NEWS RELEASE, 08/19/98

UC Berkeley professor wins highest honor in mathematics, the prestigious Fields Medal

By Robert Sanders, Public Affairs

BERKELEY -- The Fields Medal, often called the Nobel Prize of mathematics, was awarded yesterday (Tuesday, Aug. 18) at an international conference in Berlin to a professor at the University of California, Berkeley, and to three other mathematicians.

Richard Ewen Borcherds, a professor of mathematics at UC Berkeley since 1993, 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 UC Berkeley, Stephen 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 T. McMullen.

Until recently, Kontsevich and McMullen also were on the UC Berkeley faculty. Kontsevich left UC Berkeley 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 given it the name 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 at UC Berkeley. "But Richard established the connection between modular functions and the Monster Group and proved it to

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

Borcherds, who has been on leave from UC Berkeley 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 began his academic career at Trinity College, Cambridge, where he obtained his PhD in 1985, and subsequently became Morrey Assistant Professor at UC Berkeley in 1987-88. He is married to mathematician Ursula Gritsch.

He 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 Monstrous Moonshine conjecture provides an interrelationship between the Monster Group and modular functions. Modular functions are used in modeling structures in two dimensions, and can be helpful, for example, in the description of molecular structures. The Monster Group, in contrast, seemed to be of importance only to pure mathematicians.

Groups are mathematical objects which can be used to describe the symmetry of structures. Expressed technically, they are a set of objects for which certain arithmetic rules apply. (For example all whole numbers and their sums form a group). An important theorem of algebra says that all groups, however large and complicated they may seem, consist of the same components - in the same way as the material world is made up of atomic particles. The Monster Group is the largest "sporadic, finite, simple" group and one of the most bizarre objects in algebra. It has more elements than there are elementary particles in the universe (a number approximately equal to 8 followed by 53 zeroes). Hence the name "monster."

In his proof, Borcherds uses many ideas of string theory - a surprisingly fruitful way of making theoretical physics useful for mathematical theory. Although still the subject of dispute among physicists, strings offer a way of explaining many of the puzzles surrounding the origins of the universe. They were proposed in the search for a single consistent theory which brings together various partial theories of cosmology. Strings have a length but no other dimension and may be open strings or closed loops.

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

The first Fields Medal was awarded in 1936. Due to the great expansion in mathematical research, four medals have been presented at each congress since 1966. The awards are often referred to as the "Nobel Prize for Mathematics," since the Swedish Academy of Sciences can only honor mathematicians indirectly through the natural or social sciences. There is no Nobel Prize for mathematics.

The Fields Medal is made of gold and shows the head of Archimedes (287-212 BC) with a quotation attributed to him: "Transire suum pectus mundoque potiri" (Rise above oneself and grasp the world). The reverse side bears the inscription: "Congregati ex toto orbe mathematici ob scripta insignia tribuere" (The mathematicians assembled here from all over the world pay tribute for outstanding work).

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