Pavel Alexandrov(1896 — 1982)
Pavel Aleksandrov
Union soviétique, Empire russe
6 min read
Russian and later Soviet mathematician, one of the founders of modern topology. A professor at Moscow University, he left a deep mark on the Soviet school of mathematics in the 20th century.
Frequently asked questions
Key Facts
- Born in 1896 in Bogorodsk (Russia), died in 1982 in Moscow
- Co-founder of general topology and algebraic topology in the 1920s and 1930s
- Introduced the notion of Aleksandrov compactification (one-point compactification)
- Professor at Moscow State University, where he trained many mathematicians
- Co-author with Heinz Hopf of a landmark topology treatise (1935)
Works & Achievements
A method that adds a single point “at infinity” to make a space compact; a fundamental tool still taught today.
Together with Urysohn, he identified and popularized the concept of a “compact” space in its current sense, central to all of general topology.
Decisive contributions to the rigorous definition of the dimension of topological spaces, continued after Urysohn's death.
A monumental treatise that gave structure to combinatorial topology and served as an international reference for decades.
Development of algebraic methods (homology groups, complexes) to study shapes, founding modern algebraic topology.
An educational textbook drawn from his Moscow lectures, which trained generations of Soviet students.
Through his seminar and his teaching, he made Moscow a world center of topology and trained many leading mathematicians.
Anecdotes
As a student, Pavel Alexandrov formed a deep friendship with Pavel Urysohn: the two young mathematicians worked together day and night and laid the foundations of modern topology. In 1924, during a holiday in Brittany, Urysohn drowned while swimming in the ocean before Alexandrov's eyes, an event that marked him for the rest of his life and led him to publish his friend's unfinished work himself.
We owe to Alexandrov the modern mathematical meaning of the word “compact.” He also invented a clever technique, the “one-point compactification” (known as the Alexandroff compactification), which makes it possible to add a single point “at infinity” to a space in order to make it easier to study.
Alexandrov formed a famous duo with Andrei Kolmogorov, one of the greatest mathematicians of the 20th century. The two men were friends and companions for more than fifty years, shared a country house at Komarovka, and organized swims and hikes with their students to blend scientific life with everyday life.
During the 1920s, he made long stays in Göttingen, then the world capital of mathematics, where he rubbed shoulders with David Hilbert, Emmy Noether, and above all Heinz Hopf. With the latter he wrote in 1935 a treatise on topology that remained a classic for decades.
For nearly thirty years (1932-1964), Alexandrov presided over the Moscow Mathematical Society. A passionate teacher, he liked to say that a good professor must convey not only results but also the excitement of discovery, and he trained generations of Soviet topologists.
Primary Sources
First volume of the great joint treatise by Alexandrov and Hopf, which systematized combinatorial topology and set the discipline's vocabulary for decades.
Article in which Alexandrov develops the study of locally compact spaces and the procedure of adjoining a point at infinity (Alexandroff compactification).
Memoirs in which Alexandrov recounts his Moscow education, his friendship with Urysohn, and his stays in Göttingen with Hilbert and Noether.
Teaching textbook drawn from his courses at Moscow University, long used to introduce students to topology.
Key Places
Town in the Russian Empire where Pavel Alexandrov was born in 1896, east of Moscow.
The heart of his entire career: here he studied under Luzin, then taught and built the Soviet topological school.
The world capital of mathematics, where Alexandrov stayed during the 1920s, mingling with Hilbert, Emmy Noether and Heinz Hopf.
The place where his friend Pavel Urysohn drowned in 1924 during their research holiday, an event that deeply shook Alexandrov.
A country house near Moscow that Alexandrov shared with Andrei Kolmogorov, a place of work, swimming and walks with their students.
The city where Alexandrov spent most of his life, presided over the Mathematical Society and died in 1982.
