ⓘ Richard Borcherds
Richard Ewen Borcherds is a British mathematician currently working in quantum field theory. He is known for his work in lattices, number theory, group theory, and infinitedimensional algebras, for which he was awarded the Fields Medal in 1998.
1. Early life
Borcherds was born in Cape Town, but the family moved to Birmingham in the United Kingdom when he was six months old. His father is a physicist and he has three brothers, two of whom are mathematics teachers. He was a promising mathematician and chess player as a child, winning several national mathematics competitions and performing exceptionally at the International Mathematical Olympiad in 1978. Borcherds "was in line for becoming a chess master" before giving up chess after coming to believe that the higher levels of competitive chess are merely about the competition rather than the fun of playing.
2. Career
After receiving his doctorate in 1985, Borcherds has held various alternating positions at Cambridge and the University of California, Berkeley, serving as Morrey Assistant Professor of Mathematics at Berkeley from 1987 to 1988. He was a Royal Society University Research Fellow. From 1996 he held a Royal Society Research Professorship at Cambridge before returning to Berkeley in 1999 as Professor of mathematics. At Berkeley, he held a Miller Research Professorship from 2000 to 2001.
Borcherdss early work included pioneering results on classification of unimodular lattices, and the introduction of new algebraic objects, most notably vertex algebras and BorcherdsKacMoody algebras. These ideas came together in his vertexalgebraic construction and analysis of the fake monster Lie algebra called the monster Lie algebra at the time.
Borcherds is best known for his resolution of the ConwayNorton monstrous moonshine conjecture, which describes an intricate relation between the monster group and modular functions on the complex upper halfplane. To prove this conjecture, he drew upon theories that he had previously introduced, namely those of vertex algebras and BorcherdsKacMoody algebras, together with techniques of string theory, and applied them to the "moonshine module", a vertex operator algebra with monster symmetry constructed by Igor Frenkel, James Lepowsky, and Arne Meurman. Additional work in moonshine concerned mod p variants of this conjecture, and were known as modular moonshine.
Later contributions include the theory of Borcherds products, which are holomorphic automorphic forms on O n,2 that have wellbehaved infinite product expansions at cusps. Borcherds used this theory to resolve some longstanding conjectures concerning quasiaffineness of certain moduli spaces of algebraic surfaces. More recently, Borcherds has rendered perturbative renormalization, in particular the t HooftVeltman proof of perturbative renormalizability of gauge theory, into rigorous mathematical language.
An interview with Simon Singh for The Guardian, in which Borcherds suggested he might have some traits associated with Asperger syndrome, subsequently led to a chapter about him in a book on autism by Simon BaronCohen. BaronCohen concluded that while Borcherds had many autistic traits, he did not merit a formal diagnosis of Asperger syndrome.
3. Awards and honours
In 1992 Borcherds was one of the first recipients of the EMS prizes awarded at the first European Congress of Mathematics in Paris, and in 1994 he was an invited speaker at the International Congress of Mathematicians in Zurich. In 1994, he was elected to be a Fellow of the Royal Society. In 1998 at the 23rd International Congress of Mathematicians in Berlin, Germany he received the Fields Medal together with Maxim Kontsevich, William Timothy Gowers and Curtis T. McMullen. The award cited him "for his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex algebras and Borcherds Lie algebras, the proof of the ConwayNorton moonshine conjecture and the discovery of a new class of automorphic infinite products." In 2012 he became a fellow of the American Mathematical Society, and in 2014 he was elected to the National Academy of Sciences.
 of Mathematics BBC News 1998 British academics Tim Gowers and Richard Borcherds win top maths awards Multiplying and dividing by whole numbers: Why
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 a theory of partisan games. This he developed with Elwyn Berlekamp and Richard Guy, and with them also co  authored the book Winning Ways for your Mathematical
 Donaldson, Richard Borcherds Timothy Gowers, Alan Baker and the four official representatives were John G. Thompson, Alan Baker, Richard Borcherds Timothy
 mathematical equivalent of the Nobel Prize Michael Atiyah, Alan Baker, Richard Borcherds and Timothy Gowers. Atiyah was also an Abel Prize winner. Other Trinity
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