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Nicolas Bourbaki - Influence on mathematics in general |  | Nicolas Bourbaki - Influence on mathematics in general: Encyclopedia II - Nicolas Bourbaki - Influence on mathematics in general |  | 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 |  | | Nicolas Bourbaki, Nicolas Bourbaki - Books by Bourbaki, Nicolas Bourbaki - Dieudonné as speaker for Bourbaki, Nicolas Bourbaki - Influence on mathematics in general, Nicolas Bourbaki - The Bourbachique influence: education institutions trends, Nicolas Bourbaki - The Bourbaki perspective and its limitations, Nicolas Bourbaki - The group |  | |
|  |  | Nicolas Bourbaki: Encyclopedia II - Nicolas Bourbaki - Influence on mathematics in general
Nicolas Bourbaki - Influence on mathematics in general
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 way or another, these were brought into line with the new foundational standards, or quietly dropped. This undoubtedly led to a gulf with the way theoretical physics is practised.
Bourbaki's influence has decreased over time. This is partly because some of the abstractions did not prove as useful as initially thought, and partly because other concepts which are now important, such as the detailed machinery of category theory, are not covered. Algebraic structure can reasonably be defined, in Bourbakiste terms; but mathematical structure is not an idea exhausted by infinitary algebraic structures, as might appear from the books.
The Bourbaki seminar series founded in post-WWII Paris continues. It is an important source of survey articles, written in a prescribed, careful style.
Other related archives1935, 1977, 20th-century, Alan Baker, Alexander Grothendieck, Algebra, Algebraic structure, André Weil, Bonn Arbeitstagung, Bourbaki seminar, Charles Denis Bourbaki, Charles Denis Sauter Bourbaki, Charles Ehresmann, Claude Chevalley, Commutative algebra, Ecole Normale Supérieure, Euclid, Fields Medal, Franco-Prussian War, French, Functions of one real variable, Greek mathematics, Göttingen, Henri Cartan, Hilbert, Integration, Jacques Hadamard, Jean Delsarte, Jean Dieudonné, Jean Leray, Jean-Pierre Serre, Jules-Henri Poincaré, Laurent Schwartz, Lie algebras, Lie groups, Mathematical Intelligencer, Pal Turán, Paris, Paul Dubreil, Radon measures, René de Possel, Riemann, Roger Godement, Samuel Eilenberg, Serge Lang, Set theory, Szolem Mandelbrojt, Topological vector spaces, Topology, Zorn's lemma, abstract algebra, algebraic geometry, algorithmic, allonym, analysis, applications, as of 2005, bijective, blackboard bold, category theory, classical analysts, combinatorial, commutative algebra, complex multiplication, elimination theory, empty set, fascicle, geometry, ideal theory, infinitary, injective, logic, manifolds, mathematical analysis, mathematical structure, mathematicians, mathematics, measure theory, multilinear algebra, number theory, numbers, problem solving, rigour, salon, set theory, soft analysis, spectral theory, surjective, synthetic geometry, tensor calculus, theoretical physics, twentieth century, École Normale Supérieure
 Adapted from the Wikipedia article "Influence on mathematics in general", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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