of Material Microstructure: June 15-18, 1988, Organized by R. D. James and R. P. Lipton Matrix-Based Signal Processing Algorithms and Architectures: June 27-29, 1988; Organized by F. T. Luk and A. W. Bojanczyk The Mittag-Leffler Institute 1988-1989 Grants

The Mittag-Leffler Institute has announced that it has a number of grants available"for 1988-1989. The grants, which are intended for recent Ph.D.s or advanced graduate students, will amount to approximately 7.500 Swedish crowns per month, or 75.000 for those who attend for the duration of the program. The Institute's program will be conducted from September 1, 1988 through May 31, 1989. Housing on the premises of the Institute will be available for some of the participants. The subject for 1988-1989 is Operator algebras. Several aspects of this field will be treated, including the following: • Special C* -algebras • Maps of C* -algebras

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K-theory Derivation C* -physics Structure of von Neumann algebras • Automorphism groups • Cohomology The following experts in the field are scheduled to participate in the program for an extended period: Charles A. Akemann; Huzihiro Araki; William Arveson; D. Buchholz; Michael Cowling; Joachim Cuntz; Sergio Doplicher; Edward G. Effros; David Evans; K. Fredenhagen; Tierry Giordano; Fred Goodman; Pierre de la Harpe; Richard Herman; Palle J0rgensen; Richard V. Kadison; Akitaka Kishimoto; Jon Kraus; Christopher Lance; Roberto Longo; Mihai Pimsner; Marc Rieffel; Jonathan Rosenberg; Shoichiro Sakai; Allan Sinclair; Colin Sutherland; Masamichi Takesaki; Dan Voiculescu; Hans Wenzl; Jim Woods; S. L. Woronowicz; Laszlo Zsido. The following persons will also be at the Institute: Erik Alfsen; Erik Bedos; Ola Bratteli; Erik Christensen; Trond Digernes; G. Elliott; Torben B. Johansen; Esben Kehlet; Dorthe Olesen; Gert Pedersen; Steen Pedersen; Michael R0rdam; Christian Skau; Jon Stefanson; Klaus Thomsen; Anne Marie Torpe; J0rgen Vesterstmm; Kari Ylinen. Applications can be obtained from the Institute and should be returned before March 31, 1988 to The Board of the Mittag-Leffler Institute, Auravagen 17, S-182 62 Djursholm, Sweden. • • • •

Walter E. Massey, AAAS President

Walter E. Massey, the President-Elect of the AAAS, has had a distinguished and varied career as an administrator, educator, and public servant. After earning his Ph.D. in physics from Washington University in St. Louis, Missouri ( 1966), Massey was for two years a postdoctoral fel-

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

low at the Argonne National Laboratory, which is operated by the University of Chicago, under contract to the U.S. Department of Energy. In 1970, he moved to Brown University in Rhode Island, where he was appointed associate professor of physics. Five years later, he became professor of physics and dean of the college at the same institution. At Brown, he founded and directed the Inner City Teachers (ICTOS), a program to educate science teachers for urban schools. For his work on this program, he was awarded the Distinguished Service Citation of the American Association of Physics Teachers in 1975. He returned to the University of Chicago in 1979 to serve as the director of the Argonne National Laboratory and professor of physics. In 1984, he was appointed vice president for research and for the Argonne National Laboratory, a position he holds today. Massey is recognized in the Midwest as a pioneer in developing cooperative projects among industry, government, and research institutions. While at the University of Chicago, he has helped form the Argonne National LaboratoryUniversity of Chicago Development Corporation (ARCH). This project is the first effort by a national laboratory and a university designed to facilitate the transfer of technology from laboratories to the marketplace. In addition to his administrative and teaching duties at the University of Chicago, Massey has served as a director of the United Way of Chicago, and is presently a trustee of the Museum of Science and Industry and the Chicago Symphony Orchestra. Massey also serves as a trustee of Brown University and the Rand Corporation, and is a member of the visiting committees for the physics departments at the Massachusetts Institute of Technology and Harvard University.

