BORCHERDS, RICHARD EWEN

born Nov. 29, 1959, Cape Town, S.Af. British mathematician who won the Fields Medal in 1998 for his work in algebra. Borcherds studied undergraduate mathematics at the University of Cambridge and went on to finish his doctorate there in 1983. Afterward he held teaching and research positions at Cambridge and at the University of California at Berkeley. Borcherds received the Fields Medal at the International Congress of Mathematicians in Berlin in 1998 for his work on vertex algebras and Kac-Moody Lie algebras, which he used to prove the so-called Moonshine conjectures. The Moonshine conjectures asserted a mysterious connection between certain families of modular functions and the representation theory of the largest sporadic simple group (the Monster). Borcherds's work also drew on superstring theory and had profound implications for conformal field theory.