Solomon Lefschetz (
3 September 1884 –
5 October 1972) was an
American mathematician who did fundamental work on
algebraic topology, its applications to
algebraic geometry, and the theory of non-linear
ordinary differential equations. He was born in
Moscow into a
Jewish family (his parents were
Turkish citizens) who moved shortly after that to
Paris. He was educated there in
engineering at
Ecole Centrale Paris, but emigrated to the USA in 1905.
He was badly injured in an industrial accident in 1907, losing both hands. He moved towards mathematics, receiving a Ph.D. in algebraic geometry from
Clark University in Worcester, Massachusetts in 1911. He then took positions in
University of Nebraska and
University of Kansas, moving to
Princeton University in 1924, where he was soon given a permanent position. He remained there until 1953.
In the application of topology to algebraic geometry, he followed the work of
Charles Émile Picard, whom he had heard lecture in Paris. He proved theorems on the topology of
hyperplane sections of algebraic varieties, which provide a basic inductive tool (these are now seen as allied to
Morse theory, though a
Lefschetz pencil of hyperplane sections is a more subtle system than a Morse function because hyperplanes intersect each other). The
Picard-Lefschetz formula in the theory of
vanishing cycles is a basic tool relating the
degeneration of families of varieties with 'loss' of topology, to
monodromy. His book
L'analysis situs et la géométrie algébrique from 1924, though opaque foundationally given the current technical state of
homology theory, was in the long term very influential (one could say that it was one of the sources for the eventual proof of the
Weil conjectures, through
SGA7). In
1924 he was awarded the
Bôcher Memorial Prize for his work in mathematical analysis.
The
Lefschetz fixed point theorem, now a basic result of topology, he developed in papers from 1923 to 1927, initially for
manifolds. Later, with the rise of
cohomology theory in the 1930s, he contributed to the
intersection number approach (that is, in cohomological terms, the ring structure) via the
cup product and duality on manifolds. His work on topology was summed up in his monograph
Algebraic Topology (1942). From 1944 he worked on
differential equations.
He was editor of
the Annals of Mathematics from 1928 to 1958. During this time,
Annals became an increasingly well-known and respected journal, and Lefschetz played an important role in this. The rise of
Annals, in turn, stimulated American mathematics.
Lefschetz came out of retirement in 1958, because of the launch of
Sputnik, to augment the mathematical component of
Glenn L. Martin Company’s Research Institute for Advanced Study (RIAS). His team became the world's largest group of mathematicians devoted to research in nonlinear differential equations. The RIAS mathematics group stimulated the growth of nonlinear differential equations through conferences and publications. It left RIAS in 1964 to form the Lefschetz Center for Dynamical Systems at Brown University, Maryland.
http://www.dam.brown.edu/lcds/about.php
See also:
Lefschetz hyperplane theorem, Lefschetz duality. 
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