Jean Dieudonné

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Jean-Alexandre-Eugène Dieudonné
Jean-Alexandre-Eugène Dieudonné
Born	July 1, 1906(1906-07-01) Lille
Died	November 29, 1992 (aged 86) Nice
Nationality	French
Fields	mathematics
Known for	abstract algebra

Jean-Alexandre-Eugène Dieudonné (July 1, 1906, Lille - November 29, 1992, Nice) was a French mathematician, known 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'.

Dieudonné was always the most explicit about Bourbaki: where the other participants gave the impression of not wishing to shed the student atmosphere of pranks, hoaxes and gratuitous secrecy and disinformative comments to outsiders, he would provide a reasoned approach to the group and its aims. 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. His seriousness on presentational matters led to outbreaks of teasing by colleagues in the group.

Bourbaki was often seen as subversive and perversely radical, wishing to change mathematical research onto 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 de Papa was an offer from the older figures, but inadequate to the needs of the day. Hence the emphasis on the more attractive 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. Bourbaki was indeed a kind of reception committee.

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 served in the French Army in World War II, and then taught in Clermont-Ferrand until the liberation of France.

He was a prolific writer, drafting much of the Bourbaki series of texts, the many fascicles of the EGA algebraic geometry series (the foundational work on scheme theory), and nine volumes of his Traité d'Analyse. The first volume of the Traité is a French translation of the (English) book Foundations of Modern Analysis (1960), which had become a distinctive 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 wrote also 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 Bourbakiste 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 IHES 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, primarily because of the sheer scale of what was being attempted. It could also be said, however, that the extrapolation of the Bourbaki approach to that context 'tested it to destruction'.