American Philosophical Society
Member History

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104. Mathematics[X]
1Name:  Dr. William Timothy Gowers
 Institution:  University of Cambridge & Trinity College
 Year Elected:  2010
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  International
 Living? :   Living
 Birth Date:  1963
Early in his career, Timothy Gowers did outstanding work in abstract Banach space theory, a theory which involves sets which are operators or functions. In a series of brilliant papers, he solved several long-standing problems, introducing extensive use of methods from combinatorial number theory. One of his surprising results is the construction of a Banach space with almost no symmetry. He is now better known to the broad mathematical community by his later work in combinatorial number theory. His very original ideas (for example "Gowers norms"), led to a new proof of Szmeredi's theorem, which concerns the occurrence of arithmetic progressions in sets of integers. His ideas have led to many breakthroughs in the field, in particular concerning the occurrence of arithmetic progressions in the primes (a longstanding conjecture of Erdos and now a theorem of Gowers’ students Ben Green and Terry Tao.) He continues to lead the research in this combinatorial number theory, which is now having impact on and benefiting computer science. Gowers has also put much effort into bringing mathematics to the public in his writing which includes his book Mathematics: A Very Short Introduction (2002) and his many public lectures. He recently organized the writing of The Princeton Companion to Mathematics (2008). This is a book of over 1,000 pages, incorporating sections by over 100 of the world's best mathematicians. It is aimed at giving anyone with some undergraduate training in mathematics a taste of current knowledge in all of modern mathematics. This kind of contribution, by one of the world's leading researchers at the height of his productive years, is very unusual.
2Name:  Dr. Shlomo Sternberg
 Institution:  Harvard University
 Year Elected:  2010
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Living
 Birth Date:  1936
Shlomo Sternberg is one of the foremost differential geometers of his generation and a mathematician who has shaped the subject with his extensive breadth and many scholarly contributions. His papers extend across many subjects, including Lie groups (finite and infinite dimensional), symplectic geometry and mechanics, quantum groups, scattering theory, conformal field theory - the list is long and inclusive of many subjects. He has written several books with V. Guillemin which are foundational references for research mathematicians in several fields, including Geometric Asymptotics (1977), Variations on a Theme by Kepler, (1990), and Symplectic Techniques in Physics (1990), as well as several of the basic graduate texts for students of mathematics and physics. He currently serves as George Putnam Professor of Pure and Applied Mathematics at Harvard University, having joined the Harvard faculty in 1959. He received his Ph.D. in 1956 from Johns Hopkins University. In 1980 he was made a permanent Fellow of the Mortimer and Raymond Sackler Institute of Advanced Studies at Tel Aviv University. He is a member of the American Academy of Arts & Sciences and the National Academy of Sciences and was elected to membership in the American Philosophical Society in 2010.
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