**Pavel Aleksandrov** was a Russian mathematician who made important contributions to general topology.

- The most common way, other than Aleksandrov, is to write it as Alexandroff.
- Later he worked in more senior positions in a hospital in Bogorodskii, which is where he was when Pavel Sergeevich was born.
- It was from her that Aleksandrov learnt French and also German.
- In 1913 Aleksandrov graduated from the grammar school being dux of the school and winning the gold medal.
- Eiges was the role model whom he was aspiring to match at this stage, for Eiges had done more than teach Aleksandrov mathematics, he had also influenced his tastes in literature and the arts.
- 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 and suggested that Aleksandrov join Egorov's seminar even in the first year of his studies in Moscow.
- In Aleksandrov's second year of study he came in contact with Luzin who had just returned to Moscow.
- 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.
- After Aleksandrov's great successes Luzin did what many a supervisor might do, he realised that he had one of the greatest mathematical talents in Aleksandrov so he thought that it was worth asking him to try to solve the biggest open problem in set theory, namely the continuum hypothesis.
- After Aleksandrov failed to solve the continuum hypothesis (which is not surprising since it can neither be proved or disproved as was shown by Cohen in the 1960s) he thought he was not capable of a mathematical career.
- Aleksandrov went to Novgorod-Severskii and became a theatre producer.
- 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.
- It was not an immediate return to Moscow for Aleksandrov, however, for he spent 1920-21 back home in Smolensk where he taught at the University.
- 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.
- After taking his examinations in 1921, Aleksandrov was appointed as a lecturer at Moscow university and lectured on a variety of topics including functions of a real variable, topology and Galois theory.
- In July 1922 Aleksandrov and Urysohn went to spend the summer at Bolshev, near to Moscow, where they began to study concepts in topology.
- Aleksandrov and Urysohn now began to push the theory forward with work on countably compact spaces producing results of fundamental importance.
- In the summers of 1923 and 1924 Aleksandrov and Urysohn visited Göttingen and impressed Emmy Noether, Courant and Hilbert with their results.
- 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.
- 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.
- Of course Aleksandrov also taught in Moscow University and from 1924 he organised a topology seminar there.
- At Göttingen, Aleksandrov also lectured and participated in Emmy Noether's seminar.
- Aleksandrov always included Emmy Noether and Hilbert among his teachers, as well as Brouwer in Amsterdam and Luzin and Egorov in Moscow.
- From 1926 Aleksandrov and Hopf were close friends working together.
- Then Aleksandrov and Hopf spent the academic year 1927-28 at Princeton in the United States.
- This was an important year in the development of topology with Aleksandrov and Hopf in Princeton and able to collaborate with Lefschetz, Veblen and Alexander.
- 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.
- Before the joint work with Hopf appeared in print, Aleksandrov had begun yet another important friendship and collaboration.
- The year 1929 marks not only the beginning of the friendship with Kolmogorov but 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.
- Here is the house owned since 1935 by Aleksandrov and Kolmogorov.
- In 1938-1939 a number of leading mathematicians from the Moscow University, among them Aleksandrov, joined the Steklov Mathematical Institute of the USSR Academy of Sciences but at the same time they kept their positions at the University.
- Aleksandrov wrote about 300 scientific works in his long career.
- Many honours were given to Aleksandrov for his outstanding contribution to mathematics.
- Many other societies elected Aleksandrov to membership including the Göttingen Academy of Sciences, the Austrian Academy of Sciences, the Leopoldina Academy in Halle, the Polish Academy of Sciences, the National Academy of Sciences of the United States, the London Mathematical Society, the American Philosophical Society, and the Dutch Mathematical Society.
- After Aleksandrov's death in November 1982, his colleagues from the Department of Higher Geometry and Topology, in which he had held the chair, sent a letter to Moscow University's rector A A Logunov proposing that one of Aleksandrov's former students should become Head of the Department, to preserve Aleksandrov's scientific school.
- Also in memory of Aleksandrov's contributions to topology at Moscow University and his work with the Moscow Mathematical Society, there is an annual topological symposium Aleksandrov Proceedings held every May.

Born 7 May 1896, Bogorodsk (also called Noginsk), Russia. Died 16 November 1982, Moscow, USSR.

View full biography at MacTutor

Origin Russia, Topology

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive