comm-steele.qxp 2/27/01 3:46 PM Page 404 2001 Steele Prizes The 2001 Leroy P. Steele Prizes were awarded at recognition of the completion of his two- the 107th Annual Meeting of the AMS in January volume work Enumerative Combinatorics. The 2001 in New Orleans. first volume appeared in 1986, and, to quote the The Steele Prizes were established in 1970 in review of Volume 2 by Ira Gessel, “since then, its honor of George David Birkhoff, William Fogg readers have eagerly awaited Volume 2. They will Osgood, and William Caspar Graustein and are not be disappointed. Volume 2 not only lives up to endowed under the terms of a bequest from the high standards set by Volume 1, but surpasses Leroy P. Steele. The prizes are awarded in three them. The text gives an excellent account of the categories: for expository writing, for a research basic topics of enumerative combinatorics not paper of fundamental and lasting importance, and covered in Volume 1, and the exercises cover an for cumulative influence extending over a career. enormous amount of additional material.” The current award is $4,000 in each category (in The field has been expanding and evolving very case of multiple recipients, the amount is divided rapidly, and it is quite remarkable that Stanley has equally). been able to take a still photograph of it, so to speak, The recipients of the 2001 Steele Prizes are that beautifully captures its subject. To appreciate RICHARD P. STANLEY for Mathematical Exposition, the scholarly qualities of this work, one need look LESLIE GREENGARD and VLADIMIR ROKHLIN for a no further than the exercises. There are roughly Seminal Contribution to Research (limited this year 250 exercises in each volume, all graded according to applied mathematics), and HARRY KESTEN for to difficulty, many being multipart, and all Lifetime Achievement. with solutions and/or references to the relevant The Steele Prizes are awarded by the AMS literature being provided. There are more than Council acting through a selection committee 500 bibliographic citations in the two volumes. whose members at the time of these selections The first volume begins with elementary were: Constantine M. Dafermos, Bertram Kostant, counting methods, such as the sieve method, Hugh L. Montgomery, Marc A. Rieffel, Jonathan M. and works through the theory of partially ordered Rosenberg, Barry Simon, François Treves (chair), sets, ending with a beautiful treatment of rational S. R. S. Varadhan, and Herbert S. Wilf. The text that generating functions. Volume 2 begins with an follows contains, for each prize recipient, the advanced, yet very clear, view of generating committee’s citation, a brief biographical sketch, functions, with special attention to algebraic and and a response from the recipient upon receiving D-finite ones, and concludes with a comprehensive the prize. discussion of symmetric functions. Yet even with all of the information that is being Mathematical Exposition: transmitted, we never lose clarity or our view of “the Richard P. Stanley big picture”. As a small example, we note that the Citation Catalan numbers seem ubiquitous in combinatorics. The Leroy P. Steele Prize for Mathematical Every student of the subject is struck by the large Exposition is awarded to Richard P. Stanley of number of questions that they answer and wonders the Massachusetts Institute of Technology in if there are bijections between the various families 404 NOTICES OF THE AMS VOLUME 48, NUMBER 4 comm-steele.qxp 2/27/01 3:46 PM Page 405 Photograph by Michael Marsland, Yale Univ. Office of Public Affairs. Richard P. Stanley Leslie F. Greengard Vladimir Rokhlin of objects that are counted by these numbers. In a extremely pleased at having been chosen for this single exercise (ex. 6.19) Stanley has collected 66 award. It is not just an award for me but for all of such questions and asks the reader to provide the combinatorics, for which such recognition would proofs which, in each case, establish the Catalan an- have been unthinkable when I was starting out in swer. All 66 of them are worked out in the solution, the subject. I only regret that it is not possible which is ten pages long, and this is just one of the for me to share the celebration of my prize with 500 or so exercises. The author even has time for Gian-Carlo Rota, who inspired me throughout an occasional smile-generator (e.g., ex. 6.24: “Ex- my career and who wrote the two forewords to plain the following sequence: un, dos, tres, quatre, Enumerative Combinatorics. cinc, sis,….” The solution tells us that they are the Catalan numbers.) Seminal Contribution to Research: This is a masterful work of scholarship which Leslie F. Greengard and Vladimir Rokhlin is, at the same time, eminently readable and teach- Citation able. It will be the standard work in the field for For the paper by L. Greengard and V. Rokhlin “A years to come. fast