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John Griggs Thompson (born October 13, 1932) is an American
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
at the
University of Florida The University of Florida (Florida or UF) is a public land-grant research university in Gainesville, Florida. It is a senior member of the State University System of Florida, traces its origins to 1853, and has operated continuously on its ...
noted for his work in the field of finite groups. He was awarded the Fields Medal in 1970, the
Wolf Prize The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for ''"achievements in the interest of mankind and friendly relations among people ... irrespective of natio ...
in 1992, and the
Abel Prize The Abel Prize ( ; no, Abelprisen ) is awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Pri ...
in 2008.


Biography

Thompson received his
Bachelor of Arts Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four yea ...
from
Yale University Yale University is a Private university, private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the List of Colonial Colleges, third-oldest institution of higher education in the United Sta ...
in 1955 and his
doctorate A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' ...
from the
University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...
in 1959 under the supervision of
Saunders Mac Lane Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg. Early life and education Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftvill ...
. 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
University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...
and later moved to the Mathematics Department of the
University of Florida The University of Florida (Florida or UF) is a public land-grant research university in Gainesville, Florida. It is a senior member of the State University System of Florida, traces its origins to 1853, and has operated continuously on its ...
as a Graduate Research Professor. He is currently a
professor emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...
of
pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications ...
at the University of Cambridge, and a professor of mathematics at the University of Florida. He received the
Abel Prize The Abel Prize ( ; no, Abelprisen ) is awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Pri ...
in 2008 together with
Jacques Tits Jacques Tits () (12 August 1930 – 5 December 2021) was a Belgian-born French mathematician who worked on group theory and incidence geometry. He introduced Tits buildings, the Tits alternative, the Tits group, and the Tits metric. Life and ...
.


Academic career

Thompson's doctoral thesis introduced new techniques and included the solution of a problem in finite group theory which had stood for around sixty years: the nilpotency of Frobenius kernels. At the time, this achievement was noted in ''
The New York Times ''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid ...
''. Thompson became a figure in the progress toward the
classification of finite simple groups In mathematics, the classification of the finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of Lie type, or els ...
. In 1963, he and Walter Feit proved that all nonabelian finite
simple group SIMPLE Group Limited is a conglomeration of separately run companies that each has its core area in International Consulting. The core business areas are Legal Services, Fiduciary Activities, Banking Intermediation and Corporate Service. The da ...
s are of even order (the '' Odd Order Paper'', filling a whole issue of the ''
Pacific Journal of Mathematics The Pacific Journal of Mathematics is a mathematics research journal supported by several universities and research institutes, and currently published on their behalf by Mathematical Sciences Publishers, a non-profit academic publishing organisati ...
''). This work was recognised by the award of the 1965
Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number ...
in Algebra 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 ...
. His N-group papers classified all finite simple groups for which the
normalizer In mathematics, especially group theory, the centralizer (also called commutant) of a subset ''S'' in a group ''G'' is the set of elements \mathrm_G(S) of ''G'' such that each member g \in \mathrm_G(S) commutes with each element of ''S'', ...
of every non-identity solvable
subgroup In group theory, a branch of mathematics, given a group ''G'' under a binary operation ∗, a subset ''H'' of ''G'' is called a subgroup of ''G'' if ''H'' also forms a group under the operation ∗. More precisely, ''H'' is a subgrou ...
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
Richard Brauer Richard Dagobert Brauer (February 10, 1901 – April 17, 1977) was a leading German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular represent ...
for the award of Thompson's Fields Medal in 1970 (Proceedings of the
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 Nevanlinna Prize (to be rename ...
,
Nice Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative c ...
,
France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of overseas regions and territories in the Americas and the Atlantic, Pacific and Indian Oceans. Its metropolitan ar ...
, 1970). The Thompson group ''Th'' is one of the 26 sporadic finite simple groups. Thompson also made major contributions to the inverse Galois problem. He found a criterion for a finite group to be a
Galois group In mathematics, in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension. The study of field extensions and their relationship to the po ...
, that in particular implies that the monster simple group is a Galois group.


Awards

In 1971, Thompson was elected to the
United States National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, 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 Nat ...
. In 1982, he was awarded the
Senior Berwick Prize The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the ...
of the
London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...
, and, in 1988, he received the honorary degree of
Doctor of Science Doctor of Science ( la, links=no, Scientiae Doctor), usually abbreviated Sc.D., D.Sc., S.D., or D.S., is an academic research degree awarded in a number of countries throughout the world. In some countries, "Doctor of Science" is the degree used f ...
from the
University of Oxford The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the world's second-oldest university in contin ...
. Thompson was awarded the United States
National Medal of Science The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social scienc ...
in 2000. He is a
Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathematic ...
and a recipient of its
Sylvester Medal The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry a ...
in 1985. He is a member of the
Norwegian Academy of Science and Letters The Norwegian Academy of Science and Letters ( no, Det Norske Videnskaps-Akademi, DNVA) is a learned society based in Oslo, Norway. Its purpose is to support the advancement of science and scholarship in Norway. History The Royal Frederick Unive ...
.


See also

*
Feit–Thompson theorem In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved by . History conjectured that every nonabelian finite simple group has even order. suggested using ...
* McKay–Thompson series * Quadratic pair *
Thompson factorization In mathematical finite group theory, a Thompson factorization, introduced by , is an expression of some finite groups as a product of two subgroups, usually normalizers or centralizers of ''p''-subgroups for some prime A prime number (or ...
* Thompson order formula * Thompson subgroup *
Thompson transitivity theorem In mathematical finite group theory, the Thompson transitivity theorem gives conditions under which the centralizer of an abelian subgroup ''A'' acts transitively Transitivity or transitive may refer to: Grammar * Transitivity (grammar), a pro ...
* Thompson uniqueness theorem


References


External links

* *
List of mathematical articles by John G. Thompson

Biography from the Abel Prize center
{{DEFAULTSORT:Thompson, John Griggs 1932 births Members of the United States National Academy of Sciences Living people People from Ottawa, Kansas Institute for Advanced Study visiting scholars Yale University alumni University of Chicago alumni Harvard University faculty University of Chicago faculty Rouse Ball Professors of Mathematics (Cambridge) University of Florida faculty 20th-century American mathematicians Fellows of Churchill College, Cambridge Fellows of the Royal Society Fields Medalists Abel Prize laureates Group theorists National Medal of Science laureates Wolf Prize in Mathematics laureates Members of the Norwegian Academy of Science and Letters Mathematicians from Kansas