The Laureates

Copyright © Klaus Tschira Stiftung / Peter Badge

Richard Borcherds

Born 29 November 1959 in Cape Town (South Africa)

Fields Medal (1998) for his work on the introduction of vertex algebras, the proof of the Moonshine conjecture and for his discovery of a new class of automorphic infinite products

Richard Ewen Borcherds, son of a physics teacher at the University of Cape Town, grew up with his three brothers in Birmingham. Even as a child Borcherds showed promising talent not only in mathematics, but also as a chess player. He played some chess but gave up the game – believing that a professional career would be more about competition than chess. In 1978, Borcherds won the gold medal at the International Mathematical Olympiad in Bucharest. The same year, he began reading Mathematics at Trinity College, Cambridge, where John Horton Conway was his supervisor. In 1983 he was appointed Research Fellow at Trinity College. In 1985, he completed his Ph.D. on the Leech lattice. He then moved to the University of California, Berkeley, where he became a Morrey Assisant Professor of Mathematics (1987/88). In the following years the mathematician constantly shuttled between Berkeley and Cambridge. Between 1988 and 1991, he was a Royal Society Research Professor at Cambridge. Thereafter, he was appointed Professor of Mathematics at the University of California, Berkeley (1993). In 1996 he returned again to Cambridge, where he spent three years as a Royal Society Professor in the Mathematics Department, before moving back to Berkeley in 1999, where he still lives today. In an interview with the Guardian, Borcherds suggested that he had some character traits which are commonly associated with Asperger’s syndrome. The British psychologist Simon Baron-Cohen examined the issue and reported it in the chapter ‘A Professor of Mathematics’ in his book “The Essential Difference”.

Borcherds is married to the topologist Ursula Gritsch. The couple has two daughters.

Borcherds is a member of the Royal Society (1994) and the American Mathematical Society (2012). He has received among other awards, the EMS Prize (1992) and the Junior Whitehead Prize from the London Mathematical Society (1992).

In the early 1980s, Borcherds found by chance a series of works in physics which described interactions between particles (vertices). Borcherds recognised the mathematical potential that lay behind these descriptions. He began to fine tune the mathematical idea and thereby created ‘vertex algebras’.

At this time, he took his doctorate under John H. Conway, who was working intensively on a catalogue of finite simple groups. Groups are mathematical objects which have a structure that can be used to describe symmetries. Conway had in the late 1960s discovered three new sporadic simple groups in the symmetries of a 24-dimensional lattice, the so-called Leech lattice. And so Borcherds also initially explored the Leech lattice.

In parallel to this, he worked for years on the use of vertex algebras to study other finite simple groups, especially the largest sporadic simple group. Because of its size it is also called the Monster group: it has nearly as many elements as the planet Jupiter has atoms. Using a vertex algebra Borcherds settled a conjecture of Conway and his doctoral student Simon Norton on how to represent this Monster group, and thereby proved what a powerful tool vertex algebras can be.

At the same time Borcherds generalised a well-known tool in algebra, ‘Kac-Moody algebras’, and put them to important use in the theory of automorphic functions. Today, vertex algebras are used for numerous tasks in algebraic geometry and string theory.