Jean Alexandre Eugène Dieudonné  

Jean Alexandre Eugène Dieudonné


Born  July
1, 1906 Lille, France 
Died 
November 29, 1992 (aged 86) Paris, France 
Nationality  France 
Fields  Mathematics 
Institutions  University of São Paulo University of Nancy University of Michigan Northwestern University Institut des Hautes Études Scientifiques University of Nice 
Alma mater  École Normale Supérieure 
Known for  CartanDieudonné Theorem 
Jean Alexandre Eugène Dieudonné (July 1, 1906, Lille  November 29, 1992, Paris) was a French mathematician, notable for research in abstract algebra 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 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'.
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Dieudonné was explicit about Bourbaki. Formative on all French mathematicians of his generation was the 'hecatomb': the loss of so many of the best students of the generation immediately before, as casualties of World War I.
Bourbaki was often seen as subversive and perversely radical, wishing to change mathematical research by a new de facto standard of definitions and pedagogy. Dieudonné's line was that continuity in the French tradition of mathematics had been lost: classical analysis was on offer from the older figures, but inadequate to the needs of the day. Hence the emphasis on the German school: David Hilbert, Emmy Noether and others of the 'school of Göttingen' such as Hermann Weyl, the Austrian Emil Artin and Hungarian John von Neumann.
He served in the French Army in World War II, and then taught in ClermontFerrand until the liberation of France. After holding professorships at the University of São Paulo (194647), the University of Nancy (19481952) and the University of Michigan (195253), 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.
He 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 translation of the book Foundations of Modern Analysis (1960), which had become a graduate textbook on functional analysis. A common attitude in France was that the elaboration of the Traité was something many could have done; this is perhaps a tribute to the success of the Bourbaki renewal, which had started with a pledge to update the analysis treatises of figures such as Goursat.
He also wrote individual monographs on Infinitesimal Calculus, Linear Algebra and Elementary Geometry, invariant theory, commutative algebra, algebraic geometry, and formal groups. A broad survey of mathematics from the Bourbaki perspective provided a natural focus of controversy. As one mathematician from another camp put it: 'good to know where's one's research field lies — down with the social diseases'.
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. This was left in an incomplete state.
Jean Alexandre Eugène Dieudonné (July 1, 1906, Lille  November 29, 1992, Paris) was a French mathematician, notable for research in abstract algebra and functional analysis.
