American Philosophical Society
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104. Mathematics[X]
1Name:  Dr. Benedict H. Gross
 Institution:  Harvard University
 Year Elected:  2017
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Living
 Birth Date:  1950
Benedict Gross has contributed decisively to number theory, algebraic geometry, modular forms and group representations. Gross and Don Zagier solved the class number problem which had been formulated by APS member Karl Friedrich Gauss in 1798. This problem was to give an algorithm to list all discrete rings embedded in the complex numbers with a given class number. The class number is a measure of the failure of unique factorization in the ring. (The analogous problem for the real numbers was already solved by the ancient Greeks. There is only one discrete ring embedded in the real numbers, namely the integers. Euclid in 300 BC proved that unique factorization holds in the integers, hence its class number is 1, the minimum possible value.) The theorem of Gross and Zagier was one of the major achievements in number theory of the 20th century. Gross is an expert on analytic number theory, which exploits the striking relationships between analysis, in the sense of calculus, and arithmetic in the sense of counting. He has made many many diverse discoveries. Most recently, he has explored the role of exceptional Lie groups in number theory. His development of arithmetic invariant theory with Manjul Bhargava promises to generate a whole new field of future research. Together with Joe Harris, he developed a mathematics course for non-mathematicians at Harvard. This led to his popular book, The Magic of Numbers, co-authored with J. Harris, which provides a readable introduction to the patterns that emerge in number behavior and the often surprising applications of these patterns.
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