Bourbaki, Nicolas

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Bourbaki, Nicolas,

pseudonym under which a group of 20th cent. mathematicians has written a series of treatises on pure mathematics. The mathematicians have all been associated with the Ecole Normale Supérieure in Paris at some point in their careers; among them are the French scholars Claude Chevalley, André Weil, Henri Cartan, and Jean Dieudonné along with the American Samuel Eilenberg. The pseudonym was jokingly adopted from Gen. Charles BourbakiBourbaki, Charles Denis Sauter
, 1816–97, French general of Greek ancestry. In the Algerian campaigns and the Crimean War he gained one of the highest military reputations in Europe. Offered the Greek throne (1862), he declined.
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, becuase of his disastrous defeat in the Franco-Prussian War.

The principal aim of the Bourbaki group (L'Association des Collaborateurs de Nicolas Bourbaki) is to provide a solid foundation for the whole body of modern mathematics. The method of exposition is axiomatic and abstract, logically coherent and rigorous, proceeding normally from the general to the particular, a style found to be not altogether congenial to many readers. The ongoing series of books began with Éléments de Mathématiques in 1939, and other books on algebra, set theory, topology, and other topics have followed. Many books in the series have become standard references, though some mathematicians are critical of their austerely abstract point of view.

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.


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.