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Berkeley Math Whiz Garners Fields Medal

by Robert Sanders, Public Affairs
posted August 26, 1998

Richard Borcherds and three other mathematicians received the Fields Medal, often called the Nobel Prize of mathematics, Aug. 18 at an international conference in Berlin.

A faculty member since 1993, Borcherds received the medal for his work in the fields of algebra and geometry, in particular for his proof of the so-called "Monstrous Moonshine" conjecture. He joins two previous Fields Medalists at Berkeley, Steven Smale and Vaughan Jones.

The medal, the highest scientific award for mathematicians, is awarded every four years at the International Congress of Mathematicians to a mathematician no older than 40. The medal and a prize of 15,000 Canadian dollars were presented at the opening ceremony of the congress in Berlin to Borcherds and to mathematicians Maxim Kontsevich, William Timothy Gowers and Curtis McMullen.

Until recently, Kontsevich and McMullen also were on the Berkeley faculty. Kontsevich left in 1997 to become a permanent professor at the Institut des Hautes Etudes in Paris. McMullen resigned in July to accept a position at Harvard University.

Gowers is a lecturer at Cambridge University in England and a Fellow of Trinity College.

Borcherds, 38, is best known for his proof of a conjecture so outlandish that people had named it Monstrous Moonshine. Formulated at the end of the 1970s by the British mathematicians John Conway and Simon Norton, the conjecture presented two mathematical structures in a totally unexpected relationship. One of these structures is the so-called Monster Group, and the other is the theory of modular functions.

In 1989, Borcherds was able to cast more light on the mathematical background of the topic and to produce a proof for the conjecture.

"When first formulated the conjecture seemed extraordinarily outlandish, hence its unusual name," said Calvin Moore, professor and chair of the Department of Mathematics. "But Richard established the connection between modular functions and the Monster Group and proved it to be true using algebraic objects called Kac-Moody Lie Algebras.

"He has made critical contributions to mathematics, and the prize is a well deserved recognition of his achievements."

Borcherds, on leave since 1996 as Royal Society Research Professor in the Department of Pure Mathematics and Mathematical Statistics at Cambridge University, is due to return to campus in 1999. A native of South Africa, he earned his PhD in 1985 from Trinity College, Cambridge, and subsequently became Morrey Assistant Professor at Berkeley in 1987-88. He is married to mathematician Ursula Gritsch.

Borcherds was made a Fellow of the Royal Society in 1994, and also received the John Whitehead Prize from the London Mathematical Society and the Prize of the Society of Paris in 1992.

The Fields Medal is the unofficial name for the "International Medal for Outstanding Discoveries in Mathematics." John C. Fields (1863-1932), a Canadian mathematician, organized the 1924 International Congress of Mathematicians in Toronto and attracted so many sponsors that money was left over at the end of the congress. This was used to fund the medals.

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