# Fields Medals 1966

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born April 22, 1929, London

Oxford University

Did joint work with Hirzebruch in *K*-theory; proved jointly with Singer the index theorem of elliptic operators on complex manifolds; worked in collaboration with Bott to prove a fixed point theorem related to the "Lefschetz formula".

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born April 2, 1934, Long Branch, New Jersey

Stanford University

Used technique called "forcing" to prove the independence in set theory of the axiom of choice and of the generalized continuum hypothesis. The latter problem was the first of Hilbert's problems of the 1900 Congress.

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born March 28, 1928, Berlin

University of Paris

Built on work of Weil and Zariski and effected fundamental advances in algebraic geometry. He introduced the idea of *K*-theory (the Grothendieck groups and rings). Revolutionized homological algebra in his celebrated "Tohoku paper".

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born July 15, 1930, Flint, Michigan

University of California, Berkeley

Worked in differential topology where he proved the generalized PoincarĂ© conjecture in dimension *n*>=5: Every closed, *n*-dimensional manifold homotopy-equivalent to the *n*-dimensional sphere is homeomorphic to it. Introduced the method of handle-bodies to solve this and related problems.

This document has been reproduced from

Albers, Donald J.; Alexanderson, G. L.; Reid, Constance:

*International mathematical congresses. An illustrated history 1893 - 1986*

Rev. ed. including ICM 1986. Springer-Verlag, New York, 1986

with friendly permission from Springer Verlag