The Info List - Andrey Nikolaevich Kolmogorov

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Andrey Nikolaevich Kolmogorov (Russian: Андре́й Никола́евич Колмого́ров, IPA: [ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf] ( listen), 25 April 1903 – 20 October 1987)[4][5] was a 20th-century Soviet mathematician who made significant contributions to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.[3][2][6]


1 Biography

1.1 Early life 1.2 Adulthood

2 Awards and honours 3 Bibliography 4 References 5 External links

Biography[edit] Early life[edit] Andrey Kolmogorov
Andrey Kolmogorov
was born in Tambov, about 500 kilometers south-southeast of Moscow, in 1903. His unmarried mother, Maria Y. Kolmogorova, died giving birth to him.[7] Andrey was raised by two of his aunts in Tunoshna (near Yaroslavl) at the estate of his grandfather, a well-to-do nobleman. Little is known about Andrey's father. He was supposedly named Nikolai Matveevich Kataev and had been an agronomist. Nikolai had been exiled from St. Petersburg
St. Petersburg
to the Yaroslavl
province after his participation in the revolutionary movement against the czars. He disappeared in 1919 and he was presumed to have been killed in the Russian Civil War. Andrey Kolmogorov
Andrey Kolmogorov
was educated in his aunt Vera's village school, and his earliest literary efforts and mathematical papers were printed in the school journal "The Swallow of Spring". Andrey (at the age of five) was the "editor" of the mathematical section of this journal. Kolmogorov's first mathematical discovery was published in this journal: at the age of five he noticed the regularity in the sum of the series of odd numbers:

1 =



; 1 + 3 =



; 1 + 3 + 5 =




displaystyle 1=1^ 2 ;1+3=2^ 2 ;1+3+5=3^ 2 ,

etc.[8] In 1910, his aunt adopted him, and they moved to Moscow, where he graduated from high school in 1920. Later that same year, Kolmogorov began to study at the Moscow
State University and at the same time Mendeleev Moscow
Institute of Chemistry and Technology.[9] Kolmogorov writes about this time: "I arrived at Moscow
University with a fair knowledge of mathematics. I knew in particular the beginning of set theory. I studied many questions in articles in the Encyclopedia of Brockhaus and Efron, filling out for myself what was presented too concisely in these articles."[10] Kolmogorov gained a reputation for his wide-ranging erudition. While an undergraduate student in college, he attended the seminars of the Russian historian S. V. Bachrushin, and he published his first research paper on the fifteenth and sixteenth centuries' landholding practices in the Novgorod Republic.[11] During the same period (1921–22), Kolmogorov worked out and proved several results in set theory and in the theory of Fourier series. Adulthood[edit] In 1922, Kolmogorov gained international recognition for constructing a Fourier series
Fourier series
that diverges almost everywhere.[12][13] Around this time, he decided to devote his life to mathematics. In 1925, Kolmogorov graduated from the Moscow
State University and began to study under the supervision of Nikolai Luzin.[3] He formed a lifelong close friendship with Pavel Alexandrov, a fellow student of Luzin; indeed several authors have claimed that the two friends were involved in a homosexual relationship.[14][15][16][17] Kolmogorov (together with Aleksandr Khinchin) became interested in probability theory. Also in 1925, he published his work in intuitionistic logic — On the principle of the excluded middle, in which he proved that under a certain interpretation, all statements of classical formal logic can be formulated as those of intuitionistic logic. In 1929, Kolmogorov earned his Doctor of Philosophy
Doctor of Philosophy
(Ph.D.) degree, from Moscow State University. In 1930, Kolmogorov went on his first long trip abroad, traveling to Göttingen and Munich, and then to Paris. He had various scientific contacts in Göttingen. First of all with Richard Courant
Richard Courant
and his students working on limit theorems, where diffusion processes turned out to be the limits of discrete random processes, then with Hermann Weyl in intuitionistic logic, and lastly with Edmund Landau
Edmund Landau
in function theory. His pioneering work, About the Analytical Methods of Probability
Theory, was published (in German) in 1931. Also in 1931, he became a professor at the Moscow
State University. In 1933, Kolmogorov published his book, Foundations of the Theory of Probability, laying the modern axiomatic foundations of probability theory and establishing his reputation as the world's leading expert in this field. In 1935, Kolmogorov became the first chairman of the department of probability theory at the Moscow
State University. Around the same years (1936) Kolmogorov contributed to the field of ecology and generalized the Lotka–Volterra
model of predator-prey systems. In 1936, Kolmogorov and Alexandrov were involved in the political persecution of their common teacher Nikolai Luzin, in the so-called Luzin affair.[18][19] In a 1938 paper, Kolmogorov "established the basic theorems for smoothing and predicting stationary stochastic processes"—a paper that had major military applications during the Cold War.[20] In 1939, he was elected a full member (academician) of the USSR Academy of Sciences. During World War II
World War II
Kolmogorov contributed to the Russian war effort by applying statistical theory to artillery fire, developing a scheme of stochastic distribution of barrage balloons intended to help protect Moscow
from German bombers.[21] In his study of stochastic processes, especially Markov processes, Kolmogorov and the British mathematician Sydney Chapman independently developed the pivotal set of equations in the field, which have been given the name of the Chapman–Kolmogorov equations.

