THE 1986 WOLF FOUNDATION PRIZE IN MATHEMATICS

The Mathematics Prize Committee for 1986 unanimously recommends that the Wolf Prize in Mathematics be shared jointly by:

**Atle Selberg Institute for Advanced Study Princeton, New Jersey, USA **

for his profound and original work on number theory and on discrete groups and automorphic forms.

Samuel Eilenberg

Columbia University

New York, N.Y., USA

for his fundamental work in algebraic topology and homological algebra.

Professor Samuel Eilenberg began his mathematical education in the Polish School of point set topology, and has since made basic contributions to algebraic topology. Among his many seminal works are those in obstruction theory and in the creation of singular homology theory. His study of the relations between homology and homotopy is fundamental. He was one of the creators of the cohomology of groups and of the cohomology of Lie algebras and in fact of homological algebra. Each of these subjects has had many applications. His work has been central in several major developments of modern mathematics.

In early work, Professor Atle Selberg proved that the zeros of the Riemann zeta function on the critical line have positive density. He conceived and developed the general sieve method, which has become a fundamental tool in analytic number theory. His ideas on sieves led him to his celebrated 'Selberg formula' which is the basis of his elementary proof of the prime number theorem. He discovered the trace formula, which bears his name. Out of it grew a new interaction of group representations and number theory. He initiated the study of the arithmeticity of lattices. His contributions are so deep and so many that his name is already part of the history of mathematic