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2000 Steele Prizes comm-steele.qxp 2/15/00 10:58 AM Page 477 2000 Steele Prizes The 2000 Leroy P. Steele Prizes were awarded at contributions in automata, the theory of games, the 106th Annual Meeting of the AMS in January lattices, coding theory, group theory, and qua- 2000 in Washington, DC. dratic forms. He has a rare gift for naming The Steele Prizes were established in 1970 in mathematical objects and for inventing useful honor of George David Birkhoff, William Fogg mathematical notations. His joy in mathematics is Osgood, and William Caspar Graustein and are clearly evident in all that he writes. Conway’s book endowed under the terms of a bequest from On Numbers and Games, London Math. Soc. Leroy P. Steele. The prizes are awarded in three Monographs, vol. 6, Academic Press, London, 1976, categories: for expository writing, for a research ISBN 0-12186-350-6, is a classic in its field and even paper of fundamental and lasting importance, and inspired a novel (Surreal Numbers by D. Knuth). In for cumulative influence extending over a career. the words of John Dawson’s review in Mathemat- The current award is $4,000 in each category. ical Reviews, “Overall, this book is a momentous The recipients of the 2000 Steele Prizes are addition to the mathematical literature: a new, JOHN H. CONWAY for Mathematical Exposition, exciting, and highly original theory is expounded BARRY MAZUR for a Seminal Contribution to Research by its creator in a style that is at once concise, (limited this year to algebra), and I. M. SINGER for literate, and delightfully whimsical.” An anony- Lifetime Achievement. mous reviewer at amazon.com of Conway’s book The Steele Prizes are awarded by the AMS The Book of Numbers, co-authored with Richard Council acting through a selection committee whose Guy, Copernicus, 1996, ISBN 0-387-97993-X, writes members at the time of these selections were: that “the book is so fascinating that it can be a real Ciprian I. Foias, Bertram Kostant, Hugh L. time sink.” Carl Riehm, reviewing Conway’s The Montgomery, Louis Nirenberg, Marc A. Rieffel, Sensual (Quadratic) Form (“with the assistance of Jonathan M. Rosenberg (chair), John T. Tate, François Francis Y. C. Fung”), based on Conway’s Hedrick Trèves, and S. R. S. Varadhan. Lectures in 1991, Carus Mathematical Monographs, The text that follows contains, for each prize vol. 26, Math. Assoc. of America, Washington, DC, recipient, the committee’s citation, a brief 1997, ISBN 0-88385-030-3, in Mathematical biographical sketch, and a response from the Reviews, states: recipient upon receiving the prize. This is a book rich in ideas. They seem to burst forth from almost every page, Steele Prize for Mathematical Exposition: and it is perhaps not surprising that it John H. Conway seems a little disorganized at times. I Citation suspect that the author’s hope that The Leroy P. Steele Prize for Mathematical Expo- “even the experts in quadratic forms sition is awarded to John H. Conway of Princeton will find some new enlightenment here” University in recognition of his many expository will be realized. The parts of the book APRIL 2000 NOTICES OF THE AMS 477 comm-steele.qxp 2/15/00 10:58 AM Page 478 dealing with topographs, and with crowd of people” obviously means the same as “a Voronoi cells, vonorms and conorms crowd of happy people”. A large set of numbers, are especially interesting. One can only on the other hand, is very different from a set of hope that this book will help to bring large numbers. them into the argot of quadratic forms. So mathematical writing is definitely hard— steel hard. This Steele Prize—what a steal!—I don’t Conway is the author or co-author of at least eight deserve it, but suppose I must steel myself to different books and of many expository articles. accept it. Thank you very much indeed. They have had substantial impact not just on re- search mathematicians but even on mathematical Steele Prize for a Seminal Contribution to amateurs. Research: Barry Mazur Biographical Sketch Citation John H. Conway is one of the preeminent theorists The Leroy P. Steele Prize for a Seminal Contribu- in the study of finite groups and one of the world’s tion to Research, which this year was limited to foremost knot theorists. He algebra (broadly interpreted), is awarded to is the author of more than Barry Mazur of Harvard University for his paper 10 books and more than 135 “Modular curves and the Eisenstein ideal” in journal articles on a wide Publications Mathématiques de l’Institut des Hautes variety of mathematical sub- Études Scientifiques, no. 47 (1978), 33–186. This jects. He has also done path- paper determined the possible torsion of the breaking work in number rational