Cartan - Élie Cartan

French mathematician. Born in Dolomieu, a small village in the Isère department, he graduated from elementary school in his hometown, became a scholarship student at Bienne Middle School, and then went on to a school equivalent to a high school in Japan, before entering the École Normale Supérieure (Higher Normal School) at the age of 19. He graduated from the school in 1891, passed the agrégé (professional qualification exam), and began his research career. In 1894, he obtained his doctorate with his thesis "On the structure of finite-dimensional continuous transformation groups," which is a major contribution to the theory of continuous transformation groups and contains content that is still discussed by young mathematicians today. After serving as a lecturer at the universities of Montpellier and Lyon and a professor at the University of Nancy, he became a professor at the University of Paris in 1912. He made many achievements in the theory of continuous groups, integral invariants, the theory of Pfaff forms, the geometry of connections, topology, and the theory of relativity, using the so-called moving coordinate system method. His eldest son, Henri (1904-2008), was a mathematician and professor at the University of Paris. His second son, Jean (1906-1932), was a composer, and his third son, Louis (1909-1943), was a theoretical physicist, but both died young.

[Kentaro Yano]

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

フランスの数学者。イゼール県の寒村ドロミューに生まれ、生地の小学校を卒業後、ビエンヌ中学校の給費生となり、さらに日本の高等学校に相当する学校を経て、19歳でエコール・ノルマル・シュペリュール（高等師範学校）に入学した。1891年同校を卒業すると同時にアグレジェ（教授資格試験）に合格し、研究生活に入った。1894年、学位論文「有限次元連続変換群の構造について」で学位を取得したが、この論文は連続変換群論への大きな貢献で、今日でも若い数学者たちが話題にする内容を含んでいる。モンペリエおよびリヨンの大学の講師、ナンシー大学教授を経て、1912年パリ大学教授に就任。いわゆる動座標系の方法を用いて、連続群論、積分不変式論、ファッフ形式論、接続の幾何学、位相幾何学、相対性理論などに多くの業績を残した。長男アンリHenri（1904―2008）は数学者でパリ大学教授となった。次男ジャンJean（1906―1932）は作曲家、三男ルイLouis（1909―1943）は理論物理学者であったが、二人とも夭折(ようせつ)した。

［矢野健太郎］

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