Four awarded Fields Medals for mathematics.

From Paris to Princeton, for research subjects ranging from harmonic analysis to complex dynamics, four mathematicians have won the Fields Medal, the most prestigious award in mathematics.

First presented in 1936 at the International Congress of Mathematics (ICM), the Fields Medal, which carries no remuneration, is awarded every 4 years to mathematicians age 40 and younger whose work is "of a seminal nature, pointing the way to current and future progress in mathematics research."

The recipients -- announced last week at ICM's quadrennial conference, held this year in Zurich--are Jean Bourgain of the Institute for Advanced Study (IAS) in Princeton, N.J.; Pierre-Louis Lions of the University of Paris-Dauphine; Jean-Christophe Yoccoz of the University of Paris-Sud; and Efim Isaakovich Zelmanov, now at the University of Chicago while on leave from the University of Wisconsin-Madison.

Bourgain, 40, a classical mathematician, conducts research in number theory, combinatorics, and probability. But his primary work in harmonic analysis, one of the oldest and most fundamental tools of modern mathematics -- and wavelets in particular--suggests new and far-reaching applications in oil exploration, medicine, and computing.

According to Norman McNatt of IAS, Bourgain's "problem-solving capacity is extraordinary.... He's published 184 papers, not one of them trivial.... He's left a mark of some significance."

Lions, 37, specializes in nonlinear partial differential equations. Mike Crandall of the University of California, Santa Barbara, notes that these equations arise in "a startling array of fields: control theory, fluid dynamics, nuclear and statistical physics, image processing, and others." Lions, Crandall adds, "has made brilliant contributions to the understanding" of these diverse equations.

Yoccoz, 37, masters complex dynamical systems, among other things. He has worked to understand the intricate connections of the Mandelbrot set (SN: 11/23/91, p.331), in addition to supplying paradigms and models of one-dimensional systems for other mathematicians. Yakov Pesin of Pennsylvania State University in University Park says, "He created new ideas that can be used by mathematicians in completely different fields. His ideas and methods of study are so promising ... a most important achievement."

Zelmanov, 38, recently received a great deal of attention for solving the longstanding "restricted Burnside problem," which has baffled mathematicians since 1902. The problem questions whether the algebraic structures that arise naturally in the symmetry of geometric objects are finite. He has also worked extensively with questioning -- and dismissing -- the assumption of the finite nature of "Jordan algebras." Richard Brualdi of the University of Wisconsin-Madison, calls Zelmanov "one of the most brilliant mathematicians of this century."