New faculty member Zelmanov wins Fields Medal

The award, given every four years by the International Mathematical Union, was announced Aug. 3 at the 22nd International Congress of Mathematicians in Zuerich, Switzerland.

Zelmanov was honored for his work in the field of abstract algebra, including group theory, and specifically for his proof of the Restricted Burnside Problem, where he showed that certain mathematical constructs known as periodic groups are finite.

Jonathan Alperin, Professor in Mathematics, called Zelmanov's solution of the Restricted Burnside Problem "a tremendous breakthrough and a real triumph."

"His proof is awesome," Alperin said, "and at a level completely ahead of any previous work in algebra. It is notable for its sheer power, but also for the volcano of new techniques he developed to bring it to completion. His single effort has completely changed and advanced the whole field of algebra and given us a whole new field on which to operate."

Zelmanov said, "I am very proud to have been selected for this award. And I am also pleased that this is a recognition of the field of algebra.

"When I first heard about the award I didn't believe it, of course," he said. "I first heard about it from the secretary of the International Mathematical Union -- by e-mail -- and I thought the message must have been a practical joke. So I called the secretary, and at least after that, if it was a joke, I knew whose joke it was!"

Before coming to Chicago, Zelmanov had been professor at the University of Wisconsin-Madison since 1990; he previously was on the faculty at the Institute of Mathematics, Academy of Sciences of the U.S.S.R., in Novosibirsk. He is currently an editor of several mathematics journals, including Transactions of the American Mathematical Society, the International Journal of Algebra and Computation, and the Nova Journal of Algebra and Geometry.

"I am very happy to be at such a distinguished university," Zelmanov said. "It has great traditions, especially in my area of mathematics. The greatest people in algebra over many years all have been at this university. I am happy and proud to work where they worked.

"Actually, in each office in the department, somebody great was once working. Though I don't know which office will be mine, I am sure that somebody great has been there before me."

The Fields Medal is generally awarded to scholars under the age of 40. The winners are not known to the public until the award ceremony.

The award, officially known as the International Medal for Outstanding Discoveries in Mathematics, owes its more commonly used title to John C. Fields, the organizer of the 8th International Mathematical Congress in Toronto in 1924. Funds raised by Fields supported the first Fields Medals, and later prizes were endowed by his estate. The first Fields Medals were awarded to two mathematicians in 1936. Since 1966, four recipients have usually been selected for each presentation.

The other three Fields medalists this year are Jean Bourgain of the Institute for Advanced Study in Princeton, N.J.; Pierre-Louis Lions of the Universite Paris-Dauphine; and Jean-Christophe Yoccoz of the Universite Paris-Sud.