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 ?
Influenced by the French structuralist group of mathematicians called Bourbaki, Piaget identifies three cognitive structures that characterize children's thinking as it develops: sensorimotor, concrete operational and formal.
Necronomicon Concordia, Volume III By Nicolaus Bourbaki (New York: Innsmouth, 2010, 666 pp.
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)
El reciente informe del Equipo Bourbaki sobre el costo humano de la guerra en Mexico apunta que el debilitamiento de los Estados-nacion hace que estos sean incapaces de responder a los grupos menos favorecidos y asi se "conforman territorios sin gobierno .
Es por ello, que es preferible ahorrarse los antecedentes y comenzar a hablar desde Newton y Leibinz (finales del siglo XVII y comienzos del XVIII) como los primeros en dar el gran paso al calculo infinitesimal (Babini, 1969; Duran, 2000; Kleiner, 2001), no sin antes destacar lo que Bourbaki (1976, p.
Siebenmann, L'invariance topologique du type simple d'homotopie, Seminaire Bourbaki, 25e anee, 1972/73, n[degrees] 428, 186-209, 1973.
Podemos decir que la topologia categorica se inicia con los trabajos de Bourbaki, y trabajos mas recientes se encuentran en J.
Bourbaki (1968) proposed to reconstruct the theories of mathematics dividing the structures of mathematics into three parts: main base sets, auxiliary base sets and typified sets.
En efecto, el calculo diferencial nos permitira "calcular" las variaciones perpetuas implicadas por la modulacion, cuyas caracteristicas son consideradas en terminos de "funcion": se trata de la derivada de la funcion que, segun la notacion de Leibniz tan elogiada por Bourbaki (39), se escribira: dy / dx.
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.
In the twentieth century, modernism becomes entrenched in algebra with the structuralist approaches of Emmy Noether and Bourbaki.