THE 1989 WOLF FOUNDATION PRIZE IN MATHEMATICS

The Mathematics Prize Committee has unanimously selected the following two candidates to equally share the 1989 Wolf Prize in Mathematics:**Alberto P. CalderonUniversity of ChicagoChicago, Illinois, USA**

for his groundbreaking work on singular integral operators and their application to and important problems in partial differential equations.

John W. Milnor

Institute for Advanced Study

Princeton, New Jersey, USA

for ingenious and highly original discoveries in geometry, which have opened important new vistas in topology from the algebraic, combinatorial, and differentiable viewpoint.

The work of Professor Alberto P. Calderon has had a lasting impact on the shape of contemporary Fourier analysis and on its connections with real variables, complex analysis, and partial differential equations. In particular, his contributions to the theory of singular integral operators (SIO) have been decisive, both through the introduction of the sharpest technical tools into that theory and through its imaginative application to important problems in partial differential equations.

Together with his teacher, Antoni Zygmund, Calderon proved the famous theorem on the LP boundedness (1

His highly original discoveries of Professor John W. Milnor in geometry have exerted a major influence on the development of contemporary mathematics. The current state of the classification of topological, piecewise linear, and differentiable manifolds rests in large measure on his work in topology and algebra.

Milnor´s discovery of differentiable structures on S7 (the 7-dimensional sphere) which are exotic, i.e. different from the standard structure, came as a complete surprise and marked the beginning of differential topology. Later, in joint work with Kervaire, Milnor turned these structures (on any Sn) into a group which could then (in part) be computed; it turns out that there are over sixteen million distinct differentiable structures on S31! In his important work in algebraic geometry on singular points of complex hypersurfaces, exotic spheres are related to links around singularities. In the combinatorial direction, Milnor disproved the long-standing conjecture of algebraic topology known as the Hauptvermutung, by constructing spaces with two polyhedral structures that cannot have a common subdivision. This was based on an unexpected use of the previously known concept of torsion, which has since become, in its various algebraic and geometric versions, a basic tool.

These are just some highlights of Milnor´s impressive body of work. Beyond the research papers, a wealth of new results are contained in his books. These are famous for their clarity and elegance and remain a source of continuing inspiration.