points of elliptic curves defined over Q and theory, game theory, coding also laid the foundation for many of the most im- theory, tiling, and the cre- portant results in arithmetic algebraic geometry ation of new number sys- over the last 20 years, including (but not tems. limited to): Beyond the academic 1. The proof of the Main Conjecture of Iwasawa world Conway is widely theory by Mazur and Andrew Wiles, in “Class fields known as the inventor of of abelian extensions of Q”, Invent. Math. 76 (1984), the “Game of Life”, a com- no. 2, 179–330. puter simulation of simple 2. Ken Ribet’s proof that the Taniyama-Shimura cellular “life”, governed by conjecture implies a proof of Fermat’s Last Theo- remarkably simple rules rem, in “On modular representations of Gal(Q/Q) which give rise to amazingly arising from modular forms”, Invent. Math. 100 complex behavior. It was (1990), no. 2, 431–476. John H. Conway popularized by Martin Gard- 3. Wiles’s proof of the Taniyama-Shimura con- ner’s columns in Scientific jecture and of Fermat’s Last Theorem, in “Modular American in the early 1970s and has had a large elliptic curves and Fermat’s last theorem”, Ann. of group of devotees ever since. Conway may well Math. (2) 141 (1995), no. 3, 443–551, using results have the distinction of having more books, articles, with R. Taylor (“Ring-theoretic properties of certain and Web pages devoted to his creations than any Hecke algebras”, ibid., 553–572). other living mathematician. 4. Loïc Merel’s proof of the uniform bounded- Conway was educated at Cambridge University ness conjecture for the torsion of elliptic curves de- and served as a professor of mathematics there fined over number fields, in “Bornes pour la torsion prior to joining Princeton University in 1986 as the des courbes elliptiques sur les corps de nombres”, John von Neumann Professor of Mathematics. A Invent. Math. 124 (1996), no. 1–3, 437–449. fellow of the Royal Society of London, he received Rarely has a single paper given rise to such a the Pólya Prize of the London Mathematical wealth of important mathematics as has Mazur’s Society and recently the Nemmers Prize in paper on “Modular curves and the Eisenstein ideal”. Mathematics from Northwestern University. Biographical Sketch Response from Professor Conway Barry Mazur spent two years as an undergraduate What a delicious surprise! But if ideas tumble out in at the Massachusetts Institute of Technology and such profusion, then why aren’t they here now when then went to graduate school at Princeton Uni- I need them to write this little acceptance? The thing versity, where he received a Ph.D. in mathematics that makes this so surprising is that I associate writ- (1959). He was a research fellow at the Institute for ing more with pain than with the pleasure I get from Advanced Study (1958–59). actually doing the mathematics. In 1959 he moved to Harvard University and has I think the pain comes from the fact that in remained there ever since. At Harvard he was a mathematical writing one has to be so terribly junior fellow (1959–62) before joining the careful to distinguish between phrases that would mathematics department in 1962. In 1966 Mazur be equivalent in ordinary English, where a “happy shared the AMS Oswald Veblen Prize in Geometry 478 NOTICES OF THE AMS VOLUME 47, NUMBER 4 comm-steele.qxp 2/15/00 10:58 AM Page 479 with Morton Brown, and in 1982 received the AMS of the fact that they arose as Cole Prize in Number Theory. Mazur is a member different avatars of the same of the National Academy of Sciences. algebraic geometry, the ques- Response tion provided quite an incen- What an honor to receive the Leroy P. Steele Prize tive for a topologist to look at for a Seminal Contribution to Research! I thank the algebraic geometry. I began to committee for its generous citation regarding the learn the elements of algebraic article for which they awarded me the prize. It is geometry working with Mike a joy to do mathematics at a time when there are Artin. Our intense and high- so many enormously talented people at work and spirited sessions were initially so many exciting new ideas being developed. That devoted to studying the dy- the committee cited the works of such mathe- namics of diffeomorphisms, maticians as Wiles, Ribet, and Merel in connection via Nash’s theory of real alge- with the prize they awarded to me is a further braic components of the loci source of joy. of real algebraic varieties. Our Sometimes a line of mathematical research ex- later work together, which tending through decades can be thought of as one moved towards number long conversation in which many mathematicians theory, was one of the most Barry Mazur take part.
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