Eilenberg, Samuel (1913-1998)

Polish-born US mathematician. His research in the field of algebraic topology led to considerable development in the theory of cohomology. Algebraic topology, sometimes called ‘combinatorial’ topology, is based on homology theory - the study of closed curves, closed surfaces, and similar geometric arrangements in a given topological space.

Much of Eilenberg's work was concerned with a modification of homology theory called cohomology theory. It is possible to define a ‘product’ of cohomology classes by means of which, together with the addition of cohomology classes, the direct sum of the cohomology classes of all dimensions becomes a ring (the cohomology ring). This is a richer structure than is available for homology groups, and allows finer results. Various very complicated algebraic operations using cohomology classes can lead to results not provable in any other way.

Eilenberg was born and educated in Warsaw. In the 1930s he emigrated to the USA. He was professor of mathematics at Indiana University 1946-49, and ended his career at Columbia University, New York. He was a leading member of the Bourbaki group.