comm-steele-prizes.qxp 3/10/98 1:39 PM Page 504 1998 Steele Prizes The 1998 Leroy P. Steele Prizes were awarded at three groups of people: students in- the 104th Annual Meeting of the AMS in January terested in doing research in Diophan- in Baltimore. These prizes were established in tine geometry, mathematicians need- 1970 in honor of George David Birkhoff, William ing a reference for standard facts about Fogg Osgood, and William Caspar Graustein and elliptic curves, and computer scientists are endowed under the terms of a bequest from interested in algorithms and needing an Leroy P. Steele. introduction to elliptic curves. For a The Steele Prizes are awarded in three cate- long time one of the standard refer- gories: for expository writing, for a research paper ences for elliptic curves has been the of fundamental and lasting importance, and for cu- survey article of J. W. S. Cassels [J. Lon- mulative influence extending over a career, in- don Math. Soc. 41 (1966), 193–291; MR cluding the education of doctoral students. The cur- 33 #7299; errata; MR 34 #2523]. In its rent award is $4,000 in each category. choice of topics this book may be The recipients of the 1998 Steele Prizes are viewed as an amplification of Cassels’ JOSEPH H. SILVERMAN for Mathematical Exposition, article, with technical details filled in, DORON ZEILBERGER and HERBERT S. WILF for a Seminal much more motivation, and an excellent Contribution to Research, and NATHAN JACOBSON for set of exercises. Lifetime Achievement. Cassels himself reviewed the book in the AMS Bul- The Steele Prizes are awarded by the AMS letin [Bull. Amer. Math. Soc. (N.S.) 17 (1987), Council acting through a selection committee 148–149]. The review is short, but to the point. It whose members at the time of these selections concludes: “In the reviewer’s opinion [Silverman]’s were: Richard A. Askey, Ciprian Foias, H. Blaine book fills the gap admirably. An old hand is hardly Lawson Jr., Andrew J. Majda, Louis Nirenberg, the best judge of a book of this nature, but reports Jonathan M. Rosenberg, and John T. Tate. of graduate students are equally favorable.” The text that follows contains for each award The review of Silverman’s second volume in the committee’s citation, a brief biographical Math. Reviews by Henri Darmon, MR 96b:11074, is sketch, and the recipient’s response upon receiv- even more enthusiastic. It says: ing the award. Since its publication almost 10 years Steele Prize for Mathematical Exposition: ago, Silverman’s book The Arithmetic of Joseph H. Silverman Elliptic Curves has become a standard Citation reference, initiating thousands of grad- The Leroy P. Steele Prize for Mathematical Expo- uate students (the reviewer among sition is awarded to Joseph H. Silverman of Brown them) to this exciting branch of arith- University for his books The Arithmetic of Elliptic metic geometry. The eagerly awaited se- Curves, Graduate Texts in Mathematics, vol. 106, quel, Advanced Topics in the Arithmetic Springer-Verlag, New York-Berlin, 1986, ISBN 0- of Elliptic Curves, lives up to the high 387-96203-4; and Advanced Topics in the Arith- expectations generated by the first vol- metic of Elliptic Curves, Graduate Texts in Math- ume....After reading Advanced Topics ematics, vol. 151, Springer-Verlag, New York, 1994, with much pleasure, we can only hope ISBN: 0-387-94328-5. The review of the first of for a third volume.... these volumes in Math. Reviews by Robert S. In short, Silverman’s volumes have become stan- Rumely, MR 87g:11070, begins as follows: dard references on one of the most exciting areas This well-written book covers the basic of algebraic geometry and number theory. facts about the geometry and arith- Biographical Sketch metic of elliptic curves, and is sure to Joseph H. Silverman was born on March 27, 1955, become the standard reference in the in New York. He received his Sc.B. from Brown subject. It meets the needs of at least University (1977) and his M.A. (1979) and Ph.D. 504 NOTICES OF THE AMS VOLUME 45, NUMBER 4 comm-steele-prizes.qxp 3/10/98 1:40 PM Page 505 Temple University News Bureau. Sabra Photography and Video. Joseph H. Silverman Herbert S. Wilf Doron Zeilberger (1982) from Harvard University. He began his ca- No writer operates in a vacuum. I would like to reer as a Moore Instructor at MIT (1982–86), fol- thank the many people from whom I learned about lowed by associate professorships at Boston Uni- the beautiful theory of elliptic curves, including versity (1986–88) and Brown University (1988–91). John Tate, Barry Mazur, Serge Lang, the members Since 1991 he has been a professor of mathemat- of the Harvard Elliptic Curves Seminar (1977–82), ics at Brown University. and many other writers, colleagues, students, and Professor Silverman has been an NSF Post-Doc- friends far too numerous to catalog. My books toral Fellow (1983–86) and an Alfred P. Sloan Foun- could never have been written without their en- dation Fellow (1987–91) and is a recipient of an couragement and inspiration. MAA Lester Ford Award (1994). In addition to the two books cited in his Steele Prize, Professor Sil- verman has written Rational Points on Elliptic Steele Prize for a Seminal Contribution to Curves (jointly with John Tate, 1992) and A Friendly Research: Herbert S. Wilf and Doron Introduction to Number Theory (1996), as well as Zeilberger numerous research articles. He has also coorga- nized two conferences, “Arithmetic Geometry” Citation (Storrs, 1984) and “Fermat’s Last Theorem” (Boston, The Leroy P. Steele Prize for Seminal Contribution 1995) and coedited the proceedings. His research to Research is awarded to Herbert S. Wilf, Thomas interests include number theory, arithmetic geom- A. Scott Professor of Mathematics, of the Univer- etry, elliptic curves, and arithmetic aspects of dy- sity of Pennsylvania, and Doron Zeilberger of Tem- namical systems. ple University for their paper Rational functions cer- Response tify combinatorial identities, J. Amer. Math. Soc. 3 I am deeply honored to receive a Steele Prize for (1990), 147–158. my two books on elliptic curves. When I wrote the New mathematical ideas can have an impact on first volume shortly after receiving my Ph.D., my experts in a field, on people outside the field, and aim was to write the book that I wished had been on how the field develops after the idea has been available when I was a graduate student. It has given introduced. The remarkably simple idea of the me great pleasure to see it fulfilling that purpose work of Wilf and Zeilberger has already changed for other students over the past decade. In the orig- a part of mathematics for the experts, for the high- inal outline for that first (and, I assumed, solitary) book, there were twenty topics to be covered. Ten level users outside the area, and for the area itself. topics and 400 pages later, the publisher and I George Andrews, one of the world’s leading experts agreed that the book was finished, but as a sop to on q-series (which arise, for example, in statistical the reader and to my conscience, I included a short mechanics), wrote the following about the method appendix briefly describing the ten omitted top- of Wilf and Zeilberger: “In my proof of Capparelli’s ics. This foolish act on my part was considered by conjecture, I was completely guided by the Wilf- many people to be a tacit promise that someday Zeilberger method, even if I didn’t use Doron’s there would be a second volume. Eventually the sec- program explicitly. I couldn’t have produced my ond volume was written, and not surprisingly, its proof without knowing the principle behind ‘WZ’. 500 pages only sufficed to cover half of the re- It is a really powerful result and does indeed merit maining material! the Steele Prize.” APRIL 1998 NOTICES OF THE AMS 505 comm-steele-prizes.qxp 3/10/98 1:40 PM Page 506 Donald Knuth, winner of the Steele Prize in now publishing its sixth volume and is in its fourth 1986 for his books on The Art of Computer Pro- year of publication. He received in 1996 the Haimo gramming, has written the following in his fore- Award of the Mathematical Association of Amer- word to the book A=B by Marko Petkovs˘ek, Wilf, ica for Distinguished Teaching of College or Uni- and Zeilberger: versity Mathematics, and he is especially proud to have supervised the dissertations of more than Science is what we understand well enough twenty Ph.D. students. The University of Pennsyl- to explain to a computer. Art is every- vania recently named him Thomas A. Scott Pro- thing else we do. During the past several fessor of Mathematics. years an important part of mathematics He was born in 1931 in Philadelphia, did un- has been transformed from an Art to a Sci- dergraduate work at MIT, and got his Ph.D. from ence. No longer do we need to get a bril- Columbia University in 1958. His first faculty po- liant insight in order to evaluate sums of sition was at the University of Illinois, and he came binomial coefficients, and many similar to the University of Pennsylvania in 1962, where formulas that arise frequently in practice; he has been ever since. He has been a Visiting Pro- we can now follow a mechanical proce- fessor at Imperial College of the University of Lon- dure and discover the answers quite sys- don, Stanford University, and Rockefeller Univer- tematically.