Nicolas Bourbaki

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Bourbaki, Nicolas

 

a collective pseudonym, used by a group of mathematicians in France who are attempting to implement an idea originated by D. Hilbert—a survey of various mathematical theories from the standpoint of a formal axiomatic method. N. Bourbaki’s multivolume (and far from finished) treatise Elements of Mathematics, which began publication in 1939, develops a formal axiomatic system that, according to the authors’ intention, should encompass if not all, then the major branches of mathematics as “separate aspects of a general concept.” The exposition is extremely abstract and formalized, and only the logical framework of the theories is given. The exposition is based on so-called structures that are determined by means of axioms—for example, structures of order, groups, and topological structures. The method of reasoning is from the general to the particular. A classification of mathematics that is based on types of structures greatly differs from the traditional classification. The Bourbaki Seminar, which is preparing the treatise, also hears reports by scientists from different countries. The group was formed in 1937 from former pupils of the Ecole Normale Supérieure. The number and precise makeup of the group are not made public.

WORKS

In Russian translation:
Osnovy strukturnogo analiza. Book 1—Teoriia mnozhestv. Moscow, 1965.
Algebra. Moscow, 1962-66. Chapters 1-9.
Obshchaia topologiia. Moscow, 1958-59. Chapters 1-8.
Funktsii deistvitel’nogo peremennogo. Moscow, 1965.
Topologicheskie vektornye prostranstva. Moscow, 1959.
Integrirovanie. Moscow, 1967-70. Chapters 1-8.
Ocherki po istorii matematiki. Moscow, 1963.
Séminaire Bourbaki: Textes des conférences, 1948/1949.
References in periodicals archive ?
The Bourbaki Group was a group of leading mathematicians in Paris including Jean Dieuedonne, Laurent Schwartz, and Andre Weil, who adopted the collective pseudonym of Nicolas Bourbaki.
In The Bourbaki Gambit, a novel about age discrimination in science, he explains simply and thoroughly (with graphics) the concepts behind a recent scientific breakthrough, the polymerase chain reaction (PCR) technique (13).
Stanislaw Ulam, complaining along with many other mathematicians about the raising of the symbolic ante in the style of Nicholas Bourbaki, writes: "I am turned off when I see only formulas and symbols, and little text.
The secret society of Bourbaki is a secret no more, thanks to Mashaal's detailed study of the group.
In his Nobel Laureate lecture and other sources, Debreu said: "To some-body trained in the uncompromising rigor of Bourbaki, counting equations and unknowns in the Walrasian system could not be satisfactory, and the nagging question of existence was posed" (Debreu 1992, 89).
the comment in Bourbaki [9, 312] about the concept of "between" in Euclid).
He presented a lecture on Woodin's work last March at the Bourbaki seminar in Paris, one of the most famous and long-standing seminars in mathematics.
Nicolas Bourbaki was beginning to publish his Elements de Mathematique, and his grandiose plan to reconstruct the entire edifice of mathematics commanded instant and total adhesion.
Bourbaki, Groupes et algebres de Lie, chapitres 4, 5 et 6, Masson, 1981, doi:10.
Bourbaki Elements of Mathematics, Lie Groups and Lie Algebras, Chapter 4-6.
September 25: Bourbaki Panorama at 13:00 at the Schweizerhof Hotel in Lucerne
Affine Hecke algebras and orthogonal polynomials, Asterisque, 237 (1996), 189-207, Seminaire Bourbaki 1994/95, Exp.