Nicolas Bourbaki is the collective allonym under which a group of mainly French 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. With the goal of founding all of mathematics on set theory, the group strove for utmost rigour and generality, creating some new terminology and concepts along the way. While Nicolas Bourbaki is an invented personage, the Bourbaki group is officially known as the Association des collaborateurs de Nicolas Bourbaki< ...

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• Nicolas Bourbaki - Books by Bourbaki
• Nicolas Bourbaki - Influence on mathematics in general
• Nicolas Bourbaki - The group
• Nicolas Bourbaki - The Bourbaki perspective and its limitations
• Nicolas Bourbaki - Dieudonné as speaker for Bourbaki
• Nicolas Bourbaki - The Bourbachique influence: education institutions trends

Read more here: » Nicolas Bourbaki: Encyclopedia - Nicolas Bourbaki

Aiming at a completely self-contained treatment of most of modern mathematics based on set theory, the group produced the following volumes (with the original French titles in brackets): I Set theory (Théorie des ensembles) II Algebra (Algèbre) III Topology (Topologie générale) IV Functions of one real variable (Fonctions d'une variable réelle) V Topological vector spaces (Espaces vectoriels topologiques ...

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Nicolas Bourbaki, Nicolas Bourbaki - Books by Bourbaki, Nicolas Bourbaki - Influence on mathematics in general, Nicolas Bourbaki - The group, Nicolas Bourbaki - The Bourbaki perspective and its limitations, Nicolas Bourbaki - Dieudonné as speaker for Bourbaki, Nicolas Bourbaki - The Bourbachique influence: education institutions trends

Read more here: » Nicolas Bourbaki: Encyclopedia II - Nicolas Bourbaki - Books by Bourbaki

Public discussion of, and justification for, Bourbaki's thoughts has in general been through Jean Dieudonné, who initially was the 'scribe' of the group, writing under his own name. In a survey of le choix bourbachique written in 1977, he didn't shy away from a hierarchical development of the 'important' mathematics of the time. He also wrote extensively under his own name: nine volumes on analysis, perhaps in belated fulfilment of the original project or pretext; and also on other topics mostly connected with algebraic geomet ...

See also:

Nicolas Bourbaki, Nicolas Bourbaki - Books by Bourbaki, Nicolas Bourbaki - Influence on mathematics in general, Nicolas Bourbaki - The group, Nicolas Bourbaki - The Bourbaki perspective and its limitations, Nicolas Bourbaki - Dieudonné as speaker for Bourbaki, Nicolas Bourbaki - The Bourbachique influence: education institutions trends

Read more here: » Nicolas Bourbaki: Encyclopedia II - Nicolas Bourbaki - Dieudonné as speaker for Bourbaki

Accounts of the early days vary, but original documents have now come to light. The founding members were all connected to the Ecole Normale Supérieure in Paris and included Henri Cartan, Claude Chevalley, Jean Coulomb, Jean Delsarte, Jean Dieudonné, Charles Ehresmann, René de Possel, Szolem Mandelbrojt and André Weil. There was a preliminary meeting, towards the end of 1934 (the minutes are in the Bourbaki archives — for a full description of the initial meeting consult Liliane Beaulieu in the Mathematical Intelligencer). Jean ...

See also:

Nicolas Bourbaki, Nicolas Bourbaki - Books by Bourbaki, Nicolas Bourbaki - Influence on mathematics in general, Nicolas Bourbaki - The group, Nicolas Bourbaki - The Bourbaki perspective and its limitations, Nicolas Bourbaki - Dieudonné as speaker for Bourbaki, Nicolas Bourbaki - The Bourbachique influence: education institutions trends

Read more here: » Nicolas Bourbaki: Encyclopedia II - Nicolas Bourbaki - The group

The emphasis on rigour may be seen as a reaction to the work of Jules-Henri Poincaré, who stressed the importance of free-flowing mathematical intuition, at a cost in completeness in presentation. The impact of Bourbaki's work initially was great on many active research mathematicians world-wide. It provoked some hostility, too, mostly on the side of classical analysts; they approved of rigour but not of high abstraction. Around 1950, also, some parts of geometry were still not fully axiomatic — in less prominent developments, one ...

See also:

Nicolas Bourbaki, Nicolas Bourbaki - Books by Bourbaki, Nicolas Bourbaki - Influence on mathematics in general, Nicolas Bourbaki - The group, Nicolas Bourbaki - The Bourbaki perspective and its limitations, Nicolas Bourbaki - Dieudonné as speaker for Bourbaki, Nicolas Bourbaki - The Bourbachique influence: education institutions trends

Read more here: » Nicolas Bourbaki: Encyclopedia II - Nicolas Bourbaki - Influence on mathematics in general

The underlying drive, in Weil and Chevalley at least, was the perceived need for French mathematics to absorb the best ideas of the Göttingen school and the German algebraists. It is fairly clear that the Bourbaki point of view, while encyclopedic, was never intended as neutral. Quite the opposite, really: more a question of trying to make a consistent whole out of some enthusiasms, for example for Hilbert's legacy, with emphasis on formalism and axiomatics. But always through a transforming process ...

See also:

Nicolas Bourbaki, Nicolas Bourbaki - Books by Bourbaki, Nicolas Bourbaki - Influence on mathematics in general, Nicolas Bourbaki - The group, Nicolas Bourbaki - The Bourbaki perspective and its limitations, Nicolas Bourbaki - Dieudonné as speaker for Bourbaki, Nicolas Bourbaki - The Bourbachique influence: education institutions trends

Read more here: » Nicolas Bourbaki: Encyclopedia II - Nicolas Bourbaki - The Bourbaki perspective and its limitations