THE 2001 WOLF FOUNDATION PRIZE IN MATHEMATICS

The Prize Committee for Mathematics has unanimously decided that the 2001 Prize be jointly awarded to:

Vladimir I. Arnold

Steklov Mathematical Institute

Moscow, Russia, and

Universite Paris-Dauphine

Paris, France

for his deep and influential work in a multitude of areas of mathematics, including dynamical systems, differential equations, and singularity theory.

Saharon Shelah

Hebrew University of Jerusalem

Jerusalem, Israel

for his many fundamental contributions to mathematical logic and set theory, and their applications within other parts of mathematics.

Professor Vladimir I. Arnold, a renaissance mathematician, has made significant contributions to an astounding number of different mathematical disciplines. His many research papers, books and lectures, plus his enormous erudition and enthusiasm, have had a profound influence on an entire generation of mathematicians.

Arnold´s Ph.D. thesis contained a solution to Hilbert´s 13th problem. His work on Hamiltonian dynamics, in particular as co-creator of the KAM (Kolmogorov-Arnold-Moser) theory and as the discoverer of 'Arnold´s diffusion', made him world-famous at an early age. Arnold´s contributions to the theory of singularities, which complements Thom´s catastrophe theory, has transformed this field. He has also made innumerable and fundamental contributions to the theory of differential equations, symplectic geometry, real algebraic geometry, the calculus of variations, hydrodynamics, and magneto-hydrodynamics, often discovering links between problems in diverse areas.

Professor Saharon Shelah, has for many years, been the leading mathematician in the foundations of mathematics and mathematical logic. His staggering output, of 700 papers and half a dozen monographs, includes the creation of several entirely new theories that changed the course of model theory and modern set theory, as well as providing the tools to settle old problems from many other branches of mathematics, including group theory, topology, measure theory, Banach spaces, and combinatorics.

Shelah created a number of subfields of set theory, most notably the theory of proper forcing and the theory of possible cofinalities, a remarkable refinement of the notion of cardinality, which led to the proofs of definite statements in areas previously considered far beyond the limits of undecidability. Shelah´s work on set theoretic algebra and its applications showed that dozens of areas of algebra involve phenomena that are not controlled by universally-recognized axioms of set theory (independence phenomena). In model theory he carried through a monumental program of deep structural analysis known as 'stability theory' which now dominates a large part of the field.