algorithm for particle simulations”, J. Comput. Biographical Sketch Phys. 73, no. 2 (1987), 325–348. Richard Stanley was born in New York City in 1944. This is one of the most important papers in He graduated from Savannah High School in 1962 numerical analysis and scientific computing in the and Caltech in 1966. He received his Ph.D. from last two decades. This paper introduces an Harvard University in 1971 under the direction of algorithm, the fast multipole method (FMM), that Gian-Carlo Rota. He was a Moore Instructor at speeds up the computation of certain types of Massachusetts Institute of Technology during sums. It showed that several ideas in harmonic 1970–71 and a Miller Research Fellow at Berkeley analysis, far field expansions, and multiscale analy- during 1971–73. He then returned to MIT, where sis based on dyadic decompositions of space, he is now a professor of applied mathematics. He together with some further innovations, such as is a member of the American Academy of Arts so-called “translation operators”, could be com- and Sciences and the National Academy of Sci- bined to produce a practical algorithm that would ences, and in 1975 he was awarded the Pólya Prize make possible scientific and engineering in Applied Combinatorics from the Society for In- computations that would have been impossible dustrial and Applied Mathematics. His main math- before. While the paper itself treats a very special ematical interest is combinatorics, especially its case, it contains the fundamental ideas for a vast connections with such other branches of mathe- variety of generalizations and applications. The matics as commutative algebra and representa- paper combines both the elegance and originality tion theory. of the algorithm itself and the “hard” analysis of Response the proofs. These sums arise in a variety of appli- I have been interested in expository writing since cations, ranging from computational astronomy graduate school and have long admired such (computing the gravitational interaction of stars in masters as Donald Knuth, George Pólya, and Jean- a galaxy), to molecular dynamics (the Coulomb Pierre Serre. I think it is wonderful that the AMS interaction of charges in a large molecule), to en- awards a prize for mathematical exposition, and I am gineering computations of radar scattering, to APRIL 2001 NOTICES OF THE AMS 405 comm-steele.qxp 2/27/01 3:47 PM Page 406 anything related to solu- introduced us. The analytic structure introduced tions of the Laplace equa- by Rokhlin was richer than that of the simple tree- tion (vortex methods for in- based codes. He became my thesis advisor, and we compressible flow). The have been collaborating ever since. FMM has been enormously Biographical Sketch: Vladimir Rokhlin influential not just because Vladimir Rokhlin was born in Russia in 1952. He of its basic scientific appli- received his M.S. in mathematics in 1973 from the cations, but also because it University of Vilnius, Lithuania, and his Ph.D. in forms the basis of com- applied mathematics from Rice University in 1983. mercial software for elec- From 1973 to 1976 he worked at the Leningrad tronic packaging analysis, Institute of Arctic Geology and from 1976 to 1985, semiconductor design, and at the Exxon Production Research Company in electro-magnetic applica- Houston, Texas. He is currently a professor of tions. It has brought previ- mathematics and computer science at Yale Uni- ously intractable computa- versity, where he has been working since 1985. He tional problems within is a member of the National Academy of Sciences. reach. Photograph by Nicola Kountoupes, Cornell University Photography. Response: Vladimir Rokhlin Biographical Sketch: Leslie Harry Kesten It is hard to express my delight at being a co- F. Greengard recipient of the 2001 Steele Prize. I have always Leslie Greengard was born viewed myself as an applied mathematician, with in London, England, and grew up in New York, the emphasis on the “applied”. When dealing with Boston, and New Haven. He received his B.A. in a problem, I tend to be interested in its computa- mathematics from Wesleyan University in 1979, his tional aspects; when things work out, the beauty Ph.D. in computer science from Yale University in of the resulting mathematics takes me by surprise. 1987, and his M.D. from Yale University in 1987. It is truly nice to see that this sense of wonder is From 1987–89 he was a National Science Foundation shared by other mathematicians. Postdoctoral Fellow at Yale University in the I met Leslie Greengard in 1985. At that point I Department of Computer Science. He is presently was convinced that the future belonged to “fast” a professor of mathematics at the Courant Institute methods; I had constructed a rudimentary fast of New York University, where he has been a fac- scheme for the solution of the Laplace equation in ulty member since 1989.