Richard Ewen Borcherds (; born 29 November 1959) is a British mathematician currently working in

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...

. He is known for his work in lattices,

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

, and infinite-dimensional

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

s,James Lepowsky
"The Work of Richard Borcherds"
''Notices of the American Mathematical Society'', Volume 46, Number 1 (January 1999). for which he was awarded the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...

in 1998. He is well known for his proof of

monstrous moonshine In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group ''M'' and modular functions, in particular the ''j'' function. The initial numerical observation was made by John McKay in 1978, ...

using ideas from

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...

Early life and education

Borcherds was born in

Cape Town Cape Town is the legislature, legislative capital city, capital of South Africa. It is the country's oldest city and the seat of the Parliament of South Africa. Cape Town is the country's List of municipalities in South Africa, second-largest ...

, South Africa, but the family moved to

Birmingham Birmingham ( ) is a City status in the United Kingdom, city and metropolitan borough in the metropolitan county of West Midlands (county), West Midlands, within the wider West Midlands (region), West Midlands region, in England. It is the Lis ...

in the United Kingdom when he was six months old. Borcherds was educated at

King Edward's School, Birmingham King Edward's School (KES) is an independent school (UK), independent day school for boys in the British Public school (UK), public school tradition, located in Edgbaston, Birmingham. Founded by Edward VI of England, King Edward VI in 1552, it ...

. As a student, Borcherds won a gold medal, silver medal, and special prize in the

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is widely regarded as the most prestigious mathematical competition in the wor ...

. He attended university at

Trinity College, Cambridge Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

, where he studied under

John Horton Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician. He was active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many b ...

Career

After receiving his doctorate in 1985, Borcherds has held various alternating positions at Cambridge and the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, serving as Morrey Assistant Professor of Mathematics at Berkeley from 1987 to 1988. He was a

Royal Society University Research Fellow __NOTOC__ The Royal Society University Research Fellowship (URF) is a research fellowship awarded to outstanding early career scientists in the United Kingdom who are judged by the Royal Society The Royal Society, formally The Royal Society ...

. From 1996 he held a

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

Research Professorship at Cambridge before returning to Berkeley in 1999 as Professor of Mathematics.

Mathematical work

He did notable work on the Monstrous moonshine theory. He introduced

vertex algebra In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string theory. In addition to physical applications, vertex operator algebras have proven usef ...

Autism

An interview with

Simon Singh Simon Lehna Singh, (born 19 September 1964) is a British popular science author and theoretical and particle physicist. His written works include ''Fermat's Last Theorem'' (in the United States titled ''Fermat's Enigma: The Epic Quest to Solve ...

for ''

The Guardian ''The Guardian'' is a British daily newspaper. It was founded in Manchester in 1821 as ''The Manchester Guardian'' and changed its name in 1959, followed by a move to London. Along with its sister paper, ''The Guardian Weekly'', ''The Guardi ...

'', in which Borcherds suggested he might have some sort of traits possibly associated with

Asperger syndrome Asperger syndrome (AS), also known as Asperger's syndrome or Asperger's, is a diagnostic label that has historically been used to describe a neurodevelopmental disorder characterized by significant difficulties in social interaction and no ...

,Simon Singh
"Interview with Richard Borcherds"
''The Guardian'' (28 August 1998) led to a chapter about him in a book on autism by

Simon Baron-Cohen Sir Simon Philip Baron-Cohen (born 15 August 1958) is a British clinical psychologist and professor of developmental psychopathology at the University of Cambridge. He is the director of the university's Autism Research Centre and a Fellow of ...

. (see external links) records conversations with Richard Borcherds and his family. Baron-Cohen insinuated that while Borcherds may have had autistic traits, he did not meet a formal diagnosis of Asperger's syndrome.

Awards and honours

In 1992 Borcherds was one of the first recipients of the EMS prizes awarded at the first

European Congress of Mathematics The European Congress of Mathematics (ECM) is the second largest international conference of the mathematics community, after the International Congresses of Mathematicians (ICM). The ECM are held every four years and are timed precisely betwee ...

in Paris, and in 1994 he was an

invited speaker at the International Congress of Mathematicians An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...

in Zurich. In 1994, he was elected to be a Fellow of the

. In 1998 at the 23rd

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

in Berlin, Germany he received the

together with

Maxim Kontsevich Maxim Lvovich Kontsevich (, ; born 25 August 1964) is a Russian and French mathematician and mathematical physicist. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami. He ...

William Timothy Gowers Sir William Timothy Gowers, (; born 20 November 1963) is a British mathematician. He is the holder of the Combinatorics chair at the Collège de France, a director of research at the University of Cambridge and a Fellow of Trinity College, Camb ...

and

Curtis T. McMullen Curtis Tracy McMullen (born May 21, 1958) is an American mathematician who is the Cabot Professor of Mathematics at Harvard University. He was awarded the Fields Medal in 1998 for his work in complex dynamics, hyperbolic geometry and Teichmülle ...

. 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 Conway-Norton moonshine conjecture and the discovery of a new class of automorphic infinite products." In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

, and in 2014 he was elected to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

.National Academy of Sciences Members and Foreign Associates Elected
,

, 29 April 2014.

References

External links

* *
Richard E Borcherds' channel at YouTube
{{DEFAULTSORT:Borcherds, Richard Ewen 20th-century British mathematicians 21st-century British mathematicians Fields Medalists Group theorists Fellows of the Royal Society Fellows of the American Mathematical Society Members of the United States National Academy of Sciences University of California, Berkeley College of Letters and Science faculty 1959 births Living people People educated at King Edward's School, Birmingham Alumni of Trinity College, Cambridge Whitehead Prize winners International Mathematical Olympiad participants British expatriate academics in the United States