Richard Ewen Borcherds (born November 29, 1959) is a mathematician specializing in group theory and Lie algebras.
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 a 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 is related to representation theory of the monster group, a very large finite simple group whose structure was previously not well-understood.