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.
His academic career comprised a number of positions in France, the USA and a time in
São Paulo, and finally in
Nice. 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'.
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