
Michael
Francis ATIYAH
born April 22, 1929, London
Oxford University
Did joint work with Hirzebruch in Ktheory; 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".




Paul Joseph
COHEN
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.




Alexander
GROTHENDIECK
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 Ktheory
(the Grothendieck groups and rings). Revolutionized homological
algebra in his celebrated "Tohoku paper".




Stephen SMALE
born July 15, 1930, Flint, Michigan
University of California, Berkeley
Worked in differential topology where he proved the generalized
Poincaré conjecture in dimension n>=5: Every closed,
ndimensional manifold homotopyequivalent to the ndimensional
sphere is homeomorphic to it. Introduced the method of handlebodies
to solve this and related problems.




This document has been reproduced from
The Website of International Congress of
Mathematicians, Berlin 1998.
Albers, Donald J.; Alexanderson, G. L.;
Reid, Constance:
International mathematical congresses. An illustrated history
1893  1986
Rev. ed. including ICM 1986. SpringerVerlag, New York, 1986
with friendly permission from Springer
Verlag

