Andrey Kolmogorov

Andrei Nikolaevich Kolmogorov (Russian: Андрей Николаевич Колмогоров pronunciation / i, scientific transliteration Andrei Nikolaevich Kolmogorov; ? * 12.jul / April 25 1903greg in Tambov, .. † October 20, 1987 in Moscow) was