View source for Biography:John G. Thompson

{{Short description|American mathematician}}
{{Infobox scientist
| name              = John Thompson
| image             = John Griggs Thompson.jpg
| caption           = Thompson in 2007
| birth_name        = John Griggs Thompson
| birth_date        = {{Birth date and age|1932|10|13}}
| birth_place       = Ottawa, Kansas, U.S.
| nationality       = American
| field             = [[Group theory]]
| work_institutions = [[Organization:Harvard University|Harvard University]] (1961–62)<br />[[Organization:University of Chicago|University of Chicago]] (1962–68)<br />{{nowrap|[[Organization:University of Cambridge|University of Cambridge]] (1968–93)}}<br />[[Organization:University of Florida|University of Florida]] (1993–)
| alma_mater        = [[Organization:Yale University|Yale University]] (BA)<br />[[Organization:University of Chicago|University of Chicago]] (PhD)
| doctoral_advisor  = [[Biography:Saunders Mac Lane|Saunders Mac Lane]]
| doctoral_students = R. L. Griess <br> [[Biography:Richard Lyons (mathematician)|Richard Lyons]] <br> [[Biography:Charles Sims (mathematician)|Charles Sims]]  <br> Nick Patterson
| thesis_title      = A Proof that a Finite Group with a Fixed-Point-Free Automorphism of Prime Order is Nilpotent
| thesis_url        = https://www.proquest.com/openview/505afaac7062eede9c95b6c1e0006542/1?cbl=18750&diss=y&pq-origsite=gscholar
| thesis_year       = 1959
| notable_students  = 
| known_for         = 
| awards            = {{no wrap|Cole Prize (1965)<br />Fields Medal (1970)<br />Fellow of the Royal Society (1979)<br />Senior Berwick Prize (1982)<br />Sylvester Medal (1985)<br />Wolf Prize (1992)<br />Médaille Poincaré (1992)<ref>[http://serge.mehl.free.fr/chrono/thompson.html Thompson, John Griggs — serge.mehl.free.fr]</ref><ref>[http://www.academie-sciences.fr/activite/prix/grande_medaille_fondations.pdf Liste des 122 fondations] {{webarchive|url=https://web.archive.org/web/20141006162842/http://www.academie-sciences.fr/activite/prix/grande_medaille_fondations.pdf |date=2014-10-06 }}. The ''médaille Poincaré'' awarded by the French Academy of Sciences was eliminated in 1997 in favor of the ''Grande Médaille''.</ref> <br />National Medal of Science (2000)<br>Abel Prize (2008)<br>De Morgan Medal (2013)}}
}}

'''John Griggs Thompson''' (born October 13, 1932) is an American [[Biography:Mathematician|mathematician]] at the [[Organization:University of Florida|University of Florida]] noted for his work in the field of [[Finite group|finite group]]s. He was awarded the Fields Medal in 1970, the Wolf Prize in 1992, and the Abel Prize in 2008.

==Biography==
Thompson received his Bachelor of Arts from [[Organization:Yale University|Yale University]] in 1955 and his [[Social:Doctorate|doctorate]] from the [[Organization:University of Chicago|University of Chicago]] in 1959 under the supervision of [[Biography:Saunders Mac Lane|Saunders Mac Lane]]. After spending some time on the mathematics faculty at the University of Chicago, he moved in 1970 to receive the Rouse Ball Professorship in Mathematics at the [[Organization:University of Cambridge|University of Cambridge]] and later moved to the Mathematics Department of the [[Organization:University of Florida|University of Florida]] as a Graduate Research Professor.  He is currently a professor emeritus of pure mathematics at the University of Cambridge, and a professor of mathematics at the University of Florida.  He received the Abel Prize in 2008 together with [[Biography:Jacques Tits|Jacques Tits]].<ref name="abel">{{cite web |date= |title=2008: John Griggs Thompson and Jacques Tits |url=https://abelprize.no/abel-prize-laureates/2008 |archive-url= |archive-date= |access-date= |publisher=Norwegian Academy of Science and Letters |quote=}}</ref>

==Academic career==
Thompson's doctoral thesis introduced new techniques and included the solution of a problem in [[Group theory#Finite group theory|finite group theory]] which had stood for around sixty years: the [[Nilpotent group|nilpotency]] of [[Frobenius group|Frobenius kernels]]. At the time, this achievement was noted in ''{{wipe|The New York Times}}''.<ref>http://www.cecm.sfu.ca/organics/papers/lam/paper/html/NYTimes.html New York Times article, April 26, 1959.</ref>

