Jean Dieudonné

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Jean Dieudonné 1970

Jean Alexandre Eugène Dieudonné (born July 1, 1906 in Lille , † November 29, 1992 ) was a French mathematician . He made valuable contributions in the fields of abstract algebra and functional analysis . He was also an important founding member of the Bourbaki group .

Life

Dieudonné studied and obtained his doctorate from 1924 to 1931 at the École normal supérieure under Paul Montel , interrupted by stays at the universities of Princeton and Berlin and the ETH Zurich . 1932–1933 he was professor in Bordeaux , 1933–1937 in Rennes , 1937–1952 in Nancy , with visiting professorships in Strasbourg and São Paulo (Brazil). In 1952 he went to the USA and initially taught at the University of Michigan in Detroit. From 1953 to 1959 he was a professor of mathematics at Northwestern University in Evanston (Illinois) near Chicago . In 1959 Dieudonné returned to Paris and was at IHES until 1964 . Since 1964 he held a chair in Nice .

In 1934 he founded the Bourbaki group together with other mathematicians . He was one of the two leading figures there (together with André Weil ). It has now been established that most of the texts published under the pseudonym Bourbaki were finalized by Dieudonné. He also mostly wrote the first version (called Dieudonné's Monster ), which then went through numerous revisions (every Bourbaki member had the right to veto). Dieudonné was also a vehement advocate of a complete renewal of mathematics teaching ( New Mathematics ), for which he issued the slogan: “Down with Euclid! Death to the triangles! ”First, this was done publicly at an international conference in the Royaumont monastery in Asnières-sur-Oise in November / December 1959. However, by no means everyone in the Bourbaki group agreed with Dieudonné's views (which was officially announced as early as 1956 when the 50th birthday from Bourbaki).

His talent for writing textbooks and the large synopsis was also evident in the monumental Éléments de géometrie algébrique, which he wrote together with Alexander Grothendieck in the 1960s, and which laid the foundations for the further development of the theory in the Séminaires de géometrie algébrique (SGA) of the Grothendieck School. In his short two-volume Cours de géometrie algébrique , he gives a brief outline, with the first volume also going into the history of this area in detail.

Other areas of work were B. group theory , Lie groups , functional analysis (theory of topological vector spaces , spectral theory ), topology (in 1944 he introduced the concept of paracompact space , the Dieudonné plank is named after him).

But he is best known for his Éléments d'Analyse, which in several volumes deal with the whole analysis , including differential geometry , Lie groups and spectral theory, but which are aimed at advanced students. He also wrote textbooks for analysis and linear algebra / geometry for beginners.

In 1944 Dieudonné was awarded a prize by the Académie des sciences and in 1968 its member. In 1971 he received the Leroy P. Steele Prize from the American Mathematical Society . In 1954 he gave a plenary lecture at the International Congress of Mathematicians in Amsterdam (Le calcul différentiel dans les corps de caractéristique p> 0). In 1964 he was President of the Société Mathématique de France .

Dieudonné was also an excellent pianist. He also went to concerts mostly with the score, whereupon he groaned when the musicians forgot a note. His interest in the history of mathematics manifested itself in several books, including a. in the excursions on the history of mathematics in the Bourbaki books (published separately in 1994 as Bourbakis Eléments of the history of mathematics ). Among other things, he wrote the articles on Henri Poincaré and Hermann Weyl in the Dictionary of Scientific Biography. He also edited the works of Camille Jordan .

