Born in Bogorodsk, his name is also spelled Pavel Sergeyevich Aleksándrov or Alexandroff is a mathematician who made important contributions to topology.
Pavel Sergeevich Aleksandrov's father Aleksandr Aleksandrovich Aleksandrov was a medical graduate from Moscow University who had decided not to follow an academic career but instead had chosen to use his skills in helping people and so he worked as a general practitioner in Yaroslavskii. Later he worked in more senior positions in a hospital in Bogorodsk.
He excelled at the grammar school in Smolensk which he attended and his mathematics teacher soon realised that his pupil had a remarkable talent for the subject. In 1913 Aleksandrov graduated from the grammar school being dux of the school and winning the gold medal. Certainly at this time he had already decided on a career in mathematics, but he had not set his sights as high as a university teacher, rather he was aiming to become a secondary school teacher of mathematics.
Aleksandrov entered Moscow University in 1913 and immediately he was helped by Stepanov. Stepanov, who was working at Moscow University, was seven years older than Aleksandrov but his home was also in Smolensk and he often visited the Aleksandrov home there. Stepanov was an important influence on Aleksandrov at this time.
Aleksandrov proved his first important result in 1915, namely that every non-denumerable Borel set contains a perfect subset. It was not only the result which was important for set theory, but also the methods which Aleksandrov used which turned out to be one of the most useful methods in descriptive set theory.
Aleksandrov went to Novgorod-Severskii and became a theatre producer. He then went to Chernikov where, in addition to theatrical work, he lectured on Russian and foreign languages, becoming friends with poets, artists and musicians. After a short term in jail in 1919 at the time of the Russian revolution, Aleksandrov returned to Moscow in 1920.
Luzin and Egorov had built up an impressive research group at the University of Moscow which the students called 'Luzitania' and they, together with Privalov and Stepanov, were very welcoming to Aleksandrov on his return. At around this time Aleksandrov became friendly with Urysohn, who was a member of 'Luzitania', and the friendship would soon develop into a major mathematical collaboration.
In 1921, Aleksandrov was appointed as a lecturer at Moscow university. In July 1922 Aleksandrov and Urysohn went to spend the summer at Bolshev, near to Moscow, where they began to study concepts in topology.
In the summers of 1923 and 1924 Aleksandrov and Urysohn visited Göttingen, where the mathematicians were particularly impressed with their results on when a topological space is metrisable. Every day Aleksandrov and Urysohn swam across the Rhine - a feat that was far from being safe.
Aleksandrov and Urysohn then visited Brouwer in Holland and Paris in August 1924 before having a holiday in the fishing village of Bourg de Batz in Brittany. On August 17, Urysohn tragically he drowned while swimming in the Atlantic later that day. Aleksandrov determined that no ideas of his great friend and collaborator should be lost and he spent part of 1925 and 1926 in Holland working with Brouwer on preparing Urysohn's paper for publication.
The atmosphere in Göttingen had proved very helpful to Aleksandrov, particularly after the death of Urysohn, and he went there every summer from 1925 until 1932. He became close friends with Hopf and the two held a topological seminar in Göttingen. Of course Aleksandrov also taught in Moscow University and from 1924 he organised a topology seminar there.
From 1926 Aleksandrov and Hopf were close friends working together. They spent some time in 1926 in the south of France with Neugebauer. Then Aleksandrov and Hopf spent the academic year 1927-28 at Princeton in the United States. During their year in Princeton, Aleksandrov and Hopf planned a joint multi-volume work on Topology the first volume of which did not appear until 1935.
This was the only one of the three intended volumes to appear since World War II prevented further collaboration on the remaining two volumes. In fact before the joint work with Hopf appeared in print, Aleksandrov had begun yet another important friendship and collaboration.
In 1929 Aleksandrov's friendship with Kolmogorov began and they journeyed a lot along the Volga, the Dnieper, and other rivers, and in the Caucuses, the Crimea, and the south of France. The year 1929 marks also the appointment of Aleksandrov as Professor of Mathematics at Moscow University.
In 1935 Aleksandrov went to Yalta with Kolmogorov, then finished the work on his Topology book in the nearby Crimea and the book was published in that year. Aleksandrov and Kolmogorov bought a house in Komarovka, a small village outside Moscow. Kolmogorov in 1982 said:
"for me these 53 years of close and indissoluble friendship were the reason why all my life was on the whole full of happiness, and the basis of that happiness was the unceasing thoughtfulness on the part of Aleksandrov.''
They a remarkable example of a couple of almost openly gay mathematicians who lived together in the recent past in the Soviet Union to the extent it was possible in the society where being gay was a criminal offense, and people convicted of it often never came back.
Aleksandrov wrote about 300 scientific works in his long career. In 1954 he organised a seminar aimed at first year students at Moscow University and in this he showed one of the aspects of his career which was of major importance to him, namely the education of students.
Many honours were given to Aleksandrov for his outstanding contribution to mathematics. He was president of the Moscow Mathematical Society from 1932 to 64, vice president of the International Congress of Mathematicians from 1958 to 62, a corresponding member of the USSR Academy of Sciences from 1929 and a full member from 1953.
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