1959-

South African mathematician who proved the "Monstrous Moonshine" conjectures, so-called because they were so bizarre. Borcherds introduced new techniques into mathematics, including vertex algebras, for which he was awarded a Fields Medal in 1998, and a new class of algebras, now called Borcherds algebras. His tools are used for studying the representations of the monster simple group, a group with more than 8 × 10⁵⁴ elements, and uncovering the mysterious connections between the Monster and other areas of mathematics.