Pavel Sergeevich Aleksandrov

One of the leading mathematicians in the former Soviet Union. Famous for Topology I (1935), co-authored with Swiss Heinz Hopf (1894-1971). Born in Bogorodsk (now Noginsk) as the son of a doctor, he was well-educated in music and other subjects, and enjoyed swimming. He was inspired by Lobachevsky's geometry at the age of 13, and was even more inspired by Cantor's Theory of Transfinite Sets at the age of 17 when he entered Moscow University. At the age of 19, he made his debut in the mathematical world by solving the problem on the cardinality of Borel sets, which made him famous overnight. During the three years from the age of 25, during which he worked closely with Ulysson, he conducted basic research on topological spaces, and later conducted many other fundamental studies on general topology, dimension theory, and other subjects. He had many acquaintances, was close to Hilbert, and was close to the Dutchman Luitzen Egbertus Jan Brouwer (1881-1966) and the German Noether, and was especially close to his compatriot Kolmogorov. He also trained many young mathematicians.

He said that the relationship between teacher and student is lifelong, like that between a parent and child, but that sometimes conflicts can become serious, and gave as examples the conflict between himself and his university teacher N. N. Luzin (1883-1950) and the conflict between Blauer and Hilbert. His autobiography, Pages from an autobiography , will be a valuable resource not only for mathematicians but also for psychologists.

[Hidetaka Terasaka]

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

旧ソ連有数の数学者。スイスのホップHeinz Hopf（1894―1971）との共著『位相幾何学Ⅰ』Topologie Ⅰ（1935）で有名。医師の子としてボゴローツク（現、ノギーンスク）に生まれ、音楽その他教養が広く、水泳を好んだ。13歳のときロバチェフスキーの幾何を知って感激し、モスクワ大学に入学した17歳のとき、カントルの『超限集合論』を読んでさらに感動し、19歳のとき早くもボレル集合の濃度の問題解決で数学界にデビュー、一躍名をあげた。25歳からの3年間、ウリソーンと親密な行動をともにした期間に位相空間の基礎的研究をし、のちに一般位相幾何、次元論など多くの基礎的研究を行った。多くの知己をもち、ヒルベルトにも近づき、オランダのブラウアーLuitzen Egbertus Jan Brouwer（1881―1966）、ドイツのネーターと親しく、同国人ではとくにコルモゴロフが親しかった。若い数学者も多く養成している。

　彼は、師弟関係は親子と同じ終生的なものだが、ときに相克が深刻になる場合があるといい、彼自身と大学時代の師ルージンН．Н．Лузин（1883―1950）との相克、ブラウアーとヒルベルトとの相克を例としてあげている。その自伝Pages from an autobiographyは、数学者のみならず、心理学者にとっても貴重な資料であろう。

［寺阪英孝］

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