AMS Prize Announcements FROM THE AMS SECRETARY 2018 Leroy P. Steele Prizes Sergey Fomin Andrei Zelevinsky Martin Aigner Günter Ziegler Jean Bourgain The 2018 Leroy P. Steele Prizes were presented at the 124th Annual Meeting of the AMS in San Diego, California, in January 2018. The Steele Prizes were awarded to Sergey Fomin and Andrei Zelevinsky for Seminal Contribution to Research, to Martin Aigner and Günter Ziegler for Mathematical Exposition, and to Jean Bourgain for Lifetime Achievement. Citation for Seminal Contribution to Research: Biographical Sketch: Sergey Fomin Sergey Fomin and Andrei Zelevinsky Sergey Fomin is the Robert M. Thrall Collegiate Professor The 2018 Steele Prize for Seminal Contribution to Research of Mathematics at the University of Michigan. Born in 1958 in Discrete Mathematics/Logic is awarded to Sergey Fomin in Leningrad (now St. Petersburg), he received an MS (1979) and Andrei Zelevinsky (posthumously) for their paper and a PhD (1982) from Leningrad State University, where “Cluster Algebras I: Foundations,” published in 2002 in his advisor was Anatoly Vershik. He then held positions at St. Petersburg Electrotechnical University and the Institute the Journal of the American Mathematical Society. for Informatics and Automation of the Russian Academy The paper “Cluster Algebras I: Foundations” is a of Sciences. Starting in 1992, he worked in the United modern exemplar of how combinatorial imagination States, first at Massachusetts Institute of Technology and can influence mathematics at large. Cluster algebras are then, since 1999, at the University of Michigan. commutative rings, generated by a collection of elements Fomin’s main research interests lie in algebraic com- called cluster variables, grouped together into overlapping binatorics, including its interactions with various areas clusters. These variables are produced by a recursive of mathematics such as representation theory, Schubert combinatorial procedure called mutation, starting from calculus, probability theory, and computational complex- an initial cluster of algebraically independent variables. ity. He is the current managing editor of the Journal of Originally, cluster algebras were introduced to provide the American Mathematical Society, a member of the AMS a combinatorial approach to total positivity in algebraic Council, and a Fellow of the AMS. He served on advisory groups and Lusztig’s canonical bases of quantum groups. boards for MSRI and HSE Moscow and was an invited speaker at the International Congress of Mathematicians However, in the fifteen years since their introduction, in Hyderabad in 2010. cluster algebras have been shown to be important in many seemingly different areas of mathematics, including root Biographical Sketch: Andrei Zelevinsky systems, Poisson geometry, Teichmüller theory, quiver Andrei Zelevinsky was born in Moscow in 1953. A gradu- representations, integrable systems, and quantum affine ate of Moscow’s famed High School #2, he studied at the algebras. This paper is a work of lasting importance, both mathematics department of the Moscow State University for its varied applications and for the intrinsic beauty of (PhD, 1978), where his main mentors were Joseph Bern- the theory. stein, Israel Gelfand, and Alexandre Kirillov. He worked at APRIL 2018 NOTICES OF THE AMS 455 AMS Prize Announcements FROM THE AMS SECRETARY the Institute of Earth Physics and at the Scientific Council where perfect proofs are kept. In Proofs from THE BOOK, for Cybernetics of the Soviet Academy of Sciences before the authors have collected a great number of sparkling moving to the United States in 1990. After a year at Cornell little mathematical gems that are their candidates for University, he took up a professorship at Northeastern Erdo˝s’s book. These mathematical vignettes are drawn University in Boston, where he remained until his untimely from number theory, geometry, analysis, combinatorics, death in April 2013. and graph theory. Most of the topics in the book require Andrei Zelevinsky made fundamental contributions to only a modest mathematical background, so that it is representation theory of p-adic groups (with Bernstein), suitable for undergraduates and mathematically inclined generalized hypergeometric systems (with Gelfand and M. nonspecialists. This is not to say that the mathematics is Kapranov), and algebraic combinatorics, total positivity, simple—even if the masterful exposition often makes it quiver representations, and cluster algebras (with various seem that way; there are answers to questions asked by collaborators). He was an invited speaker at the ICM in Hilbert, Borsuk, Sylvester, and, of course, Erdo˝s himself. Berlin (1998), a Fellow of the AMS (2012), and a recipient For the research mathematician, the appeal of the book of the Humboldt Research Award (2004). He served on the is that the proofs themselves are indeed beautiful. Aigner Scientific Advisory Committee of MSRI and on editorial and Ziegler have succeeded in writing a book in which the boards of several leading research