Jean Alexandre Eugène Dieudonné (; 1 July 1906 – 29 November 1992) was a French mathematician, notable for research in
abstract algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...
,
algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
, and
functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics ...
, for close involvement with the
Nicolas Bourbaki
Nicolas Bourbaki () is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure (Paris), École normale supérieure (ENS). Founded in 1934–1935, the Bourbaki group originally intende ...
pseudonym
A pseudonym (; ) or alias () is a fictitious name that a person assumes for a particular purpose, which differs from their original or true meaning ( orthonym). This also differs from a new name that entirely or legally replaces an individual's o ...
ous group and the ''
Éléments de géométrie algébrique
The (''EGA''; from French: "Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné) is a rigorous treatise on algebraic geometry that was published (in eight parts or fascicles) from 1960 through 1967 by the . ...
'' project of
Alexander Grothendieck
Alexander Grothendieck, later Alexandre Grothendieck in French (; ; ; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research ext ...
, and as a historian of mathematics, particularly in the fields of functional analysis and
algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...
. His work on the
classical group
In mathematics, the classical groups are defined as the special linear groups over the reals \mathbb, the complex numbers \mathbb and the quaternions \mathbb together with special automorphism groups of Bilinear form#Symmetric, skew-symmetric an ...
s (the book ''La Géométrie des groupes classiques'' was published in 1955), and on
formal group In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by . The term formal group sometimes means the same as formal group law, and sometimes means one o ...
s, introducing what now are called
Dieudonné modules, had a major effect on those fields.
He was born and brought up in
Lille
Lille (, ; ; ; ; ) is a city in the northern part of France, within French Flanders. Positioned along the Deûle river, near France's border with Belgium, it is the capital of the Hauts-de-France Regions of France, region, the Prefectures in F ...
, with a formative stay in
England
England is a Countries of the United Kingdom, country that is part of the United Kingdom. It is located on the island of Great Britain, of which it covers about 62%, and List of islands of England, more than 100 smaller adjacent islands. It ...
where he was introduced to
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 ...
. In 1924 he was admitted to the
École Normale Supérieure
École or Ecole may refer to:
* an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing i ...
, where
André Weil
André Weil (; ; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was one of the most influential mathematicians of the twentieth century. His influence is du ...
was a classmate. He began working in
complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...
. In 1934 he was one of the group of ''normaliens'' convened by Weil, which would become '
Bourbaki'.
Education and teaching
He served in the
French Army
The French Army, officially known as the Land Army (, , ), is the principal Army, land warfare force of France, and the largest component of the French Armed Forces; it is responsible to the Government of France, alongside the French Navy, Fren ...
during
World War II
World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
, and then taught in
Clermont-Ferrand
Clermont-Ferrand (, , ; or simply ; ) is a city and Communes of France, commune of France, in the Auvergne-Rhône-Alpes regions of France, region, with a population of 147,284 (2020). Its metropolitan area () had 504,157 inhabitants at the 2018 ...
until the liberation of France. After holding professorships at the
University of São Paulo
The Universidade de São Paulo (, USP) is a public research university in the Brazilian state of São Paulo, and the largest public university in Brazil.
The university was founded on 25 January 1934, regrouping already existing schools in ...
(1946–47), the
University of Nancy
A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Uni ...
(1948–1952) and the
University of Michigan
The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...
(1952–53), he joined the Department of Mathematics at
Northwestern University
Northwestern University (NU) is a Private university, private research university in Evanston, Illinois, United States. Established in 1851 to serve the historic Northwest Territory, it is the oldest University charter, chartered university in ...
in 1953, before returning to France as a founding member of the
Institut des Hautes Études Scientifiques
The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics (also with a small theoretical biology g ...
. He moved to the
University of Nice
A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Univ ...
to found the Department of Mathematics in 1964, and retired in 1970. He was elected as a member of the
Académie des Sciences
The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...
in 1968.
Career
Dieudonné drafted much of the Bourbaki series of texts, the many volumes of the
EGA algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
series, and nine volumes of his own
Éléments d'Analyse. The first volume of the ''Traité'' is a French version of the book ''Foundations of Modern Analysis'' (1960), which had become a graduate textbook on functional analysis.
He also wrote individual monographs on ''Infinitesimal Calculus'', ''Linear Algebra and Elementary Geometry'',
invariant theory
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit descr ...
,
commutative algebra
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideal (ring theory), ideals, and module (mathematics), modules over such rings. Both algebraic geometry and algebraic number theo ...
,
algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
, and formal groups.
With
Laurent Schwartz he supervised the early research of
Alexander Grothendieck
Alexander Grothendieck, later Alexandre Grothendieck in French (; ; ; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research ext ...
. Later from 1959 to 1964 he was at the
Institut des Hautes Études Scientifiques
The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics (also with a small theoretical biology g ...
alongside Grothendieck, and collaborating on the expository work needed to support the project of refounding
algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
on the new basis of
schemes.
Selected works
*
*
* 9 volumes of ''
Éléments d'analyse'' (1960-1982), éd. Gauthier-Villars
**
*; Eng. trans:
*
* (a reprint of )
*
*
*;
Eng. trans:
*
*
*
*
*
*
*
*
References
*
*
*
External links
*
* A talk on the history of Algebraic Geometry given by Jean Dieudonné at the Department of Mathematics of the University of Wisconsin-Milwaukee in 1972 has been recently restored and is availabl
here* Dieudonné appears in the
Horizon
The horizon is the apparent curve that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This curve divides all viewing directions based on whethe ...
BBC documentar
A Mathematical Mystery Tour
{{DEFAULTSORT:Dieudonne, Jean
1906 births
1992 deaths
20th-century French mathematicians
Algebraic geometers
French historians of mathematics
École Normale Supérieure alumni
Nicolas Bourbaki
Academic staff of the University of São Paulo
Members of the French Academy of Sciences
Scientists from Lille
Academic staff of Nancy-Université
University of Michigan faculty
Academic staff of Côte d'Azur University