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Name and Name Modifications: Andrej Nikolayevich Kolmogoroff Dates of Birth and Death: (∗) 25 April 1903 in Tambov, Russia (†) 20 October 1987 in Moscow, Soviet Union Family Data: Kolmogorov’s parents were not married. His mother died in childbirth of her son, when Andrey was born. The father Nikolai Kataev was a farmer and son of a clergyman, who lived in exile. After the Russian Revolution, he became head of a department in the Russian Ministry of Agriculture, but died in 1919. He had never took care of his son’s education. Andrey was raised by his aunt, Vera Yakovlena at the estate of his grandfather, Yakov Stepanovich Kolmogorov. Kolmogorov married Anna Dmitrievna Egorova in 1942. Education: In 1920 Kolmogorov entered the State University of Moscow, where he stud- ied Mathematics, Metallurgy and Russian history. His professors and/or friends were Pavel Aleksandrov (1896-1982), Nikolai Luzin (1883-1950), Dmitri Egorov (1869-1931), Mikhail Yakovlevich Suslin (1894-1919) and Stepanov did arouse his interest in mathematics. In 1925 he finished his studies. In 1929 Kolmogorov finished his Dissertation. Professional Career: Kolmogorov started research already as a student and soon became famous. He was guided in his research by Luzin and published eight papers in 1925. In the same year, he published together with Khinchin his first article on probability. In 1931, Kolmogorov became Professor at the University of Moscow, two years later he became director of the Mathematical Institute of this Univer- sity. His work on the theory of probability Grundbegriffe der Wahrschein- lichkeit was published in 1933. It is based on fundamental axioms. In 1938, Kolmogorov laid the foundations for the theory of the Markov processes with
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Together with Aleksandrov, Kolmogorov bought a house in Komarovka, a little village nearby Moscow, where they were visited by many famous mathematicians, like Jacques Salomon Hadamard (1865-1963), Maurice Ren´e Fr´echet (1876-1973), Stefan Banach (1892-1945), Heinz Hopf (1894-1971), Kazimierz Kuratowski (1896-1980) etc. In 1938-39, many of the important professors of mathematics of the Uni- versity of Moscow joined the Steklov Institute of the Academy of Sciences, among them Pavel Aleksandrov (1896-1982), Israil Gelfand (born in 1913), Ivan Georgievich Petrovsky (1901-1973) und Aleksandr Khinchin (1894-1959). They founded a department for Statistics, Kolmogorov became its head. Kolmogorov not only dealt with Statistics, but also with the movement of the Planets, for which he also used the theory of probability. Kolmogorov was the leading Russian Mathematician and founder of a whole school at the University of Moscow, he had 74 students and nearly 1000 de- scendants of his school. Therefore he had great influence on several branches of Mathematics. He invented some basic postulates for the theory of prob- ability, which became a part of the Analysis. He formulated two systems of partial differential equations which bear his name. Important Publications: It is not possible to list Kolmogorov’s publications in cyril letters. • P. S. Aleksandrov (ed.), Izbrannye trudy, 4 vols. (Moskva 1978; 2007), English: Tikhomirov (ed.), Selected works, vol. 1: Mathematical logic, algebra, number theory, probability theory (Basel 1992), vol. 2: Proba- bility theory and mathematical statistics (Dordrecht 1992); vol. 3: In- formation theory and the theory of algorithms (Dordrecht 1991-1993). • “Une s´erie de Fourier-Lebesgue divergente presque partout”, Funda- menta Mathematicae 4 (1923) pp. 324-328. • “Une s´erie de Fourier-Lebesgue divergente partout”, Comptes rendus de l’Acad´emie des Sciences 183 (1926) pp. 1327-1328. • “ ¨ Uber die analytischen Methoden der Wahrscheinlichkeitsrechnung”, Mathematische Annalen 104 (1931) pp. 415-458. • “On the empirical determination of a distribution”, in: Samuel Kotz, Norman L. Johnson (eds.), Breakthroughs in Statistics, vol. II (New Copyright c by Stochastikon GmbH ( http: // encyclopedia. stochastikon. com ) 3
• “General Theory of Measure and Probability Theory” (1929), expanded as monography: Grundbegriffe der Wahrscheinlichkeitsrechnung (Berlin 1933, 1973, 1977), English: Foundations of the Theory of Probability (New York 1950, New York 1956, 1977; Providence 2000). • Zur topologisch-gruppentheoretischen Begr¨undung der Geometrie (Berlin 1930). • ¨ Uber die Kompaktheit der Funktionenmengen bei der Konvergenz im Mittel (Berlin 1931). • “Solution of a problem in probability theory connected with the prob- lem of the mechanism of stratification”, American Mathematical Society 53 (1951). • “Unbiased estimtes”, American Mathematical Society (1953). • Together with Boris Gnedenko: Limit distributions for sums of inde- pendent random variables (Cambridge, Mass. 1954; Reading, Mass. 1968).
