Jean Dieudonné
Encyclopedia
Jean Alexandre Eugène Dieudonné (1 July 1906 – 29 November 1992) was a French
mathematician, notable for research in abstract algebra
and functional analysis
, for close involvement with the Nicolas Bourbaki
pseudonym
ous group and the Éléments de géométrie algébrique
project of Alexander Grothendieck
, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology
. His work on the classical group
s (the book La Géométrie des groupes classiques was published in 1955), and on formal group
s, introducing what now are called Dieudonné module
s, had a major effect on those fields.
He was born and brought up in Lille
, with a formative stay in England
where he was introduced to algebra
. In 1924 he was accepted for the École Normale Supérieure
, where André Weil
was a contemporary. He began working, conventionally enough, in complex analysis
. In 1934 he was one of the group of normaliens convened by Weil, which would become 'Bourbaki
'.
during World War II
, and then taught in Clermont-Ferrand
until the liberation of France. After holding professorships at the University of São Paulo
(1946–47), the University of Nancy (1948–1952) and the University of Michigan
(1952–53), he joined the Department of Mathematics at Northwestern University
in 1953, before returning to France as a founding member of the Institut des Hautes Études Scientifiques
. He moved to the University of Nice to found the Department of Mathematics in 1964, and retired in 1970. He was elected as a member of the Académie des Sciences in 1968.
algebraic geometry
series, and nine volumes of his own Traité d'Analyse. The first volume of the Traité is a French translation 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
, commutative algebra
, algebraic geometry, and formal groups.
With Laurent Schwartz
he supervised the early research of Alexander Grothendieck; later from 1959 to 1964 he was at IHÉS alongside Grothendieck, and collaborating on the expository work needed to support the project of refounding algebraic geometry
on the new basis of schemes
.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician, notable for research in abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
and functional analysis
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 and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, for close involvement with the Nicolas Bourbaki
Nicolas Bourbaki
Nicolas Bourbaki is the collective pseudonym under which a group of 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. With the goal of founding all of mathematics on set theory, the group strove for rigour and generality...
pseudonym
Pseudonym
A pseudonym is a name that a person assumes for a particular purpose and that differs from his or her original orthonym...
ous group and the Éléments de géométrie algébrique
Éléments de géométrie algébrique
The Éléments de géométrie algébrique by Alexander Grothendieck , or EGA for short, is a rigorous treatise, in French, on algebraic geometry that was published from 1960 through 1967 by the Institut des Hautes Études Scientifiques...
project of Alexander Grothendieck
Alexander Grothendieck
Alexander Grothendieck is a mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory...
, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology
Algebraic topology
Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...
. His work on the classical group
Classical group
In mathematics, the classical Lie groups are four infinite families of Lie groups closely related to the symmetries of Euclidean spaces. Their finite analogues are the classical groups of Lie type...
s (the book La Géométrie des groupes classiques was published in 1955), and on formal group
Formal group
In mathematics, a formal group law is 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 of several generalizations. Formal groups are intermediate between...
s, introducing what now are called Dieudonné module
Dieudonné module
In mathematics, a Dieudonné module introduced by , is a 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 and Verschiebung operators...
s, had a major effect on those fields.
He was born and brought up in Lille
Lille
Lille is a city in northern France . It is the principal city of the Lille Métropole, the fourth-largest metropolitan area in the country behind those of Paris, Lyon and Marseille. Lille is situated on the Deûle River, near France's border with Belgium...
, with a formative stay in England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
where he was introduced to algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
. In 1924 he was accepted for the École Normale Supérieure
École Normale Supérieure
The École normale supérieure is one of the most prestigious French grandes écoles...
, where André Weil
André Weil
André Weil was an influential mathematician of the 20th century, renowned for the breadth and quality of his research output, its influence on future work, and the elegance of his exposition. He is especially known for his foundational work in number theory and algebraic geometry...
was a contemporary. He began working, conventionally enough, in complex analysis
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 useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
. In 1934 he was one of the group of normaliens convened by Weil, which would become 'Bourbaki
Nicolas Bourbaki
Nicolas Bourbaki is the collective pseudonym under which a group of 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. With the goal of founding all of mathematics on set theory, the group strove for rigour and generality...
'.
Education and teaching
He served in the French ArmyFrench Army
The French Army, officially the Armée de Terre , is the land-based and largest component of the French Armed Forces.As of 2010, the army employs 123,100 regulars, 18,350 part-time reservists and 7,700 Legionnaires. All soldiers are professionals, following the suspension of conscription, voted in...
during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, and then taught in Clermont-Ferrand
Clermont-Ferrand
Clermont-Ferrand is a city and commune of France, in the Auvergne region, with a population of 140,700 . Its metropolitan area had 409,558 inhabitants at the 1999 census. It is the prefecture of the Puy-de-Dôme department...
until the liberation of France. After holding professorships at the University of São Paulo
University of São Paulo
Universidade de São Paulo is a public university in the Brazilian state of São Paulo. It is the largest Brazilian university and one of the country's most prestigious...
(1946–47), the University of Nancy (1948–1952) and the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
(1952–53), he joined the Department of Mathematics at Northwestern University
Northwestern University
Northwestern University is a private research university in Evanston and Chicago, Illinois, USA. Northwestern has eleven undergraduate, graduate, and professional schools offering 124 undergraduate degrees and 145 graduate and professional degrees....
in 1953, before returning to France as a founding member of the Institut des Hautes Études Scientifiques
Institut des Hautes Études Scientifiques
The Institut des Hautes Études Scientifiques is a French institute supporting advanced research in mathematics and theoretical physics...
. He moved to the University of Nice to found the Department of Mathematics in 1964, and retired in 1970. He was elected as a member of the Académie des Sciences in 1968.
Career
He drafted much of the Bourbaki series of texts, the many volumes of the EGAÉléments de géométrie algébrique
The Éléments de géométrie algébrique by Alexander Grothendieck , or EGA for short, is a rigorous treatise, in French, on algebraic geometry that was published from 1960 through 1967 by the Institut des Hautes Études Scientifiques...
algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
series, and nine volumes of his own Traité d'Analyse. The first volume of the Traité is a French translation 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
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties from the point of view of their effect on functions...
, commutative algebra
Commutative algebra
Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra...
, algebraic geometry, and formal groups.
With Laurent Schwartz
Laurent Schwartz
Laurent-Moïse Schwartz 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 1950 for his work...
he supervised the early research of Alexander Grothendieck; later from 1959 to 1964 he was at IHÉS alongside Grothendieck, and collaborating on the expository work needed to support the project of refounding algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
on the new basis of schemes
Scheme (mathematics)
In mathematics, a scheme is an important concept connecting the fields of algebraic geometry, commutative algebra and number theory. Schemes were introduced by Alexander Grothendieck so as to broaden the notion of algebraic variety; some consider schemes to be the basic object of study of modern...
.
Works
- Foundations of Modern Analysis (1960), Academic Press (a reprint of )