# Andrei Nikolajewitsch Kolmogorow

Andrei Nikolajewitsch Kolmogorow

Andrey Kolmogorov ( Russian Андрей Николаевич Колмогоров pronunciation ? / I , scientific transliteration Andrei Nikolaevich Kolmogorov ; born 12 jul. / 25. April 1903 greg. In Tambov , † 20th October 1987 in Moscow ) was a Soviet mathematician and one of the most important 20th century mathematician . Kolmogorow made significant contributions in the fields of probability theory and topology , he is considered the founder of the algorithmic complexity theory . His most famous mathematical achievement was the axiomatization of probability theory .

As a doctoral student, he also worked and published on logic and Fourier series , later on the application of probability theory in turbulence and classical mechanics .

## life and work

Kolmogorov's mother died in his birth on April 25 in Tambov. She was on the way from the Crimea to Tunoschna near Yaroslavl , where her father Jakow Stepanowitsch Kolmogorow lived (he came from the nobility and was a large landowner until the revolution). His father Nikolai Katajew was the son of a priest and farmer. (After the revolution he returned from exile and held a post at the Ministry of Agriculture. In 1919 he fell in the civil war .) The parents were not married and his father did not care for the son, so he was taken care of by his mother's sister, Wera Jakowlewna Kolmogorowa, who was raised in Tunoshna. She and her sisters organized a small school, which Kolmogorov also attended, based on the educational ideas that were progressive at the time. After moving to Moscow in 1910 and attending a private high school (organized by Yevgenia Repman and Vera Fedorova) that was public after the revolution, he graduated from school in 1920, worked for a while as a conductor on the railroad and from 1920 attended Moscow University and parallel in addition the Mendeleev Institute for Chemistry and Technology . In addition to mathematics, he studied Russian history (with SW Bachruschin , where he dealt with cadastres of landowners in Novgorod of the 15th and 16th centuries) and metallurgy . In 1921 Nikolai N. Lusin accepted him as a student.

In 1922 Kolmogorow published the first results in descriptive set theory , in 1923 a work in Fourieranalysis , which made him internationally known (see below), and he published eight papers on integration theory , Fourier analysis and, for the first time from 1925 on, probability theory . After graduating in 1925, he began his ( “small” ) doctorate with Lusin, which he completed in 1929.

In 1923 he constructed an integrable function whose Fourier series diverges almost everywhere (and in 1926 one whose Fourier series does not converge anywhere), contrary to the assumptions of his teacher Lusin, who suspected the point-wise convergence of the Fourier series. These results made Kolmogorov internationally known. For square-integrable functions (class ) it was also long assumed that counterexamples would be found until Lennart Carleson proved Lusin's conjecture for this class in 1966. ${\ displaystyle L ^ {1}}$${\ displaystyle L ^ {2}}$

1925 (and again in 1932), he also dealt with the intuitionistic logic of Brouwer , he sought to formalize.

While traveling to the Volga and the Caucasus , he made a lifelong friendship with Pawel Alexandrow , with whom he undertook study trips to Göttingen, Munich and Paris in 1930/31. In 1931 he was appointed full professor at Moscow University. Kolmogorov later lived with Alexandrov in a dacha , which both bought in Komarowka near Moscow in 1935 and where they received many famous mathematicians and regularly worked with their students. They went on vacation and to conferences together. When Lusin refused Alexandrov's admission to the Academy of Sciences in 1946, there was a scandal when Kolmogorov publicly slapped his former teacher Lusin, which reached as far as Stalin. Kolmogorov had already quarreled with Lusin when Kolmogorov was one of the young mathematicians with Alexandrow and others who campaigned against Lusin in 1936 (Lusin affair, see article Nikolai Lusin ). The friendship with Alexandrov was also described as homosexual, which was, however, a punishable offense in the former Soviet Union and was therefore not expressed publicly. According to Robert MacPherson , however, it was an open secret and the slap Kolmogorov gave Lusin when his friend Alexandrov was not elected to the Academy of Sciences was a reaction to an allusion to Luzin because of their homosexuality. When Alexandrov died, Kolmogorov recognized this friendship as the source of his happiness for 53 years. Kolmogorow spent four days a week at his dacha, where he also regularly did sports (rowing and swimming in the river, cross-country skiing in winter and hiking up to 50 km). Kolmogorow was a passionate mountaineer.