Kolmogorov (left) delivers a talk at a Soviet information theory symposium. (Tallinn, 1973).

Kolmogorov works on his talk (Tallinn, 1973).

Later, Kolmogorov focused his research on turbulence, where his publications (beginning in 1941) significantly influenced the field. In classical mechanics, he is best known for the Kolmogorov–Arnold–Moser theorem, first presented in 1954 at the International Congress of Mathematicians. In 1957, working jointly with his student Vladimir Arnold, he solved a particular interpretation of Hilbert's thirteenth problem. Around this time he also began to develop, and was considered a founder of, algorithmic complexity theory – often referred to as Kolmogorov complexity theory. Kolmogorov married Anna Dmitrievna Egorova in 1942. He pursued a vigorous teaching routine throughout his life, not only at the university level but also with younger children, as he was actively involved in developing a pedagogy for gifted children (in literature, music, and mathematics). At the Moscow
State University, Kolmogorov occupied different positions, including the heads of several departments: probability, statistics, and random processes; mathematical logic. He also served as the Dean of the Moscow
State University Department of Mechanics and Mathematics. In 1971, Kolmogorov joined an oceanographic expedition aboard the research vessel Dmitri Mendeleev. He wrote a number of articles for the Great Soviet Encyclopedia. In his later years, he devoted much of his effort to the mathematical and philosophical relationship between probability theory in abstract and applied areas.[22] Kolmogorov died in Moscow
in 1987, and his remains were buried in the Novodevichy cemetery. A quotation attributed to Kolmogorov is [translated into English]: "Every mathematician believes that he is ahead of the others. The reason none state this belief in public is because they are intelligent people." Vladimir Arnold
Vladimir Arnold
once said: "Kolmogorov – Poincaré – Gauss – Euler – Newton, are only five lives separating us from the source of our science". Awards and honours[edit] Kolmogorov received numerous awards and honours both during and after his lifetime:

Member of the Russian Academy of Sciences[1] Awarded the Stalin Prize in 1941 Award the Balzan Prize
Balzan Prize
in 1962 Elected a Foreign Member of the Royal Netherlands Academy of Arts and Sciences in 1963[23] Elected a Foreign Member of the Royal Society (ForMemRS) in 1964.[2] Awarded the Lenin Prize
Lenin Prize
in 1965 Awarded the Wolf Prize in 1980 Awarded the Lobachevsky Prize in 1986

The following are named in Kolmogorov's honour:

Fisher–Kolmogorov equation Kolmogorov axioms Kolmogorov equations (also known as the Fokker–Planck equations in the context of diffusion and in the forward case) Kolmogorov dimension (upper box dimension) Kolmogorov–Arnold theorem Kolmogorov–Arnold–Moser theorem Kolmogorov continuity theorem Kolmogorov's criterion Kolmogorov extension theorem Kolmogorov's three-series theorem Kolmogorov homology Kolmogorov's inequality Landau–Kolmogorov inequality Kolmogorov integral Brouwer–Heyting–Kolmogorov interpretation Kolmogorov microscales Kolmogorov's normability criterion Fréchet–Kolmogorov theorem Kolmogorov space Kolmogorov complexity Kolmogorov–Smirnov test Kolmogorov automorphism Kolmogorov's characterization of reversible diffusions Borel–Kolmogorov paradox Chapman–Kolmogorov equation Hahn–Kolmogorov theorem Johnson–Mehl–Avrami–Kolmogorov equation Kolmogorov–Sinai entropy Astronomical seeing
Astronomical seeing
described by Kolmogorov's turbulence law Kolmogorov structure function Kolmogorov's zero–one law Kolmogorov–Zurbenko filter

Bibliography[edit] A bibliography of his works appeared in "Publications of A. N. Kolmogorov". Annals of Probability. 17 (3): 945–964. July 1989. doi:10.1214/aop/1176991252. 

Kolmogorov, Andrey (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung (in German). Berlin: Julius Springer. [24]

Translation: Kolmogorov, Andrey (1956). Foundations of the Theory of Probability
(2nd ed.). New York: Chelsea. ISBN 0-8284-0023-7. Retrieved 2016-02-17. 

