Award-winning links twixt math and physics.

Award-winning links twixt math and physics

Mathematicians at a major international conference this week in Kyoto, Japan, turned the spotlight on four members of their community by awarding each a Fields Medal. Among mathematicians, the award -- first presented in 1936 and now given every four years at the International Congress of Mathematicians -- carries the prestige if not the monetary value of a Nobel Prize.

Medalist Vaughan F.R. Jones, 37, a topologist at the University of California, Berkeley, is best known for his work in knot theory (SN: 5/21/88, p.328). In 1984, he unexpectedly discovered a connection between von Neumann algebras (mathematical techniques that play a role in quantum mechanics) and knot theory. That link led Jones to formulate an improved method for distinguishing among knots. The discovery also generated a great deal of activity in the mathematical community and prompted renewed speculation about connections between knot theory and physics.

The work of award winner Edward Witten, 39, of the Institute for Advanced Study in Princeton, N.J., illustrates how blurred the distinction between theoretical physics and mathematics can get. Witten, better known as a physicist, is one of the chief proponents of string theory, which attempts to provide a unified picture of gravity and quantum mechanics. He contends that string theory will ultimately flourish as a new branch of geometry. Witten's recently developed "topological quantum field theories" hint at what such a geometrical foundation would look like (SN: 3/18/89, p.174).

Shigefumi Mori, 39, of Kyoto University, has devoted much of his career to pioneering methods of classifying certain kinds of surfaces defined by algebraic equations, thereby extending the classical theory of algebraic surfaces to three dimensions.

Award winner Vladimir G. Drinfeld, 36, of the Institute for Low Temperature Physics and Engineering in Kharkov, USSR, has contributed significantly to the fields of algebraic geometry and number theory, proving several fundamental conjectures in number theory and introducing a number of concepts useful in other fields.

Unlike Nobel Prizes, the mathematics awards go only to individuals who are "less than or equal to" 40 years of age. The emphasis on youth is designed to encourage recipients to continue their research while recognizing novel ideas that open up new mathematical frontiers for others to explore.