• Gr¨oße (Leipzig 1954). • Sammelband zur statistischen Theorie der Turbulenz (Berlin 1958). • Together with S.V. Formin: Elements of the theory of functions and functional analysis, 2 vols. (London 1957; Mineola 1999). • Together with Peter Franken et al.: Arbeiten zur Informationstheorie (Berlin 1960). • Measure, Lebesgue integrals, and Hilbert space (New York 1962; Balti- more 1965). • Together with Aleksandrov: Mathematics. Its content, methods, and meaning, 3 vols. (Cambridge 1962, 1965). • Elementy teorii funkcij i funkcional’nogo analiza, 2 vols. (Moskva 1954- 60; 1968), German: Reelle Funktionen und Funktionalanalysis (Berlin 1975).
• Introductory real analysis (Englewood Cliffs Prentice Hall 1970; New York 1975).
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Matematica XIX veka, vol. 1: Geometrija, teorija analiceskich funkcij, vol. 2: Matematiceskaja logika, algebra, teoirja cisel, teorija verojat- nostej (Moskva 1978-81), English: Mathematics of the 19th century, vol. 1: Mathematical logic, algebra, number theory, probability the- ory (Basel 2001); vol. 2: Geometry, analytic function theory (Basel 1996); vol. 3: Function theory according to Chebyshev, ordinary dif- ferential equations, calculus of variations, theory of finite differences (Basel 1998). • Together with Pavel S. Aleksandrov: “A.I. Markushevich as a historian of mathematics”, Historia Mathematica 8 (1981) pp. 124-132. • Matematika XIX veka cebysevskoe napravlenie v teorii funkcij: oby- knovennye differencial’nye uravnenija; variacipnnoe iscislenie; teorija konecnyvh raznostej (Moskva 1987). • Novgorodskoe zemlevladenie XV veka (Moskva 1994). Scientific Honors: In 1939 Kolmogorov was elected into the Russian Academy of Sciences. In 1965 he received the Lenin Medal, six times the Lenin decoration, and in 1987 the Lobachevsky Medal. Kolmogorov also was elected in many other Academies, in the Romanian he Academy of Sciences (1956), into the Royal Statistical Society of London (1956), into the Leopoldina in Germany (1959), into the American Academy of Arts and Sciences (1959), into the Lon- don Mathematical Society (1959), in to the American Philosophical Society (1961), into the Indian Statistical Society (1962), into the Dutch Academy of Sciences (1963), into the Royal Society of London (1964), into the National Academy of the United States (1967), into the French Acad´emie des Sciences (1968). In 1962 Kolmogorv received the Balzan International Prize. Many Universities honored him with a Doctor honoris causa. References and Literature: • Kolmogorov in perspective (Providence 2000). • V.I. Arnold, “A.N. Kolmogorov“, in: Smilka Zdravkovska, P. A. Duren (eds.), Golden years of Moscow Mathematics (Providence, R.I. 1993) pp. 129-153.
• Sergey Bagdasarov, Chebyshev splines and Kolmogorov inequalities (Basel 1998).
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crofiche). • Sergej N. Bernstein, From Bortkiewicz to Kolmogorov (Egelsbach 1999, Mi- crofiches). • J¨urgen Braun, Michael Gabriel, On a constructive proof of Komogorov’s supposition theorem (preprint, Bonn 2007). • Cristian S. Calude, Randomness and complexity: from Leibniz to Chaitin (Singapore 2007). • Eric Charpentier (ed.), Kolmogorov’s heritage in mathematics (Berlin 2007). • Elart von Collani (ed.), Defining the Science of Stochastics (Lemgo 2004). • H. Cram´er, Random variables and probability distributions (London 1937). • H. Cram´er, “Entwicklungslinien der Wahrscheinlichkeitsrechnung”, in: Neuvi`eme Congr`es des Math´ematiciens Scandinaves (Helsingfors 1939) pp. 67-86. • H. Cram´er, “Fifty years of probability theory”, The Annals of Probability 4 (1976) pp. 509-546. • Giuseppe Da Prato, Kolmogorov equations for stochastic PDEs (Basel 2004).