journals. Northeastern density of elegant ideas per page is extraordinarily high, University posthumously honored Zelevinsky by a Distin- and they sustain this quality throughout the text. It is guished University Professorship and by inaugurating a also worth noting that it is not just the mathematics that postdoctoral program named after him, the Andrei Zele- is aesthetically pleasing; the authors did the typesetting vinsky Research Instructorships. themselves, and the cartoons by mathematician Karl Hein- rich Hofmann add a light-hearted touch. This book does Response from Sergey Fomin an invaluable service to mathematics, by illustrating for It is a great honor to receive the Leroy P. Steele Prize from nonmathematicians what it is that mathematicians mean the AMS. I am thankful to the prize committee for their when they speak about beauty. selection. I would like to view it as a sign of appreciation for the inherent beauty and importance of the field of Biographical Sketch: Martin Aigner algebraic combinatorics, the mathematical love of my life. Martin Aigner was born in 1942 in Linz, Austria. In The feeling is bittersweet, as my coauthor Andrei Zele- 1960 he started his studies of mathematics, physics, and vinsky did not live to enjoy this recognition of his research philosophy at the University of Vienna and received his accomplishments. He was a dear friend, an inspiring PhD in mathematics from the same university in 1965. teacher, and a brilliant mathematician. After shorter stays at various institutions in the United Although Andrei and I lived until our mid-thirties in States, he worked from 1968 to 1970 as research associate Moscow and St. Petersburg, a short train ride from each with Raj Chandra Bose at the University of North Carolina other, we first met in 1992 in Boston, where our 20-year- at Chapel Hill during the Special Combinatorics Year long collaboration took root. I am forever thankful to the Program. He moved to Tübingen, Germany, with a Habil- fate—and to Andrei—for this most momentous partner- itations-Fellowship of the German Science Foundation in ship of my professional life. 1970 and became professor at the Freie Universität Berlin We discovered cluster algebras in May 2000 at the in 1973. He has been in Berlin ever since, from 2010 on as Erwin Schrödinger Institute in Vienna. George Lusztig’s professor emeritus. pioneering work on total positivity and canonical bases His field of research is enumerative and algebraic was a major source of inspiration. Our mathematical tastes combinatorics, graph theory, and search theory. He is the and philosophies were deeply influenced by our mentors author of twelve books, among them the monographs Joseph Bernstein, I. M. Gelfand, Richard Stanley, and A. Combinatorial Theory (Springer, 1979), reprinted in the M. Vershik. Last but not least, I would like to acknowl- Springer Classics in Mathematics series (1997); Combina- edge the great many mathematicians who over the years torial Search (1988); A Course in Combinatorics (2007); and contributed to the development of the theory of cluster Proofs from THE BOOK (with Günter M. Ziegler, Springer algebras. I hope that this field continues to thrive, finding 1998++), which is available in fourteen languages. new exciting applications. He is a member of the Austrian Academy of Sciences and the Berlin-Brandenburg Academy of Sciences and Hu- Citation for Mathematical Exposition: manities. In 1996 he received the Lester R. Ford Award of Martin Aigner and Günter Ziegler the MAA. He was the Richard-Rado-Lecturer at the British The 2018 Steele Prize for Mathematical Exposition is Combinatorial Conference in 2001 and acted as vice pres- awarded to Martin Aigner and Günter M. Ziegler of the ident of the Organizing Committee for the International Freie Universität Berlin for Proofs from THE BOOK. It is Congress of Mathematicians 1998 in Berlin. almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and back- Biographical Sketch: Günter Ziegler grounds, yet Aigner and Ziegler accomplish this feat of Günter M. Ziegler was born in München, Germany, in 1963. exposition with virtuoso style. The inspiration for this He got a PhD at the Massachusetts Institute of Technology book is Paul Erdo˝s’s assertion that there is a celestial book with Anders Björner in 1987. After four years in Augsburg 456 NOTICES OF THE AMS VOLUME 65, NUMBER 4 AMS Prize Announcements FROM THE AMS SECRETARY and a winter in Stockholm, he arrived in Berlin in 1992. In and proofs that we could achieve. A book about beauty 1995 he became a professor of mathematics at TU Berlin; in mathematics naturally requires an equally attractive in 2011 he moved to Freie Universität Berlin. He has been appearance. An enormous amount of time went into the a member of the DFG Research Center MATHEON (Math- crafting of the text and the margins, the selection of the ematics for Key Technologies) since its start in 2002. He photos, and the pictures and illustrations. We are very was the founding chair of the Berlin Mathematical School, grateful to Karl H.