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.


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 ?
See Aczel's (2006) book on the story of the Bourbaki group based on the fictional character Nicholas Bourbaki who was responsible for the 'new math' that sweep American education and other education systems around the world.
Other notable structuralists and their major works include the psychoanalyst Jacques Lacan ( ecrits, 1966), the linguists Ferdinand de Saussure ( Cours de linguistique generale, 1916) and Noam Chomsky ( Language and Mind, 1968), the philosophers Jacques Derrida ( L 'ecriture et la difference, 1967) and Michel Foucault ( Les Mots et les choses, 1966), and the group of mathematicians known as Nicholas Bourbaki.