Andrey Kolmogorov
| Andrey Kolmogorov | |
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| Born | 25 April 1903 Tambov, Imperial Russia |
| Died | 20 October 1987 (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 Sergey Nikolsky 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) |
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Andrey Nikolaevich Kolmogorov (Russian: Андрей Николаевич Колмогоров) (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.
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[edit] Biography
[edit] 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).
[edit] Maturity
In 1922 Kolmogorov constructed a Fourier series that diverges almost everywhere, gaining international recognition.[citation needed] 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, where 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 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.
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.
[edit] 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.
- Kolmogorov, Andrey (1933) (in German). Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin: Julius Springer.
- Translation: Kolmogorov, Andrey (1956). Foundations of the Theory of Probability (2nd ed.). New York: Chelsea. ISBN 0828400237. http://www.mathematik.com/Kolmogorov/index.html.
- 1991–93. Selected works of A.N. Kolmogorov, 3 vols. Tikhomirov, V. M., ed., Volosov, V. M., trans. Dordrecht:Kluwer Academic Publishers. ISBN 9027727961
- 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. MR178484
- Kolmogorov, Andrei N. (1963). "On Tables of Random Numbers". Theoretical Computer Science 207 (2): 387–395. doi:10.1016/S0304-3975(98)00075-9. MR1643414
[edit] See also
- Kolmogorov axioms
- Kolmogorov equations (also known as the Fokker–Planck equations)
- Kolmogorov dimension (upper box dimension)
- Kolmogorov continuity theorem
- Kolmogorov’s criterion
- Kolmogorov extension theorem
- Kolmogorov's inequality
- Landau–Kolmogorov inequality
- Brouwer–Heyting–Kolmogorov interpretation
- Kolmogorov microscales
- Kolmogorov space
- Kolmogorov complexity
- Kolmogorov–Smirnov test
- Kolmogorov's zero-one law
- Kolmogorov's characterization of reversible diffusions
- Borel–Kolmogorov paradox
- Chapman–Kolmogorov equation
- Sydney Chapman (mathematician)
- Chaitin–Kolmogorov randomness
- Hahn–Kolmogorov theorem
- Astronomical seeing described by Kolmogorov's turbulence law
- Kolmogorov structure function
[edit] Notes
[edit] References
- Kendall, D. G., "Andrei Nikolaevich Kolmogorov. April 25, 1903 – October 20, 1987," Biographical Memoirs of Fellows of the Royal Society, Vol. 37, pages 300–319 (November 1991).
- Gessen, M., "Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century". Houghton Mifflin Harcourt, 2010.
[edit] External links
- Biography at Scholarpedia
- O'Connor, John J.; Robertson, Edmund F., "Andrey Kolmogorov", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Kolmogorov.html.
- Andrey Kolmogorov at the Mathematics Genealogy Project
- The Legacy of Andrei Nikolaevich Kolmogorov Curriculum Vitae and Biography. Kolmogorov School. Ph.D. students and descendants of A. N. Kolmogorov. A. N. Kolmogorov works, books, papers, articles. Photographs and Portraits of A. N. Kolmogorov.
- The origins and legacy of Kolmogorov's Grundbegriffe
- A Short Biography of A. N. Kolmogorov, national research institute for Mathematics and Computer Science in the Netherlands
- Collection of links to Kolmogorov resources
- Andrei Nikolaevich Kolmogorov (in Russian)
- Kolmogorov School at Moscow University
- Annual Kolmogorov Lecture at the Computer Learning Research Centre at Royal Holloway, University of London
- O'Connor, John J.; Robertson, Edmund F., "The 1936 Luzin affair", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Extras/Luzin.html.
- Lorentz G. G., Mathematics and Politics in the Soviet Union from 1928 to 1953
- Kutateladze S. S., The Tragedy of Mathematics in Russia