1991–93. Selected works of A.N. Kolmogorov, 3 vols. Tikhomirov, V. M., ed., Volosov, V. M., trans. Dordrecht:Kluwer Academic Publishers. ISBN 90-277-2796-1 1925. "On the principle of the excluded middle" in Jean van Heijenoort, 1967. A Source Book in Mathematical Logic, 1879–1931. Harvard Univ. Press: 414–37. Kolmogorov, Andrei N. (1963). "On Tables of Random Numbers". Sankhyā Ser. A. 25: 369–375. MR 0178484.  Kolmogorov, Andrei N. (1998) [1963]. "On Tables of Random Numbers". Theoretical Computer Science. 207 (2): 387–395. doi:10.1016/S0304-3975(98)00075-9. MR 1643414.  Kolmogorov, Andrei N. (2005) Selected works. In 6 volumes. Moscow
(in Russian)


A. N. Kolmogorov and B. V. Gnedenko. "Limit distributions for sums of independent random variables", 1954. A. N. Kolmogorov and S. V. Fomin. "Elements of the Theory of Functions and Functional Analysis", Publication 1999, Publication 2012


^ a b Youschkevitch, A.P. (1983), "A.N.Kolmogorov: Historian and philosopher of mathematics on the occasion of his 80th birfhday", Historia Mathematica, 10 (4): 383–395, doi:10.1016/0315-0860(83)90001-0  ^ a b c Kendall, D. G. (1991). "Andrei Nikolaevich Kolmogorov. 25 April 1903-20 October 1987". Biographical Memoirs of Fellows of the Royal Society. 37: 300–326. doi:10.1098/rsbm.1991.0015.  ^ a b c d Andrey Kolmogorov
Andrey Kolmogorov
at the Mathematics
Genealogy Project ^ "Academician Andrei Nikolaevich Kolmogorov (obituary)". Russian Mathematical Surveys. 43: 1–9. 1988. Bibcode:1988RuMaS..43....1.. doi:10.1070/RM1988v043n01ABEH001555.  ^ Parthasarathy, K. R. (1988). "Obituary: Andrei Nikolaevich Kolmogorov". Journal of Applied Probability. 25 (2): 445–450. doi:10.2307/3214455.  ^ O'Connor, John J.; Robertson, Edmund F., "Andrey Kolmogorov", MacTutor History of Mathematics
archive, University of St Andrews . ^ Encyclopædia Britannica Online, s. v. "Andrey Nikolayevich Kolmogorov", accessed February 22, 2013. ^ "Andrei N Kolmogorov prepared by V M Tikhomirov". Wolf Prize in Mathematics, v.2. World Scientific. 2001. pp. 119–141. ISBN 9789812811769.  ^ "Андрей Николаевич КОЛМОГОРОВ. Curriculum Vitae".  ^ Kolmogorov in Perspective (History of Mathematics). 2000. p. 6. ISBN 978-0821829189.  ^ Salsburg, David (2001). The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century. New York: W. H. Freeman. pp. 137–50. ISBN 0-7167-4106-7.  ^ Kolmogorov, A. (1923). "Une série de Fourier–Lebesgue divergente presque partout" [A Fourier–Lebesgue series that diverges almost everywhere] (PDF). Fundamenta Mathematicae (in French). 4 (1): 324–328.  ^ V. I. Arnold-Max Dresden. "In Brief". Archived from the original on 2013-10-05.  ^ Graham, Loren R.; Kantor, Jean-Michel (2009). Naming infinity: a true story of religious mysticism and mathematical creativity. Harvard University Press. p. 185. ISBN 978-0-674-03293-4. The police soon learned of Kolmogorov and Alexandrov's homosexual bond, and they used that knowledge to obtain the behavior that they wished.  ^ Gessen, Masha (2011). Perfect Rigour: A Genius and the Mathematical Breakthrough of a Lifetime. Icon Books Ltd. p. 17. Kolmogorov alone among the top Soviet mathematicians avoided being drafted into the postwar military effort. His students always wondered why-and the only likely explanation seems to be Kolmogorov's homosexuality. His lifelong partner, with whom he shared a home starting in 1929, was the topologist Pavel Alexandrov.  ^ Graham, Loren; Kantor, Jean-Michel (2009), Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity, Harvard University Press, p. 185, ISBN 9780674032934  ^ Szpiro, George (2011), Pricing the Future: Finance, Physics, and the 300-year Journey to the Black-Scholes Equation, Basic Books, p. 152, ISBN 9780465022489, It was generally known that they had a homosexual relationship, although they never acknowledged their liaison  ^ Lorentz, G. G. (2001). "Who discovered analytic sets?". The Mathematical Intelligencer. 23 (4): 28–32. doi:10.1007/BF03024600.  ^ O'Connor, John J.; Robertson, Edmund F., "The 1936 Luzin affair", MacTutor History of Mathematics
archive, University of St Andrews . ^ Salsburg, p. 139. ^ Gleick, James (2012). The Information: a history, a theory, a flood. New York: Vintage Books. p. 334. ISBN 978-1-4000-9623-7.  ^ Salsburg, pp. 145–7. ^ "A.N. Kolmogorov (1903–1987)". Royal Netherlands Academy of Arts and Sciences. Retrieved 22 July 2015.  ^ Rietz, H. L. (1934). "Review: Grundbegriffe der Wahrscheinlichkeitsrechnung by A. Kolmogoroff" (PDF). Bull. Amer. Math. Soc. 40 (7): 522–523. doi:10.1090/s0002-9904-1934-05895-6. 

External links[edit]

Wikimedia Commons has media related to Andrey Kolmogorov.

dedicated to AN Kolmogorov (his scientific and popular publications, articles about him).(in Russian) The Legacy of Andrei Nikolaevich Kolmogorov Biography at Scholarpedia The origins and legacy of Kolmogorov's Grundbegriffe Vitanyi, P.M.B., Andrey Nikolaevich Kolmogorov. Scholarpedia, 2(2):2798; 2007 Collection of links to Kolmogorov resources Interview with Professor A. M. Yaglom about Kolmogorov, Gelfand and other (1988, Ithaca, New York) Kolmogorov School at Moscow
University Annual Kolmogorov Lecture at the Computer Learning Research Centre at Royal Holloway, University of London Lorentz G. G., Mathematics
and Politics in the Soviet Union
Soviet Union
from 1928 to 1953 Kutateladze S. S., The Tragedy of Mathematics
in Russia Video recording of the G. Falkovich's lecture: "Andrey Nikolaevich Kolmogorov (1903–1987) and the Russian school" Andrey Kolmogorov
Andrey Kolmogorov
at the Mathematics
Genealogy Project

v t e

Laureates of the Wolf Prize in Mathematics


Israel Gelfand
Israel Gelfand
/ Carl L. Siegel (1978) Jean Leray
Jean Leray
/ André Weil
André Weil


Henri Cartan
Henri Cartan
/ Andrey Kolmogorov
Andrey Kolmogorov
(1980) Lars Ahlfors
Lars Ahlfors
/ Oscar Zariski
Oscar Zariski
(1981) Hassler Whitney
Hassler Whitney
/ Mark Krein
Mark Krein
(1982) Shiing-Shen Chern
Shiing-Shen Chern
/ Paul Erdős
Paul Erdős
(1983/84) Kunihiko Kodaira
Kunihiko Kodaira
/ Hans Lewy
Hans Lewy
(1984/85) Samuel Eilenberg
Samuel Eilenberg
/ Atle Selberg
Atle Selberg
(1986) Kiyosi Itô
Kiyosi Itô
/ Peter Lax
Peter Lax
(1987) Friedrich Hirzebruch
Friedrich Hirzebruch
/ Lars Hörmander
Lars Hörmander
(1988) Alberto Calderón
Alberto Calderón
/ John Milnor
John Milnor


Ennio de Giorgi / Ilya Piatetski-Shapiro (1990) Lennart Carleson
Lennart Carleson
/ John G. Thompson
John G. Thompson
(1992) Mikhail Gromov / Jacques Tits
Jacques Tits
(1993) Jürgen Moser
Jürgen Moser
(1994/95) Robert Langlands
Robert Langlands
/ Andrew Wiles
Andrew Wiles
(1995/96) Joseph Keller / Yakov G. Sinai (1996/97) László Lovász
László Lovász
/ Elias M. Stein
Elias M. Stein


Raoul Bott
Raoul Bott
/ Jean-Pierre Serre
Jean-Pierre Serre
(2000) Vladimir Arnold
Vladimir Arnold
/ Saharon Shelah
Saharon Shelah
(2001) Mikio Sato / John Tate
John Tate
(2002/03) Grigory Margulis
Grigory Margulis
/ Sergei Novikov (2005) Stephen Smale
Stephen Smale
/ Hillel Furstenberg (2006/07) Pierre Deligne
Pierre Deligne
/ Phillip A. Griffiths / David B. Mumford (2008)


Dennis Sullivan
Dennis Sullivan
/ Shing-Tung Yau
Shing-Tung Yau
(2010) Michael Aschbacher / Luis Caffarelli (2012) George Mostow / Michael Artin
Michael Artin
(2013) Peter Sarnak
Peter Sarnak
(2014) James G. Arthur (2015) Richard Schoen
Richard Schoen
/ Charles Fefferman
Charles Fefferman
(2017) Alexander Beilinson
Alexander Beilinson
/ Vladimir Drinfeld (2018)

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WorldCat Identities VIAF: 36980195 LCCN: n50070283 ISNI: 0000 0001 1055 0346 GND: 119056399 SELIBR: 284015 SUDOC: 031679862 BNF: cb12284905m (data) BPN: 36118476 MGP: 10480 NDL: 00446065 NKC: jn20000700