Jean Dieudonné

Jean Alexandre Eugène Dieudonné
Jean Alexandre Eugène Dieudonné
Born	1 July 1906 Lille, France
Died	29 November 1992 (aged 86) Paris, France
Nationality	French
Fields	Mathematics
Institutions	Institut des Hautes Études Scientifiques University of Nice University of São Paulo University of Nancy University of Michigan Northwestern University
Alma mater	École Normale Supérieure
Doctoral advisor	Paul Montel
Doctoral students	Edmond Fedida Alexander Grothendieck Kishore Marathe Paulo Ribenboim
Known for	Cartan–Dieudonné theorem
Notable awards	Leroy P. Steele Prize (1971)

Jean Alexandre Eugène Dieudonné (French: [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 in the École Normale Supérieure, where André Weil was a classmate.^[1] 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'.

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 Traité 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 IHÉS alongside Grothendieck, and collaborating on the expository work needed to support the project of refounding algebraic geometry on the new basis of schemes.

See also

• Cartan–Dieudonné theorem
• Dieudonné determinant
• Dieudonné plank
• Dieudonné's theorem
• Dieudonné module

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]
  • Foundations of Modern Analysis. Academic Press. 1960.^[5]
• Algèbre linéaire et géométrie élémentaire. Hermann. 1964.; Eng. trans: Linear algebra and geometry. 1969.
• "The work of Nicolas Bourbaki". Amer. Math. Monthly 77: 134–145. 1970.
• Dieudonné, Jean A.; Carrell, James B. (1971), "Invariant theory, old and new", Advances in Mathematics (Boston, MA: Academic Press) 4: 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)
• Historical development of algebraic geometry (PDF). American Mathematical Monthly 79. Oct 1972. pp. 827–866. doi:10.2307/2317664.
• 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.
• Cours de géométrie algébrique II. P.U.F. 1974.^[6]
• Dieudonné, Jean Alexandre (1982), A panorama of pure mathematics, Pure and Applied Mathematics 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 611149
• Dieudonné, Jean (1981), Choix d'œuvres mathématiques. Tome II (in French), Paris: Hermann, ISBN 978-2-7056-5923-3, MR 611150
• History of functional analysis. North-Holland. 1981.^[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.
• Mathematics - the music of reason. Springer. 1992.

References

1. Weil, A. (1992). The apprenticeship of a mathematician. Springer.
2. Kolchin, E. 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.
3. 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.
4. Marsden, J. 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.
5. 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.
6. 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.
7. Halmos, P. 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.
8. Doran, R. 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.

• Dugac, Pierre (1995), Jean Dieudonné: Mathématicien complet (Plus de lumiere) (in French), Editions Jacques Gabay, ISBN 978-2-87647-156-6
• O'Connor, John J.; Robertson, Edmund F., "Jean Dieudonné", MacTutor History of Mathematics archive, University of St Andrews.
• Jean Dieudonné at the Mathematics Genealogy Project

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