Pavel Alexandrov


Pavel Sergeyevich Alexandrov, sometimes romanized Paul Alexandroff, was a Soviet mathematician. He wrote roughly three hundred papers, making important contributions to set theory and topology. In topology, the Alexandroff compactification and the Alexandrov topology are named after him.

Biography

Alexandrov attended Moscow State University where he was a student of Dmitri Egorov and Nikolai Luzin. Together with Pavel Urysohn, he visited the University of Göttingen in 1923 and 1924. After getting his Ph.D. in 1927, he continued to work at Moscow State University and also joined the Steklov Institute of Mathematics.
He was made a member of the Russian Academy of Sciences in 1953.

Personal life

Luzin challenged Alexandrov to determine if the continuum hypothesis is true. This problem, was too much for Alexandrov and he had a creative crisis at the end of 1917. The failure was a heavy blow for Alexandrov:
"It became clear to me that the work on the continuum problem ended in a serious disaster. I also felt that I could no longer move on to mathematics and, so to speak, to the next tasks, and that some decisive turning point must come in my life."
In 1964, the continuum hypothesis was proved to be independent from ZFC,
Alexandrov went to Chernihiv, where he participated in the organization of the drama theater:
"I met L. V. Sobinov there, who was at that time the head of the Department of Arts of the Ukrainian People's Commissariat of Education."
During this period, Alexandrov visited Denikin prison and was ill with typhus.
In 1955, he signed the "Letter of Three Hundred" with criticism of Lysenkoism.
He was buried at the Kavezinsky cemetery of the Pushkinsky district of the Moscow region.

Private life

In 1921, he married, who was a poet and memoirist, library worker and mathematician. However, they divorced only after a few days, since he was in fact gay, and declared:
"Any marriage would have been a mistake for me."
He then started a relationship with Pavel Urysohn, with whom he shared a passion for swimming. Unfortunately, Urysohn died when they swam together in the Atlantic Ocean, in Batz-sur-Mer, during their vacations in August 1924.
Later, he got together with Andrey Kolmogorov, and stayed with him for the rest of his life. Looking back at their relationship, he stated:
"In 1979 this friendship celebrated its fiftieth anniversary and over the whole of this half century there was not only never any breach in it, there was also never any quarrel, in all this time there was never any misunderstanding between us on any question, no matter how important for our lives and our philosophy; even when our opinions on one of these questions differed, we showed complete understanding and sympathy for the views of each other."

Scientific activity

Alexandrov's main works are on topology, set theory, theory of functions of a real variable, geometry, calculus of variations, mathematical logic, and foundations of mathematics.
He introduced the new concept of compactness. Together with P. S. Urysohn, Alexandrov showed the full meaning of this concept; in particular, he proved the first general metrization theorem and the famous compactification theorem of any locally compact Hausdorff space by adding a single point.
From 1923 P. S. Alexandrov began to study combinatorial topology, and he managed to combine this branch of topology with general topology and significantly advance the resulting theory, which became the basis for modern algebraic topology. It was he who introduced one of the basic concepts of algebraic topology — the concept of an exact sequence. Alexandrov also introduced the notion of a nerve of a covering, which led him to the discovery of Alexandrov-Cech Cohomology.
In 1924, Alexandrov proved that in every open cover of a separable metric space, a locally finite open cover can be inscribed.
He significantly advanced the theory of dimension and Introduction to Homological Dimension Theory.
The textbook Topologie I, written together with Heinz Hopf in German became the classic course of topology of its time.

The Luzin Affair

In 1936, Alexandrov was an active participant in the political offensive against his former mentor Luzin that is known as the Luzin affair.
Despite the fact that P. S. Alexandrov was a student of N. N. Luzin and one of the members of the, during the persecution of Luzin, Alexandrov was one of the most active persecutors of the scientist. Relations between Luzin and Alexandrov remained very strained until the end of Luzin's life, and Alexandrov became an academician only after Luzin's death.

Students

Among the students of P. S. Alexandrov, the most famous are Lev Pontryagin, Andrey Tychonoff and Aleksandr Kurosh. The older generation of his students includes L. A. Tumarkin, V. V. Nemytsky, A. N. Cherkasov, N. B. Vedenisov, G. S. Chogoshvili. The group of "Forties" includes Yu. M. Smirnov, K. A. Sitnikov, O. V. Lokutsievsky, E. F. Mishchenko, M. R. Shura-Bura. The generation of the fifties includes A.V. Arkhangelsky, B. A. Pasynkov, V. I. Ponomarev, as well as E. G. Sklyarenko and A. A. Maltsev, who were in graduate school under Yu.M. Smirnov and K. A. Sitnikov, respectively. The group of the youngest students is formed by V. V. Fedorchuk, V. I. Zaitsev and E. V. Shchepin.

Honours and awards

*