Fonts

  • La géométrie des groupes classiques , Springer 1955, 3rd edition 1973
  • Introduction to the theory of formal groups , Dekker 1973
  • Basics of modern analysis , 9 vols., Vieweg Verlag (English Foundations of Modern Analysis , French Éléments d'Analyse , 1960 to 1982)
    • With chapter information from the English edition: Volume 1 (Chapter 1 Elements of the theory of sets, 2 Real numbers, 3 Metric spaces, 4 Additional properties of the real line, 5 Normed spaces, 6 Hilbert spaces, 7 Spaces of continuous functions, 8 Differential calculus, 9 Analytic functions. Appendix to 9: Applications of analytic functions to plane topology, 10 Existence theorems, 11 Elementary spectral theory), Volume 2 (Chapter 12 Topology and topological algebra, 13 Integration, 14 Integration in locally compact groups, 15 Normed algebras and spectral theory), Volume 3 (Chapter 16 Differential manifolds, 17 Differential calculus on a differential manifold, Appendix Multilinear Algebra), Volume 4 (Chapter 18 Differential calculus on a differential manifold 2 (elementary global theory of first- and second-order differential equations. Elementary local theory of differential systems), 19 Lie Groups and Lie algebras, 20 Principal connections and Riemannian geometry, Appendix: Tensor products and formal power series), Volume 5 (Chapter 21 Compact Lie groups and semisimple Lie groups, Appendix: Modules), Volume 6 (Chapter 22 Harmonic analysis), Volume 7 (Chapter 23 Linear functional equations, Part 1 Pseudodifferential Operators), Volume 8 (Chapter 23 Linear functional equations, part 2 Boundary value problems), Volume 9 was only published in French (1982) and German (Chapter 24 Topologie algébrique et topologie différentielle élémentaire). A planned tenth volume on nonlinear problems was never published.
    • German edition by Vieweg (1972 to 1987): Volume 1 (Chapter 1 Foundations of Set Theory, 2 Real Numbers, 3 Metric Spaces, 4 Further Properties of Real Number Lines, 5 Normalized Spaces, 6 Hilbert Spaces, 7 Spaces of Continuous Functions, 8 Differential Calculus , 9 Analytical Functions, Appendix: Applications of Analytical Functions to the Topology of the Plane, 10 Theorems of Existence, 11 Elementary Spectral Theory), Volume 2 (12 Topology and Topological Algebra, 13 Integration, 14 Integration on Locally Compact Groups, 15 Normalized Algebras and Spectral Theory), Volume 3 (Chapter 16 Differentiable Manifolds, 17 Differential Calculus on a Differentiable Manifold: 1. Distributions and Differential Operators), Volume 4 (Chapter 18 Differential Calculus on a Differentiable Manifold, Part 2: Elementary global theory of first and second order differential equations. Elementary local theory differentiable Systems, 19 Liesche groups and Liesc he algebras, 20 main relationships and Riemannian geometry), Volume 5/6 (Chapter 21 Compact Lies Groups and Semi-Simple Lies Groups, 22 Harmonic Analysis), Volume 7 (Chapter 23 Linear Functional Equations 1: Pseudodifferential Operators), Volume 8 (Chapter 23 Linear Functional Equations: Boundary Value Problems), Volume 9 (Chapter 24: Algebraic Topology and Differential Topology)
  • Calcul infinitesimal , Hermann 1968
  • Algèbre linéaire et géométrie élémentaire , Hermann 1964, also engl. Linear algebra and geometry 1969
  • with Grothendieck Éléments de geometrie algebrique , several volumes, from 1960
  • Cours de géometrie algébrique , 2 vols. 1974 (first volume historical overview)
  • Historical development of algebraic geometry , American Mathematical Monthly 1972, No. 10
  • A history of algebraic and differential topology 1900-1960 , Birkhäuser Verlag 1988
  • History of functional analysis , North-Holland 1981
  • Une brève histoire de la topologie , in Jean-Paul Pier ed. Development of Mathematics 1900–1950 , Birkhäuser 1994, pp. 35–150
  • L'école mathématique francaise du 20.siècle , in J.-P.Pier ed. Development of Mathematics 1950–2000 , Birkhäuser 2000
  • as editor and co-author: Geschichte der Mathematik 1700–1900 - ein Abriss , Vieweg 1985 ( online at archive.org ), French. Original: Abrégé d'histoire des mathématiques: 1700–1900 , Hermann 1978
  • Mathematics - the music of reason , Springer 1992
  • Pour l'honneur de l'esprit humain: les mathématiques aujourd'hui , Hachette 1987
  • A panorama of pure mathematics - as seen by Nicolas Bourbaki , Academic Press 1982 (French original Gauthier-Villars 1977)

literature

  • Pierre Dugac: Jean Dieudonné, mathématicien complet . Gabay, Paris 1995. ISBN 2-87647-156-6
  • Laurent Schwartz: Souvenirs sur Jean Dieudonné , Pour la Science, June 1994

Web links

Individual evidence

  1. ↑ The move of one of the leading French mathematicians from IHES near Paris to Nice came as a complete surprise, since Nice was considered a blank slate when it came to mathematics. C. Bartozzi et al. a., Mathematical Lives. Protagonists of the Twentieth Century From Hilbert to Wiles, Springer, 2011, p. 129
  2. ^ Siobhan Roberts King of Infinite Space , Walker Publ. 2006, p. 157
  3. ^ Dieudonné New Thinking in School Mathematics , in New Thinking in School Mathematics , Organization for European Economic Cooperation 1961, pp. 31–45
  4. ^ Memoirs of Pierre Cartier cited in Siobhan Roberts King of Infinite Space , Walker Publ. 2006, p. 154
  5. ↑ Review by Jerrold Marsden, Bulletin AMS (NS), Vol.3, No. 1, 1980 , pp. 719-724
  6. ^ Review of the first volume by Leopoldo Nachbin, Bulletin AMS, Volume 67, No. 3, 1961
personal data
SURNAME Dieudonné, Jean
ALTERNATIVE NAMES Dieudonné, Jean-Alexandre-Eugène
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH July 1, 1906
PLACE OF BIRTH Lille
DATE OF DEATH November 29, 1992