He was born in Cape Town, and educated at Cambridge University, where he studied under John Horton Conway. After receiving his doctorate he has held various positions at Cambridge and at the University of California, Berkeley, where he is currently professor of mathematics.

Borcherds is best known for his work connecting the theory of finite groups with other areas in mathematics. In particular he invented the notion of vertex algebras, which he used to prove the Conway-Norton conjecture. This has to do the with representation theory of the monster group, a very large finite simple group whose structure was not well-understood.

Borcherds was awarded the Fields Medal in 1998.

- "Borcherds, Gowers, Kontsevich, and McMullen Receive Fields Medals",
*Notices of the American Mathematical Society*, Volume 45, Number 10 (November 1998), electronic copy at [1] - James Lepowsky, "The Work of Richard Borcherds",
*Notices of the American Mathematical Society*, Volume 46, Number 1 (January 1999), electronic copy at [1] - Richard Borcherds, "What is ... The Monster?",
*Notices of the American Mathematical Society*, Volume 49, Number 9 (October 2002), electronic copy at [1] - Richard Borcherds' web site [1]. (has links to some relatively informal lecture notes describing his work)