French mathematician (1906–1992)
Jean Alexandre Eugène Dieudonné (French:
[ʒɑ̃ alɛksɑ̃dʁ øʒɛn djødɔne] ; 1 July 1906 – 29 November 1992) was a French mathematician, notable for research in
abstract algebra ,
algebraic geometry , and
functional analysis , for close involvement with the
Nicolas Bourbaki
pseudonymous 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 groups (the book La Géométrie des groupes classiques was published in 1955), and on
formal groups , introducing what now are called
Dieudonné modules , 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 admitted to the
École Normale Supérieure , where
André Weil was a classmate.
[1] He began working in
complex analysis . 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 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.
Career
Dieudonné drafted much of the Bourbaki series of texts, the many volumes of the
EGA
algebraic geometry 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 ,
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 the
Institut des Hautes Études Scientifiques alongside Grothendieck, and collaborating on the expository work needed to support the project of refounding
algebraic geometry on the new basis of
schemes .
Selected works
Sur les groupes classiques . Paris: Hermann. 1948.
[2]
Dieudonné, Jean (1955),
La géométrie des groupes classiques , Ergebnisse der Mathematik und ihrer Grenzgebiete (N.F.), Heft 5, Berlin, New York:
Springer-Verlag ,
ISBN
978-0-387-05391-2 ,
MR
0072144
[3]
9 volumes of
Éléments d'analyse (1960-1982), éd. Gauthier-Villars
[4]
Algèbre linéaire et géométrie élémentaire . Hermann. 1964. ; Eng. trans: Linear algebra and geometry . 1969.
Dieudonné, Jean A. (1970).
"The work of Nicolas Bourbaki" .
American Mathematical Monthly . 77 (2): 134–145.
doi :
10.2307/2317325 .
JSTOR
2317325 .
Dieudonné, Jean A.;
Carrell, James B. (1971), "Invariant theory, old and new",
Advances in Mathematics , 4 , Boston, MA:
Academic Press : 1–80,
doi :
10.1016/0001-8708(70)90015-0 ,
ISBN
978-0-12-215540-6 ,
MR
0279102 (a reprint of Dieudonné, Jean A.;
Carrell, James B. (1970), "Invariant theory, old and new",
Advances in Mathematics , 4 : 1–80,
doi :
10.1016/0001-8708(70)90015-0 ,
ISSN
0001-8708 ,
MR
0255525 )
Dieudonne, J. (Oct 1972).
"Historical development of algebraic geometry" (PDF) .
American Mathematical Monthly . 79 (8): 827–866.
doi :
10.2307/2317664 .
JSTOR
2317664 .
Introduction to the theory of formal groups . Dekker. 1973.
Cours de géométrie algébrique I . P.U.F. 1974. ;
[6] Eng. trans:
History of Algebraic Geometry . Wadsworth Inc. 1985.
ISBN
9780534037239 .
Cours de géométrie algébrique II . P.U.F. 1974.
[6]
Dieudonné, Jean Alexandre (1982),
A panorama of pure mathematics , Pure and Applied Mathematics, vol. 97, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers],
ISBN
978-0-12-215560-4 ,
MR
0478177
[7]
Dieudonné, Jean (1981), Choix d'œuvres mathématiques. Tome I (in French), Paris: Hermann,
ISBN
978-2-7056-5922-6 ,
MR
0611149
Dieudonné, Jean (1981), Choix d'œuvres mathématiques. Tome II (in French), Paris: Hermann,
ISBN
978-2-7056-5923-3 ,
MR
0611150
History of functional analysis . North-Holland. 1981.
ISBN
9780080871608 .
[8]
Pour l'honneur de l'esprit humain: les mathématiques aujourd'hui . Hachette. 1987.
A History of Algebraic and Differential Topology 1900-1960 . Birkhäuser Boston. 1988.
ISBN
9780817649074 .
Mathematics - the music of reason . Springer. 1992.
ISBN
9783540533467 .
References
^
Weil, André (1992). The apprenticeship of a mathematician. Springer.
^
Kolchin, Ellis R. (1949).
"Review: Sur les groupes classiques , by Jean Dieudonné" (PDF) . Bull. Amer. Math. Soc . 55 (3, Part 1): 317–320.
doi :
10.1090/s0002-9904-1949-09196-6 .
^
Reiner, Irving (1956).
"Review: La géométrie des groupes classiques , by Jean Dieudonné" (PDF) . Bull. Amer. Math. Soc . 62 (4): 417–420.
doi :
10.1090/s0002-9904-1956-10056-6 .
^
Marsden, Jerrold E. (1980).
"Review: Treatise on analysis , by Jean Dieudonné, trans. by I. G. MacDonald" (PDF) . Bull. Amer. Math. Soc. (N.S.) . 3 (1): 719–724.
doi :
10.1090/S0273-0979-1980-14804-1 .
^
Nachbin, Leopoldo (1960).
"Review: Foundations of Modern Analysis , by Jean Dieudonné" (PDF) . Bull. Amer. Math. Soc . 67 (3): 246–250.
doi :
10.1090/s0002-9904-1961-10566-1 .
^
a
b
Hartshorne, Robin (1976).
"Review: Cours de géométrie algébrique , vols. I and II by Jean Dieudonné; Basic Algebraic Geometry , by I R. Shararevich, trans. by K. A. Hirsch" (PDF) . Bull. Amer. Math. Soc . 82 (3): 455–459.
doi :
10.1090/S0002-9904-1976-14042-6 .
^
Halmos, Paul R. (1979).
"Review: Panorama des mathématiques pure , by Jean Dieudonné" (PDF) . Bull. Amer. Math. Soc. (N.S.) . 1 (4): 678–681.
doi :
10.1090/s0273-0979-1979-14661-5 .
^
Doran, Robert S. (1982).
"Review: History of functional analysis , by Jean Dieudonné" (PDF) . Bull. Amer. Math. Soc. (N.S.) . 7 (2): 403–409.
doi :
10.1090/s0273-0979-1982-15049-2 .
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 available
here
Dieudonné appears in the
Horizon BBC documentary
A Mathematical Mystery Tour
International National Academics People Other