Stony Brook University Mathematics Professor Recognized with Steele Prize for Lifetime Achievement by the AMS

John W. 'Jack' Milnor wins third AMS award for overall career achievements

STONY BROOK, N.Y., January 18, 2011 – John W. “Jack” Milnor, Ph.D., Professor of Mathematics and Co-director of the Institute for Mathematical Sciences at Stony Brook University, has been awarded The American Mathematical

Society’s prestigious Steele Prize for Lifetime Achievement. The award, presented during the recent AMS Joint Mathematics Meetings in New Orleans, is among the world's most important honors given for outstanding contributions to mathematics. The award includes a $5,000 prize.

"The AMS Lifetime Achievement Award is a well-deserved honor and recognition," said Samuel L. Stanley, Jr., M.D., President of Stony Brook University. "Jack's continuous contributions to his field constitute a tremendous legacy, he is an outstanding member of the Stony Brook community, and we are very proud of his accomplishments."

The citation that accompanied the Lifetime Achievement award noted that Dr. Milnor “stands out from the list of great mathematicians in terms of his overall achievements and his influence on mathematics in general, both through his work and through his excellent books”.

“It is a particular pleasure to receive an award for what one enjoys doing anyway,” Dr. Milnor said. “I have been very lucky to have had so many years to explore and enjoy some of the many highways and byways of mathematics, and I want to thank the three institutions that have supported and inspired me for most of the past 60 years: Princeton University, where I learned to love mathematics; the Institute for Advanced Study for many years of uninterrupted research; and Stony Brook University where I was able to reconnect with students and, to some extent, with teaching.

“I am very grateful to my many teachers, from Ralph Fox and Norman Steenrod long ago to Adrien Douady in more recent years, and I want to thank the family, friends, students, colleagues, and collaborators who have helped me over the years. Finally, my grateful thanks to the selection committee for this honor.”

Dr. Milnor had previously won two other Steele Prizes from the AMS – for a Mathematical Exposition (2004) and for a Seminal Contribution to Research (1982).

Founded in 1888 to further mathematical research and scholarship, the more than 30,000-member American Mathematical Society today fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.

Dr. Milnor spent his undergraduate and graduate student years at Princeton, studying knot theory under the supervision of Ralph Fox. He received an A.B. and a Ph.D. in Mathematics from Princeton. After many years at Princeton University and the Institute for Advanced Study, with shorter stays at UCLA and MIT, he has settled at Stony Brook University, where he is now co-director of the Institute for Mathematical Sciences. Over the years, he has studied game theory, differential geometry, algebraic topology, differential topology, quadratic forms, and algebraic K-theory. For the past 25 years, his main focus has been on dynamical systems and particularly on low dimensional holomorphic dynamical systems. Among his current projects is the preparation of a book to be called Dynamics, Introductory Lectures. Five volumes of his older collected papers have been published by the AMS.

A member of the National Academy of Sciences, he has also won the Fields Medal – the International Medal for Outstanding Discoveries in Mathematics awarded to mathematicians under the age of 40 by the International Congress of the International Mathematical Union (IMU) – and the Wolf Prize in Mathematics, Israel’s highest honor in mathematics.

According to the AMS, “Dr. Milnor’s discovery of 28 nondiffeomorphic smooth structures on the 7-dimensional sphere and his further work developing the surgery techniques for manifolds shaped the development of differential topology beginning in the 1950s. Another of his famous results from this period is a counterexample to the Hauptvermutung: an example of homeomorphic but not combinatorially equivalent complexes. This counterexample is a part of a general big picture of the relation between the topological, combinatorial, and smooth worlds developed by Milnor. Jointly with M. Kervaire, Milnor proved the first results showing that the topology of 4-dimensional manifolds is exceptional, by revealing obstructions for the realization of 2-dimensional spherical homology classes by smooth embedded 2-spheres. This is one of the founding results of 4-dimensional topology.

“In this way, Milnor opened several fields: singularity theory, algebraic K-theory, and the theory of quadratic forms. Although he did not invent these subjects, his work gave them completely new points of view. For instance, his work on isolated singularities of complex hypersurfaces presented a great new topological framework for studying singularities, and at the same time provided a rich new source of examples of manifolds with different extra structures. The concepts of Milnor fibers and Milnor number are today among the most important notions in the study of complex singularities.

“The significance of Milnor’s work goes much beyond his own spectacular results. He wrote several books (Morse Theory (Princeton University Press, Princeton, 1963), Lectures on h-Cobordism Theorem (Princeton University Press, Princeton, 1965), and Characteristic Classes (Princeton University Press, Princeton, 1974), among others) which became classical, and several generations of mathematicians have grown up learning beautiful mathematical ideas from these excellent books. Milnor’s survey “Whitehead torsion” (Bull. Amer. Math. Soc. 72 (1966), no. 3, 358–426) provided an entry point for topologists to algebraic K-theory. This was followed by a number of Milnor’s own important discoveries in algebraic K-theory and related areas: the congruence subgroup theorem, the computation of Whitehead groups, the introduction and study of the functor K2 and higher K-functors, numerous contributions to the classical subject of quadratic forms and in particular his complete resolution of the theory of symmetric inner product spaces over a field of characteristic 2, just to name a few. Milnor’s introduction of the growth function for a finitely presented group and his theorem that the fundamental group of a negatively curved Riemannian manifold has exponential growth was the beginning of a spectacular development of the modern geometric group theory and eventually led to Gromov’s hyperbolic group theory.

“During the past 30 years, Milnor has been playing a prominent role in development of low-dimensional dynamics, real and complex. His pioneering work with Thurston on the kneading theory for interval maps laid down the combinatorial foundation for the interval dynamics putting it into the focus of intense research for decades. Milnor and Thurston’s conjecture on the entropy monotonicity brought together real and complex dynamics in a deep way, prompting a firework of further advances. And of course, his book Dynamics in One Complex Variable (Friedr. Vieweg & Sohn, Braunschweig, 1999) immediately became the most popular gateway to this field.

“The Steele Prize honors John Willard Milnor for all of these achievements.”

**About Stony Brook University
**Part of the State University of New York system, Stony Brook University encompasses 200 buildings on 1,450 acres. In the 53 years since its founding, the University has grown tremendously, now with nearly 24,700 students and 2,200 faculty and is recognized as one of the nation’s important centers of learning and scholarship. It is a member of the prestigious Association of American Universities, and ranks among the top 100 national universities in America and among the top 50 public national universities in the country according to the 2010 U.S. News & World Report survey. One of four University Centers in the SUNY system, Stony Brook University co-manages Brookhaven National Laboratory, joining an elite group of universities, including Berkeley, University of Chicago, Cornell, MIT, and Princeton that run federal research and development laboratories. SBU is a driving force of the Long Island economy, with an annual economic impact of $4.65 billion, generating nearly 60,000 jobs, and accounts for nearly 4% of all economic activity in Nassau and Suffolk counties, and roughly 7.5 percent of total jobs in Suffolk County.