Thompson became a figure in the progress toward the [[Classification of finite simple groups|classification of finite simple groups]].  In 1963, he and [[Biography:Walter Feit|Walter Feit]] proved that all [[Abelian group|nonabelian]] finite [[Simple group|simple group]]s are of [[Parity (mathematics)|even]] [[Order (group theory)|order]] (the ''[[Feit–Thompson theorem|Odd Order Paper]]'', filling a whole issue of the ''[[Pacific Journal of Mathematics]]''). This work was recognised by the award of the 1965 Cole Prize in Algebra of the American Mathematical Society. His [[N-group (finite group theory)|N-group]] papers classified all finite simple groups for which the [[Centralizer and normalizer|normalizer]] of every non-identity [[Solvable group|solvable]] [[Subgroup|subgroup]] is solvable. This included, as a by-product, the classification of all minimal finite simple groups (simple groups for which every proper subgroup is solvable). This work had some influence on later developments in the classification of finite simple groups, and was quoted in the citation by [[Biography:Richard Brauer|Richard Brauer]] for the award of Thompson's Fields Medal in 1970 (Proceedings of the International Congress of Mathematicians, Nice, {{wipe|France}}, 1970).

The Thompson group ''Th'' is one of the 26 [[Sporadic group|sporadic finite simple groups]]. Thompson also made major contributions to the [[Inverse Galois problem|inverse Galois problem]]. He found a criterion for a finite group to be a [[Galois group]], that in particular implies that the [[Monster group|monster simple group]] is a Galois group.

==Awards==
In 1971, Thompson was elected to the United States National Academy of Sciences.   In 1982, he was awarded the Senior Berwick Prize of the London Mathematical Society, and, in 1988, he received the honorary degree of [[Social:Doctor of Science|Doctor of Science]] from the [[Organization:University of Oxford|University of Oxford]]. Thompson was awarded the United States National Medal of Science in 2000.<ref>{{cite web|url=http://www-history.mcs.st-and.ac.uk/Biographies/Thompson_John.html|title=John Griggs Thompson|publisher=University of St. Andrews|access-date=24 October 2016}}</ref> He is a Fellow of the Royal Society and a recipient of its Sylvester Medal in 1985.<ref>{{cite web|url=http://royalsociety.org/awards/sylvester-medal|title=Royal Society Sylvester Medalists|access-date=2 March 2014}}</ref> He is a member of the Norwegian Academy of Science and Letters.<ref>{{cite web|url=http://www.dnva.no/c26849/artikkel/vis.html?tid=40116 |title=Gruppe 1: Matematiske fag |publisher=Norwegian Academy of Science and Letters |language=no |access-date=7 October 2010 |url-status=dead |archive-url=https://web.archive.org/web/20131110152102/http://www.dnva.no/c26849/artikkel/vis.html?tid=40116 |archive-date=10 November 2013 }}</ref>

==See also==

*[[Feit–Thompson theorem]]
*McKay–Thompson series
*[[Quadratic pair]]
*[[Thompson factorization]]
*[[Thompson order formula]]
*[[Thompson subgroup]]
*[[Thompson transitivity theorem]]
*[[Thompson uniqueness theorem]]

==References==
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{{Reflist}}

==External links==
* {{MacTutor Biography|id=Thompson_John}}
* {{MathGenealogy|id=6488}}
* [https://web.archive.org/web/20050414155503/http://www.math.ufl.edu/fac/facmr/Thompson.html List of mathematical articles by John G. Thompson]
* [http://www.abelprize.no/c53860/binfil/download.php?tid=53792 Biography from the Abel Prize center] {{Webarchive|url=https://web.archive.org/web/20160611151241/http://www.abelprize.no/c53860/binfil/download.php?tid=53792 |date=2016-06-11 }}

{{Abel Prize laureates}}
{{Fields medalists}}
{{Wolf Prize in Mathematics}}
{{Winners of the National Medal of Science|math-stat-comp}}


{{DEFAULTSORT:Thompson, John Griggs}}
[[Category:Group theorists]]

{{Sourceattribution|John G. Thompson}}