People: Math `Nobel' Awarded In Kyoto, Japan; Knots And Strings Net Fields Medals

The 1990 Fields Medals, mathematics' most prestigious international awards, were announced on August 21 in Kyoto, Japan, at the International Congress of Mathematicians. Four mathematicians received the award, which is accompanied by $15,000 Canadian. The Fields Medal, regarded as the Nobel Prize in mathematics and given every four years, was conceived by Canadian mathematician John Charles Fields. Vaughan F.R. Jones, professor of mathematics at the University of California, Berkeley, was recognized for his contributions to knot theory, which uses mathematical equations to describe knots. A mathematical knot can be pictured as a knotted piece of string that forms a closed, continuous loop. If the string can be deformed without cutting it into a simple circle, with no twists or crossings, it is not a true knot rather, it is an unknot. Sometimes, two knots may appear different, but with enough twisting and pulling, they can be deformed into the same knot. In 1984, while working with von Neumann algebras, a mathematical foundation of quantum mechanics, Jones discovered the Jones polynomials, a powerful tool for determining whether two complex knots that look very dissimilar are really the same. Nicholas Cozzarelli, a professor of biochemistry and molecular biology at UC-Berkeley, has been using the Jones polynomials to help characterize the intricately knotted strands of DNA formed during replication and recombination. This technique has enabled Cozzarelli and his colleagues to predict some of the DNA configurations formed in certain biological reactions. Jones's work in knot theory also has vast implications for quantum physics and statistical mechanics, his own primary areas of interest. Jones is currently working on applying knot theory to statistical mechanics. Jones, 37, was born in New Zealand. He earned his doctorate at the Ecole de Mathematiques in Geneva, Switzerland, and after teaching at UCLA, the University of Pennsylvania, and the Universit‚ de Geneve, joined the faculty of UC-Berkeley in 1985. Jones says he has no immediate plans for the money he wins with the medal. However, he hopes the prestige of the award will inspire the university to give him a raise. Perhaps more important, he says, I might even get a parking place. Edward Witten, a professor at the Institute for Advanced Study in Princeton, N.J., was recognized for his recent work with quantum field theory and the differential topology of two- and three-dimensional manifolds, and for earlier work relating gauge field theories to the classifications of four-dimensional manifolds. While not an originator of the string theory of unification, Witten has been one of its major proponents. According to Witten, his work has brought together string theory and quantum gauge theory, two areas hitherto considered separate. According to Jones, Witten's work has also had major implications for knot theory. Previously, the Jones polynomial described knots only in ordinary three-dimensional space. Witten's work, says Jones, helps characterize knots in abstract three-dimensional spaces, such as a 3-torus. Work in these areas is still in its infancy. What little bits that we know are probably very little bits of a bigger picture, says Witten. It's very hard to see what it will look like in just five to 10 years. While acknowledging the esoteric nature of his work, Witten feels that people shy away from these subjects unnecessarily. I'm sure many people could learn more in high school, and have a greater fascination for these subjects, eventually ending up working in the field, he says. Mathematics and physics have a beauty which is hard to imagine unless you've been exposed to them. Previous honors won by Witten include a 1982 MacArthur Award, the National Science Foundation's 1986 Alan T. Waterman Award, and a 1985 Dirac Medal from the International Center for Theoretical Physics. Witten received his Ph.D. from Princeton University in 1976. This year, The Scientist identified him as a top contender for the Nobel Prize in Physics (Sept. 3, 1990, page 16). From 1977 to 1980 he was a Junior Fellow in the Harvard Society of Fellows, and joined the faculty of Princeton University in 1980. He has been with the Institute for Advanced Study since 1987. Vladimir Gershonovich Drinfeld, a senior fellow at the Institute for Low Temperature Physics and Engineering in Kharkov, U.S.S.R., received a Fields Medal in recognition of his contributions to algebraic geometry, number theory, the theory of automorphic forms, and, most recently, quantum groups, a branch of theoretical physics. Drinfeld was a member of the Institute for Advanced Study's School of Mathematics in 1989-90. Shigefumi Mori, a faculty member of Nagoya University and the Research Institute of Mathematical Sciences of Kyoto University, was cited for his work on the classification of complex algebraic varieties of dimensions bigger than two. He recently completed a 10-year project on algebraic three-dimensional manifolds, resulting in the extension of classical theory of algebraic surfaces to dimension three.

People: Math `Nobel' Awarded In Kyoto, Japan; Knots And Strings Net Fields Medals

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