Pavel Sergeevich Alexandrov

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Pavel Sergeevich Alexandrov

Pavel Alexandrov ( Russian Павел Сергеевич Александров , English Alexandrov, German and Paul Alexandroff ; born April 25, jul. / 7. May  1896 greg. In Bogorodsk ; † 16th November 1982 in Moscow ) was a Soviet mathematician , mainly with Topology dealt with.


Alexandrow studied at the Lomonossow University in Moscow with Dmitri Jegorow (1869-1931) and Nikolai Lusin (1883-1950), the head of a great school of real analysis. In answer to a question from Lusin in 1915, Alexandrow determined the cardinality of Borel sets (with which he solved the continuum problem for these sets) and made significant contributions to the descriptive set theory developed in the Lusin school (introduction of Operation A, by Mikhail Jakowlewitsch Suslin after Alexandrov named). Soon afterwards, Alexandrov turned to the theater and was involved in artistic circles (after Andrei Kolmogorow, out of disappointment that he could not prove the continuum hypothesis in general (as Paul Cohen later found, it cannot be proven in principle from the Zermelo-Fraenkel axioms), on which Lusin had put him) and did not return to the university until 1920.

Together with his friend Pawel Urysohn (1898-1924), also a pioneer in topology, he was at the University of Göttingen in 1923/24 , where he studied or worked with Emmy Noether , David Hilbert and Richard Courant , among others . After his friend Urysohn's fatal swimming accident on the French Atlantic coast in 1924, he published his works. After receiving his doctorate in 1927, he was with Heinz Hopf , with whom he was already working closely in Göttingen, at Princeton University until 1928 . From 1929 he was a professor at the Lomonossow University in Moscow and at the Steklow Institute there .


Alexandrow initially worked in general topology and set theory, but is best known as a pioneer of algebraic topology, where he received important suggestions for an abstract group-theoretical treatment from Emmy Noether . With Heinz Hopf he wrote the book “Topologie” in 1935, one of the first textbooks on this field. The one-point compactification of a locally compact space is also called Alexandrov compactification of space after him .

In 1915 he proved: Every uncountable Borel set contains a non-empty perfect subset and is therefore of the strength of the continuum.

In 1936 Alexandrov was one of the group of young mathematicians who led a campaign against Lusin (Lusin affair), his former teacher (see article Nikolai Lusin ). When Lusin later voted against Alexandrov's admission to the Academy of Sciences, Alexandrov's friend and Academy member Kolmogorov slapped him, which led to a scandal in the Academy of Sciences that drew its circles as far as Stalin.

His students include Alexander Kurosch , Lev Pontryagin and Andrei Tichonow .


Alexandrov was a close friend of Andrei Kolmogorov , with whom he lived , from 1929 and until his death . Both bought a house near Moscow in 1935, where they also received many foreign mathematicians. According to Jean-Michel Kantor and Loren Graham , Alexandrow was homosexual and had a relationship with Pawel Urysohn even before his relationship with Kolmogorow . Both got to know each other better at a Beethoven concert in the Bolshoi Theater in 1921, on the eve of Alexandrow's wedding, whose marriage did not last long.

He definitely had a sense of humor, as the following memory from Kurt Reidemeister after his visit to the Euler celebration of the German Academy of Sciences in Berlin on March 21, 1957 shows:

“The second keynote speaker was the head of the delegation from the Academy of Sciences of the USSR, Professor Alexandroff from Moscow - who, by the way, spent several years in Göttingen as a young lecturer and thought of those carefree days with warmth in a personal conversation. In order to characterize Euler, Alexandroff took up the interplay of ability and understanding and explained this using a word joke from doctors about doctors. The surgeons, it is said, understand little, but can do a lot; internal medicine specialists understand a lot but can do little, and psychiatrists understand everything but can do nothing. In the sense of this three-way division, he then went on before the now thoroughly amused festive meeting, Euler was a surgeon. Euler was an expert, more precisely, an ingenious calculator both on the material of the numbers and on the material of the formulas. "

Honors and memberships

In 1928 he was elected a corresponding member of the Göttingen Academy of Sciences . Since 1946 he was a member of the American Philosophical Society and since 1947 of the National Academy of Sciences , in 1929 he became a corresponding and in 1953 a full member of the Soviet Academy of Sciences , in 1950 he became a corresponding member of the German Academy of Sciences in Berlin and in 1959 a member of the Leopoldina . In 1969 he received the Cothenius Medal of the Leopoldina. Alexandrov was president of the Moscow Mathematical Society from 1932 to 1964 . He was a member of the Austrian Academy of Sciences, the Polish Academy of Sciences, the Royal Netherlands Academy of Sciences and the London Mathematical Society.

Alexandrov received the Decoration of Honor of the Soviet Union (1940), the Stalin Prize (1943), the Order of the Red Banner of Labor (1945), the Order of Lenin (1946, 1954, 1961, 1966, 1969, 1975), the Order of the Hero of Socialist Labor ( 1969) and the Order of the October Revolution (1980).

In 1954 he gave a plenary lecture at the International Congress of Mathematicians in Amsterdam ( From the set theoretical topology of the last twenty years ).

In 2001 the asteroid (16810) Pavelaleksandrov was named after him.


  • Introduction to group theory . 11th edition. Harri Deutsch, 2001.
  • Textbook of set theory . 7th edition. Harri Deutsch, 2001.
  • Section Simplest Basic Concepts of Topology in David Hilbert, Stephan Cohn-Vossen: Descriptive Geometry . 2nd Edition. Springer Verlag, 1996.
  • Editor and co-author of the Encyclopedia of Elementary Mathematics , 4 vol., Deutscher Verlag der Wissenschaften, Berlin (East), 1977–1980
  • Editor and co-author; Hannelore Bernhardt , Walter Purkert (Red. Of the German edition): The Hilbert problems , Verlag Harri German in 1998, first in 1971 (Ostwald classics vol 252nd)
  • with Heinz Hopf Topologie , Vol. 1, Springer, 1935, new 1974


  • Günther Frei, Urs Stammbach: Pawel Sergejewitsch Alexandroff 1896–1982 , DMV Mitteilungen 1996, No. 3, p. 17

Web links

Sources and footnotes

  1. Yegorov was the victim of Stalin's terror in 1931 - he was arrested and died in exile a year later - Lusin was dismissed from his professorship in 1936 because of his international contacts and other allegations. A number of younger mathematicians, including Alexandrow and Sobolev, were actively involved in his disempowerment.
  2. Khimchenko (ed.): From the last interview of AN Kolmogorov , Mathematical Intelligencer, Volume 23, 2001, No. 1, p. 34. In the same interview, he confirmed the interviewer's question that he and Alexandrov had a difficult relationship too their teacher Lusin.
  3. A perfect set contains all of its accumulation points and each of its points is an accumulation point
  4. ^ Graham, Kantor, Naming Infinity, Harvard University Press 2009, p. 174
  5. Kurt Reidemeister. About Leonhard Euler . Mathematical-physical semester reports. Vol. 6, No. 1/2, p. 4, 1958, ZBL 0086.00401
  6. Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 25.
  7. ^ Members of the previous academies. Pavel Sergeevich Alexandrov. Berlin-Brandenburg Academy of Sciences and Humanities , accessed on February 14, 2015 .
  8. ^ Member entry of Pavel S. Aleksandrov at the German Academy of Natural Scientists Leopoldina , accessed on September 25, 2017.