Pavel Sergeyevich Alexandrov (Russian: Па́вел Серге́евич Алекса́ндров), sometimes romanized Paul Alexandroff (7 May 1896 – 16 November 1982), was a Soviet mathematician.

He wrote roughly three hundred papers, making important contributions to set theory and topology.

Alexandrov attended Moscow State University where he was a student of Dmitri Egorov and Nikolai Luzin.

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."

"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."

[3] Alexandrov made lifelong friends with Andrey Kolmogorov, about whom he said: "In 1979 this friendship [with Kolmogorov] 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.

[12] Alexandrov also introduced the notion of a nerve of a covering, which led him (independently of E. Cech) to the discovery of Alexandrov-Cech Cohomology.

Among the students of P. S. Alexandrov, the most famous are Lev Pontryagin, Andrey Tychonoff and Aleksandr Kurosh.