Jean-Alexandre-Eugène Dieudonné (July 1, 1906 - November 29, 1992) 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. July 1 is the 182nd day of the year (183rd in leap years) in the Gregorian Calendar, with 183 days remaining. ... 1906 was a common year starting on Monday (see link for calendar). ... November 29 is the 333rd (in leap years the 334th) day of the year in the Gregorian calendar. ... 1992 is a leap year starting on Wednesday of the Gregorian calendar. ... Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ... Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... Nicolas Bourbaki is the pseudonym under which a group of mainly French 20th-century mathematicians wrote a series of books of exposition of modern advanced mathematics, beginning in 1935. ... A pseudonym is a fictitious name used by an individual as an alternative to their legal name (whereas an allonym is the name of another actual person assumed by one person in authorship of a work of art; e. ... Alexander Grothendieck (born March 28, 1928, Berlin) is one of the greatest mathematicians of the 20th century, with major contributions to algebraic geometry, homological algebra, and functional analysis. ... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ... In mathematics, a formal group law is (roughly speaking) the formal power series analogue of a Lie group. ...

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'. City motto: – City proper (commune) Région Nord-Pas de Calais Département Nord (59) Mayor Martine Aubry (PS) (since 2001) Area 39. ... Royal motto: Dieu et mon droit (French: God and my right) Englands location within the UK Official language English de facto Capital London de facto Largest city London Area  - Total Ranked 1st UK 130,395 km² Population  - Total (2001)  - Density Ranked 1st UK 49,138,831 377/km² Religion... Algebra is a branch of mathematics which may be roughly characterized as a generalization and extension of arithmetic, in which symbols are employed to denote operations, and letters to represent number and quantity; it also refers to a particular kind of abstract algebra structure, the algebra over a field. ... The quadrangle at the main ENS building on rue dUlm is known as the Cour aux Ernests – the Ernests being the goldfish in the pond. ... André Weil (May 6, 1906 _ August 6, 1998) was one of the great mathematicians of the 20th century, a founding member of the influential Bourbaki group. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ...

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. Missing image Ypres, 1917, in the vicinity of the Battle of Passchendaele. ...

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 on 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. Analysis is that branch of mathematics which deals with the real numbers, complex numbers, and their functions. ... David Hilbert David Hilbert ( January 23, 1862 – February 14, 1943) was a German mathematician born in Wehlau, near Königsberg, Prussia (now Znamensk, near Kaliningrad, Russia) who is recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ... Emmy Noether (March 23, 1882 – April 14, 1935) was one of the most talented mathematicians of the early 20th century, with penetrating insights that she used to develop elegant abstractions which she formalized beautifully. ... The Georg-August University of Göttingen (Georg-August-Universität Göttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... Hermann Weyl (November 9, 1885 - December 8, 1955) was a German mathematician and physicist, one of the first people to combine general relativity with the laws of electromagnetism. ... Emil Artin (March 3, 1898-December 20, 1962) was a mathematician born in Vienna, Austria who spent his career in Germany (mainly in Hamburg) until the Nazi threat when he emigrated to the USA in 1937 where he was at Indiana University 1938-1946, and Princeton University 1946-1958. ... A separate article covers Saint John Neumann, the American priest. ...

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. Sao Paulo and São Paulo (city) redirect here. ... City motto: Nicæa civitas. ... The French Army (Armée de Terre, Ground Army) is one component in the Military of France. ... Mushroom cloud from the nuclear explosion over Nagasaki rising 18 km into the air. ... Clermont-Ferrand is a city of France, in the Auvergne region, with a population of approximately 140,000. ...

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, translated into English as Foundations of Modern Analysis (1960), became 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. Fascicles are sections of a book, usually a reference work, that because of its length, is issued in parts so that the information may be made available to the public as soon as possible rather than waiting years or decades to complete the entire work. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... In mathematics, a scheme is an important concept connecting the fields of algebraic geometry, commutative algebra and number theory. ...

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'. In mathematics, invariant theory refers to the study of invariant algebraic forms (equivalently, symmetric tensors) for the action of linear transformations. ... In abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras. ...

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'. Laurent Schwartz (5 March 1915 – 4 July 2002) was a French mathematician. ... IHÉS main building The Institut des Hautes Études Scientifiques (I.H.É.S.) is a French institute supporting advanced research in mathematics and theoretical physics. ...

Reference

• Jean Dieudonné: Mathématicien complet (1995) Pierre Dugac

External link

• MacTutor page (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dieudonne.html)