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. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''a ...
,
algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
, 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 (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...
, 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 - PSL (ENS). Founded in 1934–1935, the Bourbaki group originally in ...
pseudonym
A pseudonym (; ) or alias () is a fictitious name that a person or group assumes for a particular purpose, which differs from their original or true name (orthonym). This also differs from a new name that entirely or legally replaces an individua ...
ous group and the ''
Éléments de géométrie algébrique
The ''Éléments de géométrie algébrique'' ("Elements of algebraic geometry, Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné), or ''EGA'' for short, is a rigorous treatise, in French language, French, on algebraic ge ...
'' project of
Alexander Grothendieck, 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 , the complex numbers and the quaternions together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or ske ...
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 module
In mathematics, a Dieudonné module introduced by , is a module (mathematics), module over the non-commutative Dieudonné ring, which is generated over the ring of Witt vectors by two special endomorphisms F and V called the Frobenius endomorphis ...
s, had a major effect on those fields.
He was born and brought up in
Lille
Lille ( , ; nl, Rijsel ; pcd, Lile; vls, Rysel) is a city in the northern part of France, in French Flanders. On the river Deûle, near France's border with Belgium, it is the capital of the Hauts-de-France Regions of France, region, the Pref ...
, with a formative stay in
England
England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest and the Celtic Sea to the southwest. It is separated from continental Europe b ...
where he was introduced to
algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary a ...
. In 1924 he was admitted to the
École Normale Supérieure
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...
, 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 a founding member and the ''de facto'' early leader of the mathematical Bourbaki group. Th ...
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 Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...
. 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 (french: Armée de Terre, ), is the land-based and largest component of the French Armed Forces. It is responsible to the Government of France, along with the other components of the Armed For ...
during
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, and then taught in
Clermont-Ferrand
Clermont-Ferrand (, ; ; oc, label=Auvergnat (dialect), Auvergnat, Clarmont-Ferrand or Clharmou ; la, Augustonemetum) is a city and Communes of France, commune of France, in the Auvergne-Rhône-Alpes regions of France, region, with a population ...
until the liberation of France. After holding professorships at the
University of São Paulo
The University of São Paulo ( pt, Universidade de São Paulo, USP) is a public university in the Brazilian state of São Paulo. It is the largest Brazilian public university and the country's most prestigious educational institution, the best ...
(1946–47), the
University of Nancy
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, th ...
(1948–1952) and the
University of Michigan
, mottoeng = "Arts, Knowledge, Truth"
, former_names = Catholepistemiad, or University of Michigania (1817–1821)
, budget = $10.3 billion (2021)
, endowment = $17 billion (2021)As o ...
(1952–53), he joined the Department of Mathematics at
Northwestern University
Northwestern University is a private research university in Evanston, Illinois. Founded in 1851, Northwestern is the oldest chartered university in Illinois and is ranked among the most prestigious academic institutions in the world.
Charte ...
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. It is located in Bures-sur-Yvette, just ...
. He moved to the
University of Nice
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the ...
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 (French: ''Académie des 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 research. It was at the ...
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, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
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 descri ...
,
commutative algebra
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent ...
,
algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
, and formal groups.
With
Laurent Schwartz
Laurent-Moïse Schwartz (; 5 March 1915 – 4 July 2002) was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields Medal in 19 ...
he supervised the early research of
Alexander Grothendieck. 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. It is located in Bures-sur-Yvette, just ...
alongside Grothendieck, and collaborating on the expository work needed to support the project of refounding
algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
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
*
*
*
See also
*
Dieudonné determinant
*
Dieudonné plank
In mathematics, the Dieudonné plank is a specific topological space introduced by . It is an example of a metacompact space that is not paracompact
In mathematics, a paracompact space is a topological space in which every open cover has an open ...
*
Dieudonné's theorem In mathematics, Dieudonné's theorem, named after Jean Dieudonné, is a theorem on when the Minkowski sum of closed sets is closed.
Statement
Let X be a locally convex space and A,B \subset X nonempty closed convex sets. If either A or B is local ...
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 line 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 line divides all viewing directions based on whether i ...
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
University of São Paulo faculty
Members of the French Academy of Sciences
Scientists from Lille
Nancy-Université faculty
University of Michigan faculty
Côte d'Azur University faculty