• J.L. Doob, “Kolmogorov’s early work on convergence theory and founda- tions”, The Annals of Probability 17 (1989) pp. 815-821. • R.M. Dudley, Stephanie L. Cook, et al., “A.N. Kolmogorov and Statistics: A Citation Bibliography”, Annals of Statistics 18 (1990) pp. 1017-1031. • Bruno Durand, Kolmogorov complexity (2002). • Uriel Frisch, Turbulence: the legacy of A.N. Kolmogorov (Cambridge 1995). • Bernard J. Geurts, Particle-Laden flow: from geophysical to Kolmogorov scales (Dordrecht 2007). • Oliver Glier, Persistent arrays, path problems, and context-free languages (Darmstadt 2005). • Ren´e Henrion, Scenario reduction instochastic programming with respect to discrepancy distances (Berlin 2006). • Thomas Hochkirchen, Die Axiomatisierung der Wahrscheinlichkeitsrech- nung und ihre Kontexte: von Hilberts sechstem Problem zu Kolmogoroffs Grundbegriffen (G¨ottingen 1999). • E. Hopf, “On causality, statistics and probability”, Journal of Mathematics and Physics (MIT) 13 (1934) pp. 51-102. • London Mathematical Society, Kolmogorov in Perspective (History of Math- ematics, V. 20) (2000). • Kendall et al., “Andrei Nikolaevich Kolmogorov (1903-1987)”, Bulletin of the London Mathematical Society 22 (1990) pp. 31-100. • John Frank Kingman, On the Chapman-Kolmogorov equation (London 1974). • Ming Li, An introduction to Kolmogorov complexity and its applications Copyright c by Stochastikon GmbH ( http: // encyclopedia. stochastikon. com ) 6
• Roberto Livi (ed.), The Kolmogorov legacy in physcis (Berlin 2003). • Harold H. McFadden, Kolmogorov in perspective (Providence 2000). • R. von Mises, Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik (Leipzig, Wien 1931). • Markus M¨uller, Quantum Kolmogorov complexity and the Quantum Turing Machine (Online-Ressource 2007). • Jan von Plato, Creating modern probability (Cambridge 1994). • Jan von Plato, “A.N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeit- srechnung (1933)”, in: I. Grattan-Guiness (ed.), Landmark. Writings in Western Mathematics 1640-1940 (Amsterdam, New York 2005) pp. 960- 969. • David Salsburg, The Lady tasting Tea. How Statistics revolutionized sci- ence in the Twentieth Century (New York 2001). • A.N. Shiryaev et al., “Andrei Nikolaevich Kolmogorov: (April 25, 1903 - October 20, 1987): in memoriam”, Theory of probability and its applications 34 (1989) pp. 5-118. • Aleksej L. Semenov, Kolmorov complexity (Amsterdam 1998). • Osca Sheynin (sel., transl.), S.N. Bernstein (ed.), From Markov to Kol- mogorov: Russian papers on probability and statistics (Egelsbach 1998). • Ludwig Staiger, The Kolmogorov complexity of Liouville numbers (Halle 1999). • Ludwig Staiger, The Kolmogorov complexity of infinite words (Halle 2006). • V.M. Tikhomirov, “The life and work of Andreii Nikolaevich Kolmogorov”, Russian Mathematical Surveys 43 (1988) pp. 1-39. • V.M. Tikhomirov, “A.N. Kolmogorov”, in: Smilka Zdravkovska, P. A. Duren (eds.), Golden years of Moscow Mathematics (Providence, R.I. 1993) pp. 101-127. • Anton Wallner, Beitr¨age zur Theorie der Intervallwahrscheinlichkeit (Ham- burg 2002). • Osamu Watanabe (ed.), Kolmogorov complexity and computational com- plexity (Berlin 1992). • J.J. O’Connor, E.F. Robertson, “Kolmogorov”, http://www-groups.dcs.st- and.ac.uk/ history/Mathematicians/Kolmogorov/html (12 July 05). • J.J. O’Connor, E.F. Robertson, “Kolmogorov”, http://www-groups.dcs.st- and.ac.uk/ history/References/Kolmogorov/html (12 July 05). • http://www.dam.brown.edu/people/yiannis.kolm.html (13 February 06). • http://www.scholarpedia.org/article/Andrey Nikolaevich Kolmogorov (22 April 2008). • http://www.exploratorium.edu/complexity/CompLexicon/kolmogorov.html Copyright c by Stochastikon GmbH ( http: // encyclopedia. stochastikon. com ) 7
• Glenn Shafer, Vladimir Vovk, “The origins and legacy of Kolmogorov’s Grundbegriffe”, http://www.probabilityandfinance.com/articles/04.pdf (Oc- tober 3, 2005) (29 March 2008). Author(s) of this contribution: Claudia von Collani Version: 1.00 Download 47.37 Kb. Do'stlaringiz bilan baham: 
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