News and Announcements

New Program Manager at ONR

Peter McCoy has accepted a parttime position as Program Manager in Applied Analysis in the Mathematical Sciences Division at the Office of Naval Research. The program has two subcomponents, boundary value and inverse problems, and the calculus of variations. McCoy is professor of mathematics at the U.S. Naval Academy in Annapolis, Maryland. University Research Initiative Receives Cuts

Because of severe budgetary constraints and a new rule written into Congressional spending bill for fiscal 1988, the University Research Initiative (URI) of the Department of Defense (DOD) is feeling a financial crunch. Some of the URI programs with a mathematical focus may be among those receiving reductions in funding. The URI was begun in 1986 to support basic research in universities, with a particular emphasis on interdisciplinary research and areas of interest to the DOD. In fiscal 1987-the first year in which the URI was operational-its budget was

FREE GROUP RINGS Narain Gupta This book deals with some aspects of linear techniques in combinatorial group theory having their origin in the work of Wilhelm Magnus in the 1930s. The central theme is the identification and properties of those subgroups of free groups which are induced by certain ideals of the integral group rings of free groups. This subject has been

$115 million. The President's request for the URI was $93 million for fiscal 1988, and Congress appropriated $85 million, amounting to a cut of about 26% from 1987 to 1988. (For more background on the URI, see "The University Research Initiative," Notices, October 1986, page 738.) In addition, Congress added language prohibiting any one state from receiving more than 14% of the URI funds. Only two states-California and Massachusetts-were affected by the rule. The rule was a reaction to those who have criticized the way research funds have been concentrated in certain geographic areas. The critics say that smaller institutions, particularly in the South and the Midwest, never get a chance to develop their research potential. After Congress passed the spending bill, meetings took place between Ronald Kerber, the Pentagon's Deputy Undersecretary for Research and Advanced Technology, and the heads of the four research agencies responsible for handling the URI: the Air Force Office of Scientific Research (AFOSR), the Army Research Office (ARO), the Defense Advanced Research Projects Agency (DARPA), and the Office of Naval Research

developed extensively, and the author seeks to present, in contemporary style, a systematic and comprehensive account of some of its developments. Included in the book are a solution of the Fox subgroup problem and an up-to-date development of the dimension subgroup problem. Aimed at graduate students and researchers in combinatorial group theory, the book requires a familiarity with the general terminology of free groups and group rings.

(ONR). The meetings were held to negotiate the way in which the cuts would be distributed among the four agencies. The negotiation was necessary because some agencies would have sustained much larger cuts than others, had the 14% rule been applied uniformly. There are eleven URI programs funded through the mathematics divisions of the DOD agencies. At the time of this writing, it was unclear how these particular programs would fare. Two of themone funded by ONR's Mathematical Science Division and one by DARPA's Applied Mathematical Sciences Program-are in California, and two-one funded by the ARO's Mathematical Sciences Division and one by the DARPA program-are in Massachusetts. The severity of these reductions and the impact of the overall 26% cut is yet to be determined. In addition to the URI cutback, the Congressional mood of fiscal restraint may indicate that some of the DOD agencies could receive smaller budgets than last year, and their mathematics programs may be affected. However, precise details are not available at this time.

Contents: Magnus embeddings and free differential calculus; Applications of Magnus embedding; Fox subgroups of free groups; Dimension subgroups; Generalized Magnus embeddings. 1980 Mathematics Subject Classifications: 20, 16 ISBN 0-8218-5072-5, LC 87-12427 ISSN 0271-4132 144 pages (softcover), June 1987 List price $22, Institutional member $18, Individual member $13 To order, please specify CONM/66NA

Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added.

