View source for Richard Borcherds

{{short description|British-American mathematician (born 1959)}}
{{Use dmy dates|date=July 2017}}
{{Infobox scientist
| name              = Richard Borcherds
| birth_name        = Richard Ewen Borcherds
| image             = Richard Borcherds.jpg
| caption           = Borcherds in 1993
| birth_date        = {{birth date and age|df=yes|1959|11|29}}<ref name="whoswho">{{cite web |url=http://www.ukwhoswho.com/view/article/oupww/whoswho/U8125 |title=BORCHERDS, Prof. Richard Ewen |work=Who's Who 2014, A & C Black, an imprint of Bloomsbury Publishing plc, 2014; online edn, Oxford University Press }}{{subscription required}}</ref>
| birth_place       = [[Cape Town]], South Africa
| nationality       = British<ref name="workGoddard">{{Cite journal | last1=Goddard | first1=Peter |url=http://www.emis.de/journals/DMJDMV/xvol-icm/Laudationes/13goddard.MAN.html | arxiv=math/9808136  | year=1998 | journal=Documenta Mathematica | issn=1431-0635 | title=The work of Richard Ewen Borcherds | pages=99–108| bibcode=1998math......8136G }}.</ref>
| death_date        = 
| death_place       = 
| field             = [[Mathematics]]
| work_institution  = {{Plainlist|
* {{nowrap|[[University of California, Berkeley]]}}
* [[University of Cambridge]]
}}
| alma_mater        = [[Trinity College, Cambridge]]
| doctoral_advisor  = [[John Horton Conway]]<ref name="mathgene">{{MathGenealogy |id=32941 }}</ref>
| thesis_title      = The leech lattice and other lattices
| thesis_url        = http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.354191
| thesis_year       = 1984
| doctoral_students = [[Daniel Allcock]]<ref name="mathgene"/>
| known_for         = [[Monstrous moonshine|Monstrous moonshine theory]]<br>[[Borcherds algebra]]<br>[[Vertex algebra]]s
| awards            = {{Plainlist|
* [[Whitehead Prize]] (1992)
* [[European Mathematical Society#Prizes|EMS Prize]] (1992)
* [[Fellow of the Royal Society|FRS]] (1994)
* [[Fields Medal]] (1998)}}
| website           = {{URL|math.berkeley.edu/~reb}}
}}
'''Richard Ewen Borcherds''' ({{IPAc-en|ˈ|b|ɔr|tʃ|ər|d|z}}; born 29 November 1959)<ref name="whoswho"/> is a British<ref>{{Cite web | url=http://www.nasonline.org/member-directory/members/20033092.html | title=Richard Borcherds}}</ref> mathematician currently working in [[quantum field theory]]. He is known for his work in [[lattice (group)|lattices]], [[group theory]], and infinite-dimensional [[algebra over a field|algebra]]s,<ref name="workAMS">James Lepowsky, [https://www.ams.org/notices/199901/fields.pdf "The Work of Richard Borcherds"], ''Notices of the American Mathematical Society'', Volume 46, Number 1 (January 1999).</ref><ref>{{cite book|author=Borcherds, Richard E.|chapter=What is moonshine?|title=Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. I|year=1998|pages=607–616|chapter-url=https://www.elibm.org/ft/10011743000}}</ref> for which he was awarded the [[Fields Medal]] in 1998. He is well known for his proof of [[monstrous moonshine]] using ideas from [[string theory]].

== Early life and education ==
Borcherds was born in [[Cape Town]], South Africa, but the family moved to [[Birmingham]] in the United Kingdom when he was six months old.<ref name=singh/>

Borcherds was educated at [[King Edward's School, Birmingham]]. As a student, Borcherds won a gold medal, silver medal, and special prize in the [[International Mathematical Olympiad]].<ref>{{Cite web|url=https://www.imo-official.org/participant_r.aspx?id=23|title=International Mathematical Olympiad|website=International Mathematical Olympiad|access-date=13 June 2025 |archive-url=https://web.archive.org/web/20250614024746/https://www.imo-official.org/participant_r.aspx?id=23 |archive-date=14 June 2025}}</ref> He attended university at [[Trinity College, Cambridge]],<ref name="ub">{{cite web|url=http://www.berkeley.edu/news/media/releases/98legacy/08-19-1998a.html|title=UC Berkeley professor wins highest honor in mathematics, the prestigious Fields Medal|date=19 August 1998|publisher=University of California, Berkeley|access-date=22 July 2009}}</ref> where he studied under [[John Horton Conway]].<ref name="ams">{{cite journal|first=Allyn|last=Jackson|date=November 1998|title=Borcherds, Gowers, Kontsevich, and McMullen Receive Fields Medals|journal=Notices of the American Mathematical Society|publisher=American Mathematical Society|volume=45|issue=10|url=https://www.ams.org/notices/199810/comm-fields.pdf}}</ref>

== 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]].<ref name=urfrs>{{cite journal|last1=Cook|first1=Alan|author-link1=Alan Cook (physicist)|title=URFs become FRS: Frances Ashcroft, Athene Donald, and John Pethica|journal=Notes and Records of the Royal Society|publisher=[[Royal Society]]|location=London|volume=54|issue=3|year=2000|pages=409–411|doi=10.1098/rsnr.2000.0181|s2cid=58095147}}</ref><ref name="ub"/> From 1996 he held a [[Royal Society]] Research Professorship at Cambridge before returning to Berkeley in 1999 as Professor of Mathematics.<ref name="ub"/> 

