Nicolas Bourbaki

Japanese: ブールバキ（英語表記）Bourbaki， Nicolas

A pseudonym for a group of about a dozen mathematicians, mostly from France. In the early 1930s, he planned to reconstruct all mathematics up to the present day, and published the unfinished large-scale work Elements of Mathematics. The first volume of Elements of Mathematics was published in 1939, and it has already reached over 30 volumes. The contents are as follows: 3 volumes and a summary on "Set Theory", 7 volumes on "Algebra", 5 volumes and a summary on "Topology", 2 volumes on "Real Functions of One Variable", 2 volumes and a summary on "Topological Linear Spaces", 5 volumes on "Integration", a summary on "Manifolds", 2 volumes on "Lie Groups and Lie Algebras", 4 volumes on "Commutative Algebra", and 1 volume on "Spectral Theory". Bourbaki's distinctive feature is that he attempts to reconstruct modern mathematics based on the concept of structure, without being bound by the traditional mathematical systems of algebra, analysis, and geometry. A "mathematical structure" is determined by adding axioms to a set, and different structures, such as algebraic structure and topological structure, arise depending on the axioms. It is certain that Bourbaki's members included H. Cartan, J. Joudonnet, A. Weille, and others, but this has since changed and the group now includes two or three mathematicians who are not French.

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

十数人の，主としてフランスの数学者の集団のペンネーム。 1930年代の初め，現代までの全数学の再構築を企画し，未完の大著『数学原論』を出版。『数学原論』は 39年に第1冊を出し，すでに三十数冊に及んでいる。その内容は次のとおり。「集合論」3冊と要約，「代数」7冊，「位相」5冊と要約，「実1変数関数」2冊，「位相線形空間」2冊と要約，「積分」5冊，「多様体」要約，「リー群とリー環」2冊，「可換代数」4冊，「スペクトル論」1冊。ブールバキの特徴は，代数，解析，幾何という従来の数学の系統にとらわれずに，構造の概念に基づいて現代数学を再構成しようとしている点にある。「数学的構造」とは，集合に対し公理を付加することによって決るもので，公理の違いによって，代数構造，位相構造など，構造の違いが生じる。ブールバキの構成員は，H.カルタン，J.ジュドンネ，A.ベイユなどが含まれていたことは確かであるが，その後変っており，フランス人以外の数学者も二，三人含まれている。

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