# Fields Medal

Fields Medals are given every four years to the most distinguished mathematicians age 40 or under. In the absence of a Nobel Prize in mathematics, they are regarded as the highest professional honor a mathematician can attain. Canadian mathematician J. C. Fields donated funds establishing the medals and they were first awarded in 1936.

## Ngô Bao Châu

Professor, Mathematics Department, 2010

**Fields Medal, 2010**

For his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro–geometric methods.

## Andrei Okounkov

L.E. Dickson Instructor, Mathematics Department, 1996–99

**Fields Medal, 2006**

For his contributions bridging probability, representation theory, and algebraic geometry.

## Efim Zelmanov

Mathematics Department, 1994–95

**Fields Medal, 1994**

For his solution to the restricted Burnside problem.

## Vladimir Drinfeld

Harry Pratt Judson Distinguished Service Professor in Mathematics, 1999–present

**Fields Medal, 1990**

For his work on quantum groups and for his work in number theory.

## Charles Louis Fefferman

Mathematics Department, 1970–73

**Fields Medal, 1978**

For several innovations that revised the study of multidimensional complex analysis by finding correct generalizations of classical low-dimensional results, through his work on partial differential equations, Fourier analysis, in particular convergence, multipliers, divergence, singular integrals, and Hardy spaces.

## John Griggs Thompson

PhD, Mathematics, 1959 Mathematics Department, 1962–68

**Fields Medal, 1970**

Proved jointly with W. Feit that all non-cyclic finite simple groups have even order. The extension of this work by Thompson determined the minimal simple finite groups, that is, the simple finite groups whose proper subgroups are solvable.

## Stephen Smale

Instructor, Department of Mathematics, 1956–58 Professor, Department of Mathematics and TTI, 2004–present

**Fields Medal, 1966**

Worked in differential topology where he proved the generalized Poincaré conjecture in dimension n>=5: Every closed, n-dimensional manifold homotopy-equivalent to the n-dimensional sphere is homeomorphic to it. Introduced the method of handle-bodies to solve this and related problems.

## Paul Joseph Cohen

PhD, Mathematics, 1958

**Fields Medal, 1966**

Used technique called “forcing” to prove the independence in set theory of the axiom of choice and of the generalized continuum hypothesis. The latter problem was the first of Hilbert’s problems of the 1900 Congress.

## Lars Hörmander

Visitor, Mathematics Department, Winter and Spring Quarters, 1956

**Fields Medal, 1962**

For his outstanding work in the theory of partial differential equations.