THE 2000 WOLF FOUNDATION PRIZE IN MATHEMATICS

The Prize Committee for Mathematics has unanimously decided that the 2000 Prize be jointly awarded to:

Raoul Bott

Harvard University

Cambridge, Massachusetts, USA

for his deep discoveries in topology and differential geometry and their applications to Lie groups, differential operators and mathematical physics,

Jean-Pierre Serre

College de France

Paris, France

for his many fundamental contributions to topology, algebraic geometry, algebra, and number theory and for his inspirational lectures and writing.

Professor Raoul Bott has been one of the leading figures in differential geometry, particularly in its links with topology and Lie groups. Through his publications, his students, and his personal qualities, he has significantly influenced the mathematics of our times.

His first major contribution was the application of Morse theory to the topology of Lie groups and homogeneous spaces, culminating in the famous 'periodicity theorems' for the stable homotopy of the classical groups. This result provided the foundation for the development of K-theory, to which he also contributed greatly, in particular through his joint work with Atiyah on the index theory of differential operators and its applications to equivariant topology. He obtained seminal results in the theory of foliations. His later work, on Yang-Mills theory, moduli spaces of vector bundles, and elliptic genera, has been marked by a combination of the same geometric insight, coupled with new points of view coming from mathematical physics.

Professor Jean-Pierre Serre is a mathematician of enormous versatility, who has had a huge influence on an astonishingly wide range of subjects.

Serre´s initial work in algebraic topology and complex geometry made him the youngest recipient ever of the Fields Medal in 1954. His application of algebraic methods to infinite dimensional spaces was to become a major theme in all modern geometry. He transformed algebraic geometry and commutative algebra, through use of sheaf-theoretical and homological methods, constructed the first sheaf cohomology in characteristic p, created modern geometric class field theory, and made major contributions to Galois cohomology and to the theory of arithmetic groups. In number theory, Serre´s influence is inestimable. He introduced the notion of l-adic representations, gave spectacular applications to elliptic curves, abelian varieties, and the theory of modular forms. His conjecture about the modularity of Galois representations was a key step toward the eventual proof of Fermat´s Last Theorem.

Through his lectures, books, courses, each of which is a gem of mathematical exposition and clarity, Serre has inspired generations of mathematicians.