Andrey Nikolaevich Kolmogorov (Russian: Андре́й
Никола́евич Колмого́ров, IPA: [ɐnˈdrʲej
nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf] ( listen), 25
April 1903 – 20 October 1987) 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
1.1 Early life
2 Awards and honours
5 External links
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. 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
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 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:
displaystyle 1=1^ 2 ;1+3=2^ 2 ;1+3+5=3^ 2 ,
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
Moscow Institute of Chemistry and Technology. 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."
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. During the same period
(1921–22), Kolmogorov worked out and proved several results in set
theory and in the theory of Fourier series.
In 1922, Kolmogorov gained international recognition for constructing
Fourier series that diverges almost everywhere. 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. 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. 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
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 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 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
In 1936, Kolmogorov and Alexandrov were involved in the political
persecution of their common teacher Nikolai Luzin, in the so-called
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. In 1939,
he was elected a full member (academician) of the USSR Academy of
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
Moscow from German bombers.
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
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
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.
Kolmogorov died in
Moscow in 1987, and his remains were buried in the
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
Vladimir Arnold once said: "Kolmogorov – Poincaré – Gauss –
Euler – Newton, are only five lives separating us from the source of
Awards and honours
Kolmogorov received numerous awards and honours both during and after
Member of the Russian Academy of Sciences
Awarded the Stalin Prize in 1941
Balzan Prize in 1962
Elected a Foreign Member of the Royal Netherlands Academy of Arts and
Sciences in 1963
Elected a Foreign Member of the Royal Society (ForMemRS) in 1964.
Lenin Prize in 1965
Wolf Prize in 1980
Lobachevsky Prize in 1986
The following are named in Kolmogorov's honour:
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 continuity theorem
Kolmogorov extension theorem
Kolmogorov's three-series theorem
Kolmogorov's normability criterion
Kolmogorov's characterization of reversible diffusions
Astronomical seeing described by Kolmogorov's turbulence law
Kolmogorov structure function
Kolmogorov's zero–one law
A bibliography of his works appeared in "Publications of A. N.
Kolmogorov". Annals of Probability. 17 (3): 945–964. July 1989.
Kolmogorov, Andrey (1933). Grundbegriffe der
Wahrscheinlichkeitsrechnung (in German). Berlin: Julius
Translation: Kolmogorov, Andrey (1956). Foundations of the Theory of
Probability (2nd ed.). New York: Chelsea. ISBN 0-8284-0023-7.
1991–93. Selected works of A.N. Kolmogorov, 3 vols. Tikhomirov, V.
M., ed., Volosov, V. M., trans. Dordrecht:Kluwer Academic Publishers.
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) . "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.
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,
^ 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 at the
Mathematics Genealogy Project
^ "Academician Andrei Nikolaevich Kolmogorov (obituary)". Russian
Mathematical Surveys. 43: 1–9. 1988. Bibcode:1988RuMaS..43....1..
^ Parthasarathy, K. R. (1988). "Obituary: Andrei Nikolaevich
Kolmogorov". Journal of Applied Probability. 25 (2): 445–450.
^ O'Connor, John J.; Robertson, Edmund F., "Andrey Kolmogorov",
MacTutor History of
Mathematics archive, University of St
^ 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.
^ "Андрей Николаевич КОЛМОГОРОВ. Curriculum
^ Kolmogorov in Perspective (History of Mathematics). 2000. p. 6.
^ 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):
^ V. I. Arnold-Max Dresden. "In Brief". Archived from the original on
^ 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
^ Lorentz, G. G. (2001). "Who discovered analytic sets?". The
Mathematical Intelligencer. 23 (4): 28–32.
^ O'Connor, John J.; Robertson, Edmund F., "The 1936 Luzin affair",
MacTutor History of
Mathematics archive, University of St
^ Salsburg, p. 139.
^ Gleick, James (2012). The Information: a history, a theory, a flood.
New York: Vintage Books. p. 334.
^ 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.
Wikimedia Commons has media related to Andrey Kolmogorov.
Portal 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,
Collection of links to Kolmogorov resources
Interview with Professor A. M. Yaglom about Kolmogorov, Gelfand and
other (1988, Ithaca, New York)
Kolmogorov School at
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 from 1928
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 at the
Mathematics Genealogy Project
Laureates of the
Wolf Prize in Mathematics
Israel Gelfand / Carl L. Siegel (1978)
Jean Leray /
André Weil (1979)
Henri Cartan /
Andrey Kolmogorov (1980)
Lars Ahlfors /
Oscar Zariski (1981)
Hassler Whitney /
Mark Krein (1982)
Shiing-Shen Chern /
Paul Erdős (1983/84)
Kunihiko Kodaira /
Hans Lewy (1984/85)
Samuel Eilenberg /
Atle Selberg (1986)
Kiyosi Itô /
Peter Lax (1987)
Friedrich Hirzebruch /
Lars Hörmander (1988)
Alberto Calderón /
John Milnor (1989)
Ennio de Giorgi /
Ilya Piatetski-Shapiro (1990)
Lennart Carleson /
John G. Thompson
John G. Thompson (1992)
Mikhail Gromov /
Jacques Tits (1993)
Jürgen Moser (1994/95)
Robert Langlands /
Andrew Wiles (1995/96)
Joseph Keller / Yakov G. Sinai (1996/97)
László Lovász /
Elias M. Stein
Elias M. Stein (1999)
Raoul Bott /
Jean-Pierre Serre (2000)
Vladimir Arnold /
Saharon Shelah (2001)
Mikio Sato /
John Tate (2002/03)
Grigory Margulis / Sergei Novikov (2005)
Stephen Smale /
Hillel Furstenberg (2006/07)
Pierre Deligne / Phillip A. Griffiths / David B. Mumford (2008)
Dennis Sullivan /
Shing-Tung Yau (2010)
Michael Aschbacher /
Luis Caffarelli (2012)
George Mostow /
Michael Artin (2013)
Peter Sarnak (2014)
James G. Arthur (2015)
Richard Schoen /
Charles Fefferman (2017)
Alexander Beilinson /
Vladimir Drinfeld (2018)
ISNI: 0000 0001 1055 0346
BNF: cb12284905m (data)