Andrey Kolmogorov

Andrey Kolmogorov

Born 25 April 1903(1903-04-25)
Tambov, Imperial Russia
Died 20 October 1987(1987-10-20) (aged 84)
Moscow, USSR
Nationality Russian
Fields Mathematician
Institutions Moscow State University
Alma mater Moscow State University
Doctoral advisor Nikolai Luzin
Doctoral students Vladimir Arnold
Grigory Barenblatt
Roland Dobrushin
Eugene B. Dynkin
Israil Gelfand
Boris V. Gnedenko
Leonid Levin
Per Martin-Löf
Yuri Prokhorov
Vladimir Rokhlin
Yakov G. Sinai
Albert N. Shiryaev
Anatoli G. Vitushkin
Andrei Monin
Alexander Obukhov
Akiva Yaglom
Known for Probability theory, topology, intuitionistic logic, turbulence, classical mechanics, mathematical analysis
Notable awards Stalin Prize (1941)
Balzan prize (1963)
Lenin Prize (1965)
Wolf prize (1980)
Lobachevsky Prize (1987)
Signature

Andrey Nikolaevich Kolmogorov (Russian: Андре́й Никола́евич Колмого́ров) (25 April 1903 – 20 October 1987) was a Soviet Russian mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.

Contents

Biography

Early life

Kolmogorov was born at Tambov in 1903. His unwed mother died in childbirth and he was raised by his aunts in Tunoshna near Yaroslavl at the estate of his grandfather, a wealthy nobleman. His father, an agronomist by trade, was deported from Saint-Petersburg for participation in the revolutionary movement. He disappeared and was presumed to have been killed in the Russian Civil War.

Kolmogorov was educated in his aunt's village school, and his earliest literary efforts and mathematical papers were printed in the school newspaper. As an adolescent he designed perpetual motion machines, concealing their (necessary) defects so cleverly that his secondary-school teachers could not discover them. In 1910, his aunt adopted him and then they moved to Moscow, where he went to a gymnasium, graduating from it in 1920.

In 1920, Kolmogorov began to study at the Moscow State University and the Chemistry Technological Institute. Kolmogorov gained a reputation for his wide-ranging erudition. As an undergraduate, he participated in the seminars of the Russian historian S.V. Bachrushin, and he published his first research paper on the landholding practices in the Novgorod Republic in the fifteenth and sixteenth centuries.[1] At the same time (1921–1922), Kolmogorov derived and proved several results in set theory and in the theory of Fourier series (trigonometrical series).

Maturity

In 1922 Kolmogorov constructed a Fourier series that diverges almost everywhere, gaining international recognition. Around this time he decided to devote his life to mathematics. In 1925 Kolmogorov graduated from Moscow State University, and began to study under the supervision of Nikolai Luzin. He made lifelong friends with Pavel Alexandrov who involved Kolmogorov in 1936 in an ugly political persecution of their common teacher, the so-called Luzin case or Luzin affair. Kolmogorov (together with A. Khinchin) became interested in probability theory. Also in 1925, he published his famous work in intuitionistic logic — On the principle of the excluded middle. In 1929 Kolmogorov earned his Doctor of Philosophy degree, Ph.D., at the Moscow State University.

In 1930, Kolmogorov went on his first long trip abroad, traveling to Göttingen and Munich, Germany, and then to Paris, France. His pioneering work About the Analytical Methods of Probability Theory was published (in German) in 1931. Also in 1931, he became a professor at Moscow University. In 1933, Kolmogorov published the book, Foundations of the Theory of Probability, laying the modern axiomatic foundations of probability theory and establishing his reputation as the world's leading living expert in this field. In 1935, Kolmogorov became the first chairman of probability theory at the Moscow State University. In 1939, he was elected a full member (academician) of the USSR Academy of Sciences. In a 1938 paper, Kolmogorov "established the basic theorems for smoothing and predicting stationary stochastic processes" — a paper that would have major military applications during the Cold War to come.[2] Around the same years (1936) Kolmogorov contributed to the field of ecology and generalized the Lotka-Volterra model of predator-prey systems.

In his study of stochastic processes (random processes), especially Markov processes, Kolmogorov and the British mathematician Sydney Chapman independently developed the pivotal set of equations in the field, the Chapman–Kolmogorov equations.

Kolmogorov (left) works on his talk (Tallinn, Estonian SSR, 1973).
Kolmogorov works on his talk (Tallinn, Estonian SSR, 1973).

Later on, Kolmogorov changed his research interests to the area of turbulence, where his publications beginning in 1941 had a significant influence on 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 he solved Hilbert's thirteenth problem (a joint work with his student V. I. Arnold). He was a founder of algorithmic complexity theory, often referred to as Kolmogorov complexity theory, which he began to develop around this time.

Kolmogorov was married to 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, and in music, as well as in mathematics. At the Moscow State University, Kolmogorov occupied different positions, including the heads of several departments: probability, statistics, and random processes; mathematical logic; and he also served as the Dean of the Moscow State University Faculty 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.[3]

Kolmogorov died in Moscow in 1987. A quotation, "Every mathematician believes he is ahead over all others. The reason why they don't say this in public, is because they are intelligent people" is attributed to him.

Bibliography

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. 

See also

Notes

  1. ↑ David Salsburg, The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century, New York, W. H. Freeman, 2001; pp. 137–50.
  2. ↑ Salsburg, p. 139.
  3. ↑ Salsburg, pp. 145–7.

References

External links

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 (1983/4) · Kunihiko Kodaira / Hans Lewy (1984/5) · Samuel Eilenberg / Atle Selberg (1986) · Kiyoshi Itō / 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 (1992) · Mikhail Gromov / Jacques Tits (1993) · Jürgen Moser (1994/5) · Robert Langlands / Andrew Wiles (1995/6) · Joseph Keller / Yakov G. Sinai (1996/7) · László Lovász / Elias M. Stein (1999) · Raoul Bott / Jean-Pierre Serre (2000) · Vladimir Arnold / Saharon Shelah (2001) · Mikio Sato / John Tate (2002/3) · Grigory Margulis / Sergei Novikov (2005) · Stephen Smale / Hillel Fürstenberg (2006/7) · Pierre Deligne / Phillip A. Griffiths / David B. Mumford (2008)  · Dennis Sullivan / Shing-Tung Yau (2010)
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