**BERLIN--**Mathematicians officially anointed four new superstars when the 1998 Fields Medals were presented here this week at the opening ceremonies of the International Congress of Mathematicians. There is no Nobel Prize in mathematics, and the Fields Medal--presented every 4 years by the International Mathematical Union (IMU)--has become the discipline's highest honor. Unlike Nobels, Fields Medals are traditionally awarded only to mathematicians no older than 40 and are intended as much to encourage future work as to recognize past achievement.

Much of the work honored by the medals shows the influence of physics. "I think that's not an accident," says medalist Richard Borcherds of the University of Cambridge and the University of California, Berkeley, who invented a fruitful new concept called a vertex algebra. "At the moment, theoretical physicists are churning out enormous numbers of amazing new ideas. My guess is that this is going to continue well into the next century."

One example is the work of Maxim Kontsevich of the Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France, and Rutgers University. A result in his doctoral thesis pointed to a surprising relationship between certain calculations in algebraic geometry and solutions of an equation from the theory of nonlinear waves. William Timothy Gowers of the University of Cambridge, in contrast, stuck to mathematics: He solved a number of famous problems originally stated in the 1930s by Polish mathematician Stefan Banach and unsolved for decades. Finally, Curtis McMullen of Harvard University was honored for his work in a variety of mathematical areas, including simple dynamical systems that can exhibit surprisingly complicated behavior.

The longest and loudest applause from the crowd of 3500 mathematicians assembled in Berlin's International Congress Center came when the IMU presented the conqueror of Fermat's Last Theorem, Andrew Wiles of Princeton University, with a special one-time tribute. In 1994, the last time the medals were awarded, Wiles's proof still contained a gap, and he is now 45--technically too old to receive a Fields Medal. One mathematician remarked that Wiles has already gotten so many prizes he doesn't need a Fields Medal. No, said another, the Fields Medal needs Wiles.