MARCH 1988, VOLUME 35, NUMBER 3

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"100 Years of American Mathematics" would like to express its appreciation to the following exhibitors who hosted the "Forces for Change in Mathematics Education" reception held at the Joint Mathematics Meetings Friday, January 8 in Atlanta, Georgia. Academic Press, Inc. Addison-Wesley Publishing Company The Benjamin/Cummings Publishing Company Birkhauser Boston, Inc. Brooks/Cole Publishing Company William C. Brown Publishers Cambridge University Press Cooke Publications Walter de Gruyter, Inc. Marcel Dekker, Inc. Elsevier Science Publishing Company, Inc. W. H. Freeman and Company Harper & Row, Publishers, Inc. D. C. Heath and Company IBM Corporation Richard D. Irwin Company MacmillanjDellen McGraw-Hill Book Company Oxford University Press Pergamon Press Personal T£X, Inc. Plenum Publishing Corporation Princeton University Press PWS-Kent Publishing Company D. Reidel Publishing Company Saunders College Publishing Science Typographers, Inc. Society for Industrial & Applied Mathematics Scott, ForesmanjLittle, Brown Springer-Verlag New York, Inc. TCI Software Research, Inc. Technical Support Software, Inc. True Basic, Inc. Wadsworth Publishing Company John Wiley & Sons

Special thanks to Scott, Foresman/Little, Brown Springer-Verlag New York, Inc. John Wiley & Sons who made significant additional contributions to the support of "100 Years of American Mathematics".

National Science Foundation News & Reports

NSF-CBMS Regional Conferences in the Mathematical Sciences

The NSF will sponsor a series of eight regional conferences between May 1988 and January 1989, designed to stimulate interest in mathematical research. The successful proposals for these conferences were selected by a panel chosen by the Conference Board of the Mathematical Sciences under a contract with the NSF. Each conference features ten lectures delivered over a five-day period by a guest lecturer and typically involves about twenty-five participants. The lecturer subsequently prepares and submits to the Conference Board a paper based on these lectures. This paper normally is published as a monograph in the Regional Conference Series in Mathematics published by the AMS, the Regional Conference Series in Applied Mathematics published by SIAM, or the new "Regional Conference Series in Probability and Statistics" to be published by ASAIMS. . The regional conferences for this coming year are: Mathematical Foundations of the Boundary Element Method, at the University of Kentucky, with Wolfgang Wendland as lecturer. Graeme Fairweather is Principal Investigator (606-257-6814). May 9-13, 1988. Applications of Operator Algebras to Knot Theory and Mathematical Physics, at the U.S. Naval Academy, with Vaughn F. R. Jones as lecturer. Mark Kidwell is the Principal Inves-

tigator (301-267-3603). June 5-11, 1988. Arrangements of Hyperplanes, at Northern Arizona University, with Peter P. Orlik as lecturer. Michael Falk is the Principal Investigator (602-523-6891). June 6-10, 1988. Nonlinear Wave Equations, at George Mason University, with Walter A. Straus as lecturer. Jeng-Eng Lin is the Principal Investigator (703323-2712). January 16-20, 1989. Empirical Processes, Theory and Applications, at The University of Iowa, with David Pollard as lecturer. Timothy J. Robertson is the Principal Investigator (319-335-0820). June 13-17, 1988. Weak Convergence Methods for Nonlinear Partial Differential Equations, at Loyola University of Chicago, with Lawrence C. Evans as lecturer. Emmanuel Barron is the Principal Investigator (312-508-3580). June 26-July 1, 1988. Kaehler Geometry and Several Complex Variables, at Eastern Illinois University with Y. T. Siu as lecturer. Patrick Coulton is the Principal Investigator (217-581-5902). August 13-17, 1988. K- Theory and Dynamics, at the University of Florida, with F. Thomas Farrell as lecturer. Christopher W. Stark is the Principal Investigator (904-392-6166). January 9-14, 1989. NSF and NASA Link Networks

The NSF and the National Aeronautics and Space Administration (NASA) have agreed to share high

