MathWorld Headline News

2002 Fields Medalists Announced

By Eric W. Weisstein

August 21, 2002--The 2002 Fields Medals and Nevanlinna Prize were awarded yesterday at the 2002 International Congress of Mathematicians in Beijing, China. The Fields Medals are commonly regarded as mathematics's closest analog to the Nobel Prize (which does not exist in mathematics) and are awarded every four years by the International Mathematical Union to one or more outstanding researchers. Fields Medals are more properly known by their official name: international medals for outstanding discoveries in mathematics. While it was agreed in 1966 that up to four medals could be awarded at each congress, the awards committee choose to award only two this year. There have been only three congresses since 1966 in which fewer than four medals have been awarded: 1974 (two), 1982 (three), and 1986 (three).

The 2002 Fields Medals were awarded to Laurent Lafforgue and Vladimir Voevodsky by the Chinese President Jiang Zemin at Beijing's Great Hall of the People, with more than four thousand people in attendance.

Lafforgue of the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France was recognized for his contributions to the so-called Langlands program. The Langlands program is a grand unified theory of mathematics that includes the search for a generalization of so-called Artin reciprocity (known as Langlands reciprocity) to non-Abelian Galois extensions of number fields. In a January 1967 letter to André Weil, Langlands proposed that the mathematics of algebra (Galois representations) and analysis (automorphic forms) are intimately related and that congruences over finite fields are related to infinite-dimensional representation theory. In particular, Langlands conjectured that the transformations behind general reciprocity theorems could be represented by means of matrices (Mackenzie 2000).

In 1998, three mathematicians proved Langlands' conjectures for local fields, and in a November 1999 lecture at the Institute for Advanced Study at Princeton University, Lafforgue presented a proof of the conjectures for function fields. Only the case of number fields is now unresolved.

Voevodsky of the Institute for Advanced Study in Princeton, New Jersey, was recognized for developing theories of the cohomology of algebraic varieties. Using new powerful techniques he developed, Voevodsky was able to solve the stubborn Milnor conjecture in algebraic K-theory that had resisted attack by numerous mathematicians for more than 30 years.

The Nevanlinna Prize went to Madhu Sudan.