From June 1930 to March 1931 he was abroad in Göttingen, Paris and Munich. In 1931 he became a professor at Moscow University (renamed Lomonosov University in 1940 ) and was there director of the Institute of Mathematics and Mechanics from 1933 to 1939.

First edition of his book Basic Concepts of Probability Theory , 1933

In 1933 Kolmogorov's textbook Basic Concepts of Probability Theory was published in German by Springer-Verlag in Heidelberg , in which he presented his axiomatization of probability theory.

In 1934 Kolmogorow published his work on cohomology and achieved a doctorate in mathematics and physics through the "great" doctorate. He presented the concept of cohomology at the 1935 International Topology Conference in Moscow. Independently of Kolmogorow, James W. Alexander introduced the concept of cohomology in the 1930s . In 1939 he became a full member of the Russian Academy of Sciences (and secretary of its mathematical-physical department) and received the chair of probability theory at Lomonosov University, which he held until 1966. He also became head of the probability theory department at the Steklow Institute , which he remained until 1958. In 1942 he married his school friend Anna Dmitrijewna Jegorowa.

Kolmogorov before one of his speeches at a conference in Tallinn
Kolmogorov gives his lecture on the blackboard. Right Akiwa Jaglom

He took an interest in turbulence in the late 1930s and became the director of the Atmospheric Turbulence Laboratory at the Institute of Geophysics of the Academy of Sciences, where he worked until 1949. In 1941 he published two important articles on the homogeneous turbulence of liquids. During the Second World War he was temporarily evacuated to Kazan with the university and did important scientific work on the war effort (ballistics, statistical theory of quality control). In contrast to other high-ranking Soviet mathematicians, however, he managed to escape involvement in military research after the war.

In 1953/54 he described the KAM theory of dynamic systems , announced at the ICM 1954 in Amsterdam , where Kolmogorov gave a plenary lecture ( general theory of dynamic systems and classical mechanics ) and further developed by Kolmogorov's student Vladimir Arnold . In 1957 he solved a generalization of Hilbert's 13th problem already mentioned by Hilbert .

1951 to 1953 he was again director of the Institute of Mathematics and Mechanics, and 1954 to 1956 and from 1978 he was dean of the mathematical section of the Mekmat Faculty (mathematics and mechanics) at Lomonosov University. In 1954 he was visiting professor for two months at the Humboldt University in Berlin and in the spring of 1958 visiting professor in Paris. In 1960 he founded the Laboratory for Probability Theory and Statistics at Lomonosov University, was its advisor and its director from 1966 to 1976. In 1970 and 1971/72 he spent four months on the research vessel Dmitri Mendeleev . 1970 to 1980 he held the newly established chair for mathematical statistics at Lomonossow University and from 1980 the chair for mathematical logic.

In the 1950s, Kolmogorov defended cybernetics , which was flourishing in the Soviet Union at the time, against attacks from the official side, and he defended classical genetics against attacks by Lysenkoism (for example in an article from 1940 in the Doklady Akad. Nauka). However, he and Alexandrov signed public condemnations of the opponents of Lysenko and later those of Alexander Solzhenitsyn in a letter in Pravda. Loren Graham and Jean-Michel Kantor see it as a consequence of their blackmail because of their homosexual relationship. Kolmogorov said at the end of his life that he had lived in constant fear of the secret service all his life. According to Graham and Kantor, the behavior in the Lusin affair is partly due to this blackmail, although personal motives also played a role here. Kolmogorov himself was never a member of the Communist Party.

He wrote around 500 scientific articles.

Most recently, he dealt with a new justification of the calculus of probability with his algorithmic complexity theory. Most recently he contracted Parkinson's disease and went blind. Many of his former students took care of him in his final years. In the last two years of his life he could neither see nor speak.