MARCH 1988, VOLUME 35, NUMBER 3

speed communication lines in an effort to link university researchers to data bases and supercomputers at NASA laboratories. The five-year agreement began January 1. The agreement is in accord with a recent report of the White House Office of Science and Technology Policy. The report, entitled "A Research and Development Strategy for High Performance Computing," recommends improvements in networking to enhance U.S. leadership in the field and to provide the linkages needed for collaborative research by scientists working at different institutions. Three NASA facilities will be linked to existing NSF regional networks, which are in tum connected through a national backbone network, NSFNET. The Goddard Space Flight Center in Greenbelt, Maryland will be linked to the Southeastern Universities Research Associates Net (SURANET); the Ames Research Center in Mountain View, California will be linked to the Bay Area Regional Research Net (BARRNET); and the Johnson Space Flight Center in Houston, Texas will be linked to SESQUINET, a regional network in Texas. Authorized scientists will be able to gain remote access to NASA data and to apply for time on NASA supercomputers. NASA-funded scientists at universities served by NSF regional networks will be able to communicate with their colleagues at the NASA centers.

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NSF News & Reports

Sharing networking resources should prevent duplication of effort by the two agencies. The NSF already shares networking facilities with the Office of Naval Research and the Defense Advanced Research Projects Agency. The OSTP report calls for accelerated efforts to expand interconnections among agencies. Federal Support for Academic Research and Development Shows No Growth

The National Science Foundation today announced the release of the most recent detailed data on federal support for university research and development, which in real dollars showed no increase for the 1986 fiscal year. Total federal support for academic research and development was $6.5 billion, about the same as in the previous year after taking inflation

into account. Although overall funding did not increase, eight of the 15 agencies which account for virtually all federal support for academic research·and development did increase funding. The Department of Health and Human Services, the source of about one-half of all federal support for academic research and development, accounted for the greatest increase, followed closely by the Department of Defense, the second largest federal source. Total obligations for all collegelevel academic programs for the surveyed agencies were $11.6 billion, including $4.2 billion for activities not directly related to science and engineering-mainly Pell Grants and Supplemental Education Opportunity Grants administered by the Department of Education's Office of Student Financial Assistance.

The top 100 universities, ranked according to federal research and development dollars received, accounted for 86 percent of total federal support for academic research and development during the 1986 fiscal year. Of these, 95 were ranked among the top 100 during the previous year. When the survey series began in 1963, the leading 100 universities received 90 percent of federal support for academic research and development. This data is part of a report entitled Federal Support to Universities, Colleges, and Selected Nonprofit Institutions: Fiscal Year 1986 (NSF 87-318). Individual copies of thereport are available from Richard Bennof of NSF's Division of Science Resources Studies, 1800 G Street, N.W., Washington, D.C. 20550, or telephone 202-634-4636. -NSF News Release

Prepublication Reviews in MR To the Mathematical Community: In order to make Mathematical Reviews (MR) more timely, the editors of MR have instituted, starting in January 1988, a procedure for reviewing articles that have been accepted for publication in certain mathematical journals directly from final manuscripts, and not waiting until the actual publication of the articles before the reviewing process is started. (i) Only manuscripts that have been finally accepted by the editors of certain journals will be so treated. (ii) MR will obtain copies of the final version of the manuscripts directly from the editorial offices of the journals. MR will send these manuscripts to reviewers. (iii) The titles of these forthcoming articles will be listed in Current Mathematical Publications (CMP) with an indication that the articles are "to appear" in the appropriate journal. (iv) The review of an article will not be published until after the article actually appears. (However, it is expected that in most cases the review will be published immediately after the publication of the article.) (v) When the article is published, CMP will give it a second listing, this time with complete bibliographic information. (vi) Initially this procedure will be instituted with journals published by the AMS (i.e., Bulletin, Journal, Memoirs, Proceedings, Transactions, Mathematics of Computation). MR will start this procedure with manuscripts accepted after January 1988. (vii) It is anticipated that additional journals may be added to this list later. We hope to add many of the SIAM journals in the near future. Robert G. Bartle

