MILNOR, JOHN WILLARD

born Feb. 20, 1931, Orange, N.J., U.S. American mathematician who was awarded the Fields Medal in 1962 for his work in differential topology. Milnor served the American Mathematical Society as vice president (197576) and was awarded the Wolf Prize in 1989. Milnor attended Princeton University (A.B., 1951; Ph.D., 1954). He held an appointment at Princeton from 1954 to 1967 and, after several years at other institutions, joined the faculty at the Institute for Advanced Study, Princeton, N.J., in 1970. In 1989 he became director of the Institute for Mathematical Sciences at the State University of New York, Stony Brook. Milnor was awarded the Fields Medal at the International Congress of Mathematicians in Stockholm in 1962. His work was part of a revival of interest in a geometric approach to topology in the 1950s. Early in the century the field had been highly geometric, but in the 1930s and '40s algebraic approaches dominated research. In particular, Milnor's discovery of multiple differential structures for the seven-dimensional sphere, S7, in 1956 was instrumental in the development of the new field of differential topology. Additionally, he contributed to algebraic geometry on singular points of complex hypersurfaces, and in 1961 he showed that a long-standing principal conjecture in the theory of manifolds concerning triangulations of n-dimensional manifolds is not true for polyhedra. Milnor's publications include Differential Topology (1958); The Representation Rings of Some Classical Groups (1963); Morse Theory (1963); Lectures on the h-Cobordism Theorem (1965); Singular Points of Complex Hypersurfaces (1968); with Dale Husemoller, Symmetric Bilinear Forms (1973); and, with James D. Stasheff, Characteristic Classes (1974). His Collected Papers was published in 1994.