Barry Simon of the California Institute of Technology will receive the 2016 AMS Leroy P. Steele Prize for Lifetime Achievement for "his impact on the education and research of a generation of mathematical scientists through his significant research achievements, his highly influential books, and his mentoring of graduate students and postdocs."

Simon's mathematical talent showed early in life. In 1962, at the age of 16, he was the subject of a short article in *The New York Times*, which recounted the story of Simon's participation in an exam contest sponsored by the Mathematical Association of America and the Society of Actuaries. After missing one question, he argued that the wording of the question had been ambiguous. The contest sponsors agreed, and Simon was awarded a perfect score.

An alumnus of Harvard University, Simon received his PhD from Princeton University in 1970 and was immediately appointed as an assistant professor. In the decade that followed, as Simon rose to the rank of full professor in 1981, Princeton became a thriving center for mathematical physics, particularly in statistical mechanics, quantum field theory, and non-relativistic quantum mechanics. One of Simon's PhD students from that time, Percy Deift, described the atmosphere this way: "Barry was a dynamo, challenging us with open problems, understanding every lecture instantaneously, writing paper after paper, often at the seminars themselves, and all the while supervising 7 or 8 PhD students." Deift made these remarks in the *laudatio* for the Poincaré Prize, awarded to Simon in 2012.

Simon's prodigious productivity continued after he moved to Caltech in 1981 to take his present position as the IBM Professor of Mathematics and Theoretical Physics. Today his list of research publications includes over 400 items. His secret? He needs "only five percent of the time ordinary mortals need" to write a research paper, quipped his collaborator Jürg Frölich, in a reminiscence prepared for a conference celebrating Simon's 60th birthday. Simon has had 31 graduate students, many of whom have gone to become leaders in mathematical physics and other areas, and he has mentored about 50 postdoctoral researchers.

Simon's own research contributions range over several areas of pure mathematics and mathematical physics. One of his most important contributions still stands as a landmark today: After nearly 40 years, work done by Simon and 4 co-authors (Fröhlich, Thomas Spencer, Freeman Dyson, and Elliott Lieb) still stands as the only rigorous proof of symmetry breaking in certain regimes fundamental to physics.

Simon was the first to give a mathematically precise definition of resonance that allowed linking of time-independent and time-dependent perturbation theory and the first to use differential-geometric invariants to understand Berry's phase and some other quantum phenomena. In work with Lieb, Simon produced the first rigorous proofs and interpretations of theories central to quantum mechanics. A leading contributor to the construction of quantum fields in two space-time dimensions, Simon (together with Francesco Guerra and Lon Rosen) established an analogy with classical statistical mechanics that led to deep new insights. Simon also proved several definitive results in the general theory of Schrödinger operators.

In addition to his outstanding contributions at the forefront of research, Simon is known for several books that have had a major influence on generations of students entering the field of mathematical physics. His 4-volume work *Methods of Modern Mathematical Physics*, written with Michael Reed during the 1970s, is where many of today's top researchers first learned this subject. Simon's uncanny ability to extract the key elements in a proof "is expressed in his books as a signature combination of economy and clarity, which accounts, I believe, for their usefulness and great popularity," remarked Deift in the Poincaré *laudatio*. Simon's two-volume set *Orthogonal Polynomials on the Unit Circle*, published by the AMS in 2005, became instant classics, connecting the theory of orthogonal polynomials with the spectral theory of Schrödinger operators and other topics in mathematical physics.

On top of all of his other contributions, Simon is also the co-author of two highly popular manuals for Windows computers: *The Mother of All Windows Books* and *The Mother of All PC Books*, which appeared in the 1990s. Written with Woody Leonhard, the books provided clear and practical advice in a witty and irreverent style, making them highly popular with computer users struggling to make sense of their costly machines.

In addition to the aforementioned Poincaré Prize (2012), Simon's previous awards include several honorary degrees and the Bolyai Prize of the Hungarian Academy of Sciences (2015). He was named a Fellow of the AMS in 2013.

Presented annually, the AMS Steele Prize is one of the highest distinctions in mathematics. The prize will be awarded on Thursday, January 7, 2016, at the Joint Mathematics Meetings in Seattle.

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Founded in 1888 to further mathematical research and scholarship, today the American Mathematical Society 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.