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 ?
In mathematics, through the Bourbaki group who beginning in the 1930s specialized in questions of topography and new vector spaces with the intention of basing mathematics on set theory; (1)
The connecting links between the Bourbaki group in mathematics and structuralism, including thinkers like Levi-Strauss and Piaget deserve special mention.
A few years ago the Bourbaki group of mathematicians attempted to isolate the fundamental structures of all mathematics.
After he met Jean Dieudonne, one of the founders of the Bourbaki group, and studied 'The Architecture of Mathematics' as Aubin's notes, 'Piaget realized that the structures that he had been talking about could be equated with Bourbaki's mother structures' (p.
Unsurprisingly, the book itself has a formalist structure, resembling as much a work by the Bourbaki group as anything else.
Actually they were developed following the model of axiomatic mathematical theories proposed by the Bourbaki Group in Paris.
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.