Two bridge builders have won mathematics' highest honor. The 2002 Fields Medals--presented today at the opening ceremonies of the International Congress of Mathematicians in Beijing--went to Laurent Lafforgue of the Institute for Advanced Scientific Study in Bures-sur-Yvette, France, and to Vladimir Voevodsky of the Institute for Advanced Study in Princeton, New Jersey. Madhu Sudan, an information theorist at the Massachusetts Institute of Technology (MIT), received the Rolf Nevanlinna Prize, an analogous award for work in computer science.
Lafforgue was honored for his work on the Langlands Program, an ambitious mathematical quest begun in 1967 by Robert Langlands, then a young professor at Princeton University. Langlands conjectured that two different-looking mathematical beasts--automorphic forms and Galois representations--were intimately connected. In 1999, Lafforgue won mathematical acclaim by proving the Langlands Conjecture for a very broad class of objects known as function fields (Science, 4 February 2000, p. 792). "I knew that it was an important result," he says. "Today, of course, I feel deeply honored and happy to obtain so much recognition for my work."
The other new Fields medalist, Voevodsky, also toiled at the intersection of two mathematical subjects: topology and algebra. In 1970, mathematician John Milnor of the State University of New York, Stony Brook, conjectured that two different tools used in these disciplines--ways of describing properties of various kinds of surfaces known as Galois cohomology and K-theory--were in fact related. The Milnor Conjecture remained the biggest problem in that area of mathematics until 1996, when Voevodsky created new mathematical tools that enabled him to verify the conjecture.
The Rolf Nevanlinna Prize honors MIT's Sudan for his work on the very concept of mathematical proof. A proof is a series of logical statements, each linked to the next according to strict rules of inference. If the statements are correct and the links obey the rules, the proof is valid; otherwise it is flawed. Sudan added shades of gray to this black-and-white dichotomy by showing that, in theory, a mathematician could figure out the probability that a new proof is correct.