Executive Editor Mathematical Reviews

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NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

1988 AMS Elections Nominations by Petition Vice-President or Member-at-Large One position of vice-president and member of the Council ex officio for a term of two years is to be filled in the election of 1988. The Council intends to nominate two candidates, whose names may be expected to appear in the June issue of Notices, which is scheduled to be mailed by the printer on May 18. Nominations by petition as described in the rules and procedures are acceptable. Five positions of member-at-large of the Council for a term of three years are to be filled in the same election. The Council intends to nominate seven candidates, whose names may be expected to appear in the June Notices. Nominations by petition in the manner described in the rules and procedures are acceptable. The Council has stated its intent to have at least ten candidates and will bring the number up to ten if the nominations by petition do not do so. Petitions are presented to the Council, which, according to Section 2 of Article VII of the bylaws, makes the nominations. The Council of 23 January 1979 stated the intent of the Council of nominating all persons on whose behalf there were valid petitions. The Council of 20 January 1987 established a policy that, beginning with the interval 1987-1996, the Council intends to approve no more than two nominations by petition of the same individual in any ten year period. Prior to presentation to the Council, petitions in aid of a candidate for the position of vice-president or of member-at-large of the Council must have at least 50 valid signatures and must conform to several rules and operational considerations, which are described below.

The Nominating Committee for 1989 Four places on the Nominating Committee will be filled by election. There will be four continuing members of the Nominating Committee, namely Roger C. Alperin Jane P. Gilman Ronald A. DeYore Leonard L. Scott The new members will be elected in a preferential ballot. The President will name six candidates for these four places. The names may be expected to appear in the June issue of Notices. Nominations by

pet1t10n, in the manner described in the rules and procedures, will be accepted. Should the final number of candidates be less than eight, the President will bring it up to eight. The name of a candidate for member of the Nominating Committee may be placed on the ballot by petition. The candidate's assent and petitions bearing at least 100 valid signatures are required for a name to be placed on the ballot. In addition, several other rules and operational considerations, described below, should be followed.

Rules and Procedures Use separate copies of the form for each candidate for vicepresident, member-at-large, or member of the Nominating Committee. 1. To be considered, petitions must be addressed to Everett Pitcher, Secretary, P. 0. Box 6248, Providence, Rhode Island 02940, and must arrive by July 6, 1988. 2. The name of the candidate must be given as it appears in the Combined Membership List. If the name does not appear in the list, as in the case of a new member or by error, it must be as it appears in the mailing lists, for example on the mailing label of the Notices. If the name does not identify the candidate uniquely, append the member code, which may be obtained from the candidate's mailing label or the Providence office. 3. The petition for a single candidate may consist of several sheets each bearing the statement of the petition, including the name of the position, and signatures. The name of the candidate must be exactly the same on all sheets. 4. On the next page is a sample form for petitions. Copies may be obtained from the Secretary; however, petitioners may make and use photocopies or reasonable facsimiles. 5. A signature is valid when it is clearly that of the member whose name and address is given in the left-hand column. 6. The signature may be in the style chosen by the signer. However, the printed name and address will be checked against the Combined Membership List and the mailing lists. No attempt will be made to match variants of names with the form of name in the CML. A name neither in the CML nor on the mailing lists is not that of a member. (Example: The name Everett Pitcher is that of a member. The name E. Pitcher appears not to be. Note that the mailing label of the Notices can be peeled off and affixed to the petition as a convenient way of presenting the printed name correctly.) 7. When a petition meeting these various requirements appears, the Secretary will ask the candidate whether he is willing to have his name on the ballot. Petitioners can facilitate the procedure by accompanying the petitions with a signed statement from the candidate giving his consent.

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NOMINATION PETITION FOR 1988 ELECTION The undersigned members of the American Mathematical Society propose the name of

as a candidate for the position of (check one):

D Vice-President D Member-at-Large of the Council

D Member of the Nominating Committee of the American Mathematical Society for a term beginning January 1, 1989. Name and Address (printed or typed, or Notices mailing label)

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Signature

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NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

For Your Information Gina Kolata Leaves Science

Gina Kalata has been known for many years for her excellent coverage of mathematics in Science magazine. Her in-depth reporting has been of great benefit in heightening public awareness of mathematics. Recently, Kalata moved to the New York Times, where she has been reporting primarily on biology and medicine. Just prior to her departure from Science, Kalata spoke with Kathleen Holmay, Public Information Director for the Joint Policy Board for Mathematics, and the following are excerpts from their conversation.

Holmay: You've written about mathematics for Science for how many years now? Kolata: As long as I've been with Science, for 14 years, I've been writing about mathematics. I have a master's degree in mathematics, from the University of Maryland, which has helped me considerably because I wasn't afraid to talk to mathematicians. Plus, my mother is a mathematician and my husband is a mathematician. I wasn't afraid to ask a lot of questions and to admit I didn't understand things, to make mathematicians back up a hundred times and explain something over and over. There's almost nothing that I studied in math that relates to anything I have covered. Mathematics is such a difficult subject. You have to know so much. I never even knew what a modern question was when I was in graduate school. We were back in the 18th Century and 19th Century. Holmay: What makes a good story in mathematics-a

researcher, a proof, work in progress? Kolata: A good story is not necessarily one that has immediate applications. A good story is simply a "story"-sorrtething unexpected-something to do with old questions that have been around-an old problem that is suddenly solved-even historical things. The Ramanujan story gEiot of publicity because it was just a good "story". his Indian was uneducated, at least uneducated\,~· ording to the standards of mathematicians, and he was able to do things without

having been taught about them. Even though his work is not dramatically affecting the course of mathematics today, just the fact that he existed is a good story. Also, this story has a narrative. It's wonderful-first he did this, then lo and behold, he discovered something that we never thought of and then it all comes together. Unless they're startling, making practical applications can be boring. The Ramanujan story wasn't one about how mathematicians think. To me it was a story about the mystery of mathematical creativity. It was incredible that somebody could be born with this kind of talent. And also it was incredible that one person, Bruce Berndt, is devoting years of his life to going through Ramanujan's notebooks. That is really astonishing to me and yet it has nothing to do with anything practical. It is just an amazing human interest story. Holmay: Do you use mathematics journals to get story

ideas? Kolata: Journals? No. Books? No. I just talk to people. And once people realize I'm interested, they tell me about events and interesting discoveries. There are few mathematicians who know what constitutes a good story. When somebody discovers something really amazing, at least one person usually calls me and tells me about it. I even get story ideas when somebody has claimed to discover something and it's not true. A recent proof made by someone in England turned out not to be so. A group of people got together in California and went over the proof to find it wasn't correct. Because this concerned a famous problem, it was interesting. Several people called and said that this thing didn't work out like it was supposed to. I also get press releases and find out about conferences. Holmay: Do you think it's necessary for more people-

the general public and public policy makers, and others-to learn more about mathematics in order to realize the importance of the field?

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For Your Information

Kolata: It's hard to say. I agree with you in theory but I don't know if physics, for example, is doing any better than math and they have been inordinately successful getting publicity for various abstract things. It's amazing what physics has accomplished. Why is it that people read about quarks and are not willing to read about topology? I don't know. On the other hand, are kids becoming physicists because they're reading a newspaper article about quarks? I don't think so and I'm not sure what would tum things around and get kids interested in mathematics. I'm sure a lot of it has to do with what happens in the classroom. I'd like to see everybody think that math was interesting and important. What I'd really like to see is more people in other sciences thinking that mathematics was really fascinating. Not necessarily that it's useful or important, but that mathematics is fascinating and fun to think about. Then you would have more people choosing mathematics because it's really exciting and not because they think it's an important subject. If something is important it might impress you but that doesn't necessarily mean it is something you want to devote your life to.

