BEJING, China, Aug. 21 (UPI) -- At the opening session of the International Congress of Mathematicians in Beijing this week, the world's best minds in math gathered in the Great Hall of the People to watch as Vladimir Voevodsky and Laurent Lafforgue were given the Fields Medal and Madhu Sudan received the Nevanlinna Prize.
The ceremony, which was presided over by President Jiang Zemin, bestowed the highest honors in mathematics. The awards are considered a combination of the Nobel Prize and the Olympics because they are awarded for outstanding achievement, but only once every four years.
Both Fields Medal winners for 2002 were recognized for research that helps build bridges between seemingly dissimilar areas of mathematics.
Russian-born Vladimir Voevodsky received the Fields Medal for his breakthrough work in algebraic geometry. Voevodsky, a professor in the School of Mathematics at the Institute of Advanced Study in Princeton, N.J., developed new theories in the field of co-homology -- a method of describing shapes using mathematical formulas.
Laurent Lafforgue, with the Institut des Hautes Etudes Scientifiques in Bures-sur-Yvette, France, also won the Fields Medal. His research advances the Langlands Program, a set of theories that can predict how disparate areas of mathematics might be connected.
Lafforgue's research has provided new links between number theory and analysis. He has invented a new geometric construction for abstract objects known as "function fields," which consist of quotients of polynomials. Such quotients can be added, subtracted, multiplied and divided like rational numbers.
The Nevanlinna Prize for math related to computer science was awarded to Madhu Sudan. All three winners were awarded their prizes Tuesday.
Sudan, associate professor in the Department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology in Cambridge, won the award for his work in several areas of theoretical computer science.
In one area, called probabilistically checkable proofs, Sudan showed it was possible to store the fundamental logic of a mathematical proof in computer bits and -- through his groundbreaking research in "verifiers" -- check only some of the bits but still determine whether the proof was likely correct.
Working with other researchers, Sudan also has made important contributions in understanding one of the fundamental questions of theoretical computer science: "Does P equal NP?"
"P" represents problems that are easier to solve using computing methods and algorithms that already exist, while "NP" problems are thought to be fundamentally harder to solve. Sudan has shown for many such problems, approximating an optimal solution can be just as hard as actually finding the optimal solution.
A third area where Sudan has made key contributions is in coming up with a new algorithm for error correcting codes. These codes are vitally important in the reliability and quality of transmitted information -- everything from music on a CD to communication over the Internet.
The "Fields Medal" is the unofficial title for the "International medal for outstanding discoveries in mathematics." It is named in honor of the Canadian mathematician, John C. Fields (1863-1932), who conceived the idea of the award. It first was given in 1936 and resumed in 1950 after the end of World War II.
A maximum of four Fields Medals are presented at each ceremony to individuals who can be no more than 40 years old at the time of the award. The age limit is designed to encourage further contributions as well as reward past work.
The Nevanlinna Prize has been given since 1983 for outstanding effort in the field of theoretical computer science. It was donated by the University of Helsinki in memory of the Finnish mathematician Rolf Nevanlinna (1895-1980), who was president of the International Mathematical Union between 1959 and 1962. Both awards come in the form of a gold medal and cash prize of $9,625 ($15,000 Canadian).