== Mathematical work ==
He did notable work on the [[Monstrous moonshine|Monstrous moonshine theory]].<ref name="workAMS" />

He introduced [[vertex algebra]]s.<ref name="workGoddard" />

== Autism ==

An interview with [[Simon Singh]] for ''[[The Guardian]]'', in which Borcherds suggested he might have some sort of traits possibly associated with [[Asperger syndrome]],<ref name=singh>Simon Singh, [http://simonsingh.net/media/articles/maths-and-science/interview-with-richard-borcherds/ "Interview with Richard Borcherds"], ''The Guardian'' (28 August 1998)</ref> led to a chapter about him in a book on autism by [[Simon Baron-Cohen]].<ref name=sbc>{{Cite book|first=Simon|last=Baron-Cohen|author-link=Simon Baron-Cohen|title=The Essential Difference: Male and Female Brains and the Truth about Autism|chapter=A Professor of Mathematics|publisher=Basic Books|year=2004|isbn=0-465-00556-X|url-access=registration|url=https://archive.org/details/essentialdiffere00baro}} (see external links) records conversations with Richard Borcherds and his family.</ref><ref>[https://www.theguardian.com/Archive/Article/0,4273,4103969,00.html High flying obsessives], ''The Guardian'', December 2000</ref> Baron-Cohen insinuated that while Borcherds may have had autistic traits, he did not meet a formal diagnosis of Asperger's syndrome.<ref name=sbc/>

== Awards and honours ==
In 1992 Borcherds was one of the first recipients of the [[European Mathematical Society|EMS prizes]] awarded at the first [[European Congress of Mathematics]] in Paris, and in 1994 he was an [[list of International Congresses of Mathematicians Plenary and Invited Speakers|invited speaker at the International Congress of Mathematicians]] in Zurich.<ref name="ams"/> In 1994, he was elected to be a Fellow of the [[Royal Society]].<ref name="royal">{{cite web |url=https://collections.royalsociety.org/DServe.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqDb=Catalog&dsqCmd=show.tcl&dsqSearch=(RefNo==%27EC%2F1994%2F05%27) |title=EC/1994/05: Borcherds, Richard Ewen |publisher=The Royal Society |archive-date=8 July 2019 |archive-url=https://web.archive.org/web/20190708083351/https://collections.royalsociety.org/DServe.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqDb=Catalog&dsqCmd=show.tcl&dsqSearch=%28RefNo%3D%3D%27EC%2F1994%2F05%27%29 |location=London |url-status=dead |df=dmy-all }}</ref> 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]].<ref name="ams"/> The award cited him "for his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex algebras and [[Generalized Kac–Moody algebra|Borcherds' Lie algebras]], the proof of the [[monstrous moonshine|Conway-Norton moonshine conjecture]]<ref name="Borcherds 1992 pp. 405–444">{{cite journal | last=Borcherds | first=Richard E. | title=Monstrous moonshine and monstrous Lie superalgebras | journal=Inventiones Mathematicae | publisher=Springer Science and Business Media LLC | volume=109 | issue=1 | year=1992 | issn=0020-9910 | doi=10.1007/bf01232032 | pages=405–444| bibcode=1992InMat.109..405B | s2cid=16145482 | citeseerx=10.1.1.165.2714 }}</ref> and the discovery of a new class of automorphic infinite products." In 2012 he became a fellow of the [[American Mathematical Society]],<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society]. Retrieved 10 November 2012.</ref> and in 2014 he was elected to the [[National Academy of Sciences]].<ref>[http://www.nasonline.org/news-and-multimedia/news/april-29-2014-NAS-Election.html National Academy of Sciences Members and Foreign Associates Elected] {{webarchive|url=https://web.archive.org/web/20150818062140/http://www.nasonline.org/news-and-multimedia/news/april-29-2014-NAS-Election.html |date=18 August 2015 }}, [[National Academy of Sciences]], 29 April 2014.</ref>

== References ==
{{reflist|30em}}

== Further reading ==
* Conway and [[Neil Sloane|Sloane]], ''[[Sphere Packings, Lattices and Groups]]'', Third Edition, Springer, 1998 {{ISBN|0-387-98585-9}}.
* Frenkel, Lepowsky and Meurman, ''Vertex Operator Algebras and the Monster'', Academic Press, 1988 {{ISBN|0-12-267065-5}}.
* [[Victor Kac|Kac, Victor]], ''Vertex Algebras for Beginners'', Second Edition, AMS 1997 {{ISBN|0-8218-0643-2}}.
* {{MacTutor Biography|id=Borcherds}}
* Mark Ronan (2007), ''Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics'', [[Oxford University Press]].

== External links ==
{{wikiquote}}
* {{Scopus|id=6701404143}}
* {{IMO results}}
* [https://www.youtube.com/@richarde.borcherds7998 Richard E Borcherds' channel at YouTube]

{{Fields medalists}}
{{FRS 1994}}
{{Authority control}}

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