Holmay: Are mathematicians able and willing to explain their work? Kolata: Oh yes, they're wonderful. They're really good. The only time I've had people who were difficult was when they didn't really know what they were talking about. I've had people who would say "This is really interesting" and then it turns out that they don't quite know it well enough to be able to explain it. But when people really understand their subject they can find analogies that I couldn't have dreamed of. One time I was talking to a man from California and he said he had to think for a day or so about how to explain something. And then he called me back and he had this fantastic analogy which had all the logic there, all the ideas there, but it wasn't couched in words that would make it sound impossible. Holmay: Speaking for the mathematics community, I feel your leaving Science is a net loss of 1 in an already very small pool of science writers who cover mathematics. What can mathematics do to encourage more coverage of the field? Kolata: I agree with you although I don't like to think that about myself, but when I go to the Times I won't be covering math very much. They have somebody who I think is wonderful, Jim Gleick, so they don't really need another person to cover those same stories. It's hard to know what's important to cover in mathematics. I've had people call me with suggestions

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for stories about problems that nobody really cares about. I think part of it is not to have mathematicians tell you about their own stories but to have their friends tell you that a story exists. Colleagues often see things with more perspective. People call me and say "I have a story." But they don't really have a story, they have a tiny little result, and it doesn't fit into anything larger. Also, I think mathematicians are going to have to rely on people like you.

Holmay: Do you think it's probable or desirable for daily newspapers to cover mathematics now and then? Will their writers be able to handle the subject matter? Kolata: I'm not sure what to say about this subject because I have mixed feelings about the publicizing of mathematics. I think that for certain readers it's fantastic. When you have a wonderful audience, like the readers of Discover or the former Science 86, then those readers will look at something about mathematics. Possibly, by its very nature you have a more specialized audience. I don't like to think that reporters have to be trained in the subject that they're covering. I don't want to say that you have to study math. But I do think that you really have to follow a logical order. You don't have to know what anything means because usually when you write these stories you don't know what these things are anyway. But you have to be able to go from step A to step B to C to D. There's this whole train of thought. And you have to not be afraid to tell people when they've gone into too much detail. Don't be afraid to ask a lot of stupid questions. That's true in any kind of reporting, but it's even more the case in math. Daily papers and popular magazines don't have mathematics writers. They wouldn't want someone who covered mathematics exclusively. What they want is somebody who does physics and math and perhaps other areas. Look at the story about the Karmarkar algorithm which got a lot of publicity. The reporters who covered it knew little mathematics. I'm sure it showed up in places like Business Week and The Wall Street Journal-places you wouldn't have expected to see a math story. And these reporters didn't have any special training, they just thought that they had an important story. The economic implications got this story into places where it wouldn't have gotten otherwise. Nobody said, "I can't do it, I don't have the ability." And most people did a pretty good job. I think there are a lot of journalists who are writing about these subjects today who could do math as a sideline if stories came along that they could understand, stories which were interesting.

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

Meetings and Conferences of the AMS

FUTURE MEETINGS East Lansing, Michigan March 18-19

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Knoxville, Tennessee March 25-26

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Las Cruces, New Mexico April 8-9

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College Park, Maryland April 23-24

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Invited Speakers and Special Sessions

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Symposium on Some Mathematical Questions in Biology Las Vegas, Nevada, May 4

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Symposium on the Legacy of John von Neumann Hofstra University, May 29-June 4

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Summer Research Institute University of New Hampshire, July 3-23

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Summer Seminar in Applied Mathematics Colorado State University, July 18-29

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Call for Topics

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FUTURE CONFERENCES

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Coming Events

The recent meeting in Atlanta was a great success, and a wonderful kickoff to "100 years of American Mathematics". An article on the meeting can be found on page 383.

The deadline for preregistration and housing requests for the Symposium on the Legacy of John von Neumann is April 4. All interested parties are urged to act now. The appropriate form can be found at the back of this issue.

The First Announcement of the Centennial Celebration will appear in the April issue, which will be mailed to all members on April 6. Since the deadline for preregistration and housing requests is June 1, all interested parties are urged to get their forms in as soon as possible after receipt of the April issue.

The location and dates for the January 1991 meeting have been chosen: January 16- 19 in San Francisco, California.

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NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

East Lansing, Michigan Michigan State University March 18-19

Program of the 840th Meeting The eight-hundred-and-fortieth meeting of the American Mathematical Society will be held at Michigan State University in East Lansing, Michigan on Friday, March 18 and Saturday, March 19, 1988. This meeting will be in conjunction with a meeting of the Association for Symbolic Logic.

Invited Addresses By invitation of the Committee to Select Hour Speakers for Central Sectional Meetings, there will be four invited one-hour addresses. The speakers, their affiliations, and titles are: BARBARA L. KEYFITZ, University of Houston, Systems of conservation laws that change type. BRIAN PARSHALL, University of Illinois at UrbanaChampaign, Modular representations of algebraic groups. KARL RUBIN, Ohio State University, Elliptic curves and the Birch and Swinnerton-Dyer conjecture. WILLIAM P. ZIEMER, Indiana University, Fine regularity in partial differential equations.

Special Sessions By invitation of the same committee, there will be five special sessions of selected twenty-minute papers. Topics, the names and affiliations of the organizers, and lists of the speakers follow. Algebraic groups and related topics, WILLIAM HABOUSH and BRIAN PARSHALL, University of Illinois at Urbana-Champaign. Speakers include: Kaan Akin, Vinay Deodhar, Richard Dipper, Steven Doty, Robert L. Griess, J. E. Humphreys, Andy R. Magid, A. Neeman, Brian Parshall, Mark Ronan, Peter Sin, Stephen D. Smith, and Lin Tan. Groups and geometries, JONATHAN HALL and BERNT StELLMACHER, Michigan State University. Speakers are Andrew Chermak, Alberto Delgado, Daniel Frohardt, Robert L. Griess, P. R. Hewitt, Peter Johnson, Peter B. Kleidman, Mark Ronan, A. Ryba, Yoav Segev, Stephen D. Smith, Gernot Stroth, F. G. Timmesfeld, and Satoshi Yoshiara.

Phase transztzon and connection matrices, KoNSTANTIN MISCHAIKOW and AMY NovicK-COHEN, Micbigan State University. Speakers include Robert Franzosa, Martin E. Gurdin, Robert L. Pego, James F. Reineck, and Peter Sternberg. Nonlinear partial differential equations, DANIEL PHILLIPS, Purdue University. Speakers include Christoph Borgers, Kuo-Shung Cheng, David Hoff, Bradley J. Lucier, Nicholas C. Owen, Daniel Phillips, Jean-Michel Rakotoson, Paul Sacks, Marshall Slemrod, and Joel Smaller. Algebraic combinatorics, BRUCE SAGAN, Michigan State University. Speakers include George E. Andrews, Lynne M. Butler, Paul H. Edelman, Francis G. Garvan, Ira M. Gessel, Curtis Greene, Gilbert Labelle, Pierre Ler01.IX, Kathleen M. O'Hara, Saul Stahl, John R. Stembridge, Sheila Sundaram, and Dennis White.

Contributed Papers There will also be sessions for contributed ten-minute papers on Friday, March 18 at 3:00 p.m., and Saturday, Marcb 19 at 8:40 a.m. and 3:00 p.m.

Registration The registration desk will be open on Friday, March 18 and Saturday morning, March 19 in the C-Wing lobby of Wells Hall. The registration fees are $30 for members of the AMS, $45 for nonmembers, and $10 for students or unemployed mathematicians.

Petition Table A petition table will be set up in the registration area. Additional information about petition tables can be found in a box in the Atlanta meeting announcement on page 68 of the January issue of Notices.

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