## Honors and memberships

In 1959 he was elected a member of the Leopoldina and the American Academy of Arts and Sciences . In 1962 he received the Balzan Prize for Mathematics and in 1980 the Wolf Prize . In 1964 he became a member of the Royal Society of London, in 1968 a member of the French Academy of Sciences and he was a member of the National Academy of Sciences (1967), the American Philosophical Society (1961) and the Romanian (1956), Hungarian, Polish and Dutch academies of Sciences (1963). He was honorary doctor in Paris ( Sorbonne ) 1955, Stockholm, Warsaw and Budapest, honorary member of the Royal Statistical Society and the Indian Statistical Institute and the London Mathematical Society (1959). In 1965 he and his student Vladimir Arnold received the Lenin Prize for work on classical mechanics , in 1941 he received the Stalin Prize and the State Prize of the USSR (with Alexander Jakowlewitsch Chintschin for work on probability theory), in 1949 with Boris Gnedenko the Chebyshev Prize and in 1987 the Lobachevsky Prize . He received the Order of Lenin several times and was a hero of socialist work . In 1953 he became an honorary member of the Moscow Mathematical Society and from 1964 to 1973 he was its president.

He attended the International Congress of Mathematicians in Amsterdam in 1954, where he gave his influential plenary lecture on celestial mechanics, which was also the final lecture of the scientific program. He took part in the ICM in Stockholm in 1962, in Moscow in 1966 and in Nice in 1970.

1946 to 1954 and from 1983 he was chief editor of the Uspekhi Math. Nauk (Russian Mathematical Surveys).

In 2016 an asteroid was named after him: (48410) Kolmogorov .

The Airbus A320-200 with the registration VQ-BIV of the Aeroflot airline bears the name A. Kolmogorov.

Since 1994, the Russian Academy of Sciences has awarded the Kolmogorov Prize for outstanding achievements in the field of mathematics. The first award winner was Albert Schirjajew .

## Fonts

Books:

• Selected Works (Izbrannye Trudy), Volumes 1 to 4 (Volume 4 in two volumes), Moscow, Nauka 2005, 2007 (Russian edition), editors Wladimir Michailowitsch Tichomirow , Albert Nikolajewitsch Schirjajew
• Selected Works, 3 volumes Dordrecht, Kluwer 1991, 1992, 1993 (English edition)
• Basic concepts of probability theory , Berlin, Springer 1933, 1973
• with Sergei Wassiljewitsch Fomin : Real functions and functional analysis (= university books for mathematics . Vol. 78). Berlin, Deutscher Verlag der Wissenschaften 1975 (English edition: Elements of the theory of functions and functional analysis , Dover 1999)
• with Sergei Wassiljewitsch Fomin: Introductory Real Analysis , Prentice-Hall 1970
• with Boris Gnedenko Limit distribution of sums of independent random variables , Akademie Verlag 1959 (English edition: Limit distributions for sums of random variables , Addison-Wesley 1954, 1968)
• Editor: Mathematics of the 19th Century , 3 volumes, Birkhäuser 1992, 1998
• with Alexander Danilowitsch Alexandrow , Michail Alexejewitsch Lavrentjew : A general view of mathematics , 4 volumes, American Mathematical Society 1962, 1963
• Contributions in: Herbert Goering (editor) anthology on the statistical theory of turbulence. The most important Soviet works on the problem of turbulence , Akademie Verlag 1958
• Kolmogorov translated the book What is Mathematics? by Richard Courant and Herbert Robbins into Russian.

Some papers available online:

## literature

• Eric Charpentier, Annick Lesne, Nikolai Kapitonowitsch Nikolski (Editor) Kolmogorovs Heritage in Mathematics , Springer 2007
• Nikolski The great Kolmogorov , in Bolibruch, Osipov, Sinai (editor) Mathematical Events of the Twentieth Century , Springer 2006, p. 283
• Kolmogorov in Perspective , American Mathematical Society 2000 (translation of the souvenir volume on Kolmogorov published by Nauka in Moscow in 1993, edited by Shiryaev and other articles, with a biography of Shiryaev, memories of his students, list of publications and two essays by Kolmogorov on Alexandrov and on Newton)
• R. Livi, A. Vulpiani (eds.), Kolmogorov's Legacy in Physics , Lecturenotes in Physics, Springer 2003 (translation from French, published 2003 by Belin)
• AN Shiryaev : (Ed.): Kolmogorov , 3 volumes, Moscow 2003 (Volume 1 Bio-Bibliography, Volume 2 Selection from the correspondence with Alexandrov, Volume 3 from the diaries)
• TO Shiryaev: Kolmogorov: Life and Creative Activities . Annals of Probability, Vol. 17, No. 3, July 1989, pp. 866-944 ( JSTOR 2244388 )
• AN Shiryaev, NG Khimchenko (ed.): Kolmogorov in the memory of his students (Russian), Moscow, MTsNMO Publ., 2006
• Khimchenko (Ed.): From the last interview of AN Kolmogorov , Mathematical Intelligencer, Volume 23, 2001, No. 1, pp. 30-38 (from interviews for a film portrait of Kolmogorov by AN Marutyan, 1983)
• Hannelore Bernhardt : To compare the probabilistic concepts of R. v. Mises and AN Kolmogorov. Perspectives of intercultural interaction for scientific progress. Contributions from scientific historians of the GDR to the XVIII. International Congress for the History of Sciences in Berkley (USA), Academy of Sciences of the GDR, Institute for the History and Organization of Sciences. Colloquia Booklet 43, pp. 205-209. Berlin 1985.

Commons : Andrei Kolmogorow  - collection of pictures, videos and audio files

## Individual evidence

1. Une série de Fourier – Lebesgue divergente presque partout , Fundamenta Mathematicae Vol. 4, 1923, p. 32
2. See Stanford Encyclopedia of Philosophy . His work in Math.Sbornik 1925 is reprinted in van Heijenoort From Frege to Gödel , 1962. This was later followed by Zur Deutung der Intuitionist Logic , Mathematische Zeitschrift, Volume 35, 1932, pp. 58–65
3. Paul Vitányi, articles Kolmogorov in Scholarpedia
4. According to Graham, Kantor, Naming Infinity, 2009, p. 186, Kolmogorov asked him about Alexandrov's importance in topology, to which Lusin replied that this was not topology, but topoloschtwo , an artificial word with echoes of the Russian word for sodomy.
5. ^ Loren Graham, Jean-Michel Kantor, Naming Infinity, Harvard University Press, 2009, p. 170
6. Masha Gessen , Perfect Rigor, Houghton Mifflin 2009
7. ^ Dana MacKenzie, Science Lifes: Robert D. MacPherson, Simons Foundation, May 30, 2012
8. Naming Infinity, 2009, pp. 185f
9. According to Graham, Kantor, p. 186, Lusin was in a certain way jealous of the success of his students, who were not satisfied with his own field of work and the descriptive set theory he founded, but rather focused on topology (Alexandrow) and probability theory (Kolmogorow) made a name for themselves
10. Bogoljubow, Gnedenko, Sobolew, Kolmogorow on the occasion of his 80th birthday, Uspekhi Akad. Nauka, Volume 38, 1983, 11-23, printed in the Selected Works, Volume 3
11. Masha Gessen, Perfect Rigor, Chapter 3
12. ^ S. Novikov: The Second Half of the 20th Century and its Conclusion: Crisis in the Physics and Mathematics Community in Russia and in the West , in: AMS Translations, Volume 212, 2004, pdf
13. Vitanyi, Scholarpedia article on Kolmogorow
14. Nikolski in Kolmogorov in Perspective, AMS, 2000, p. 115
15. A. N. Kolmogorow Prize. Russian Academy of Sciences, accessed August 6, 2018 ( Russian Премия имени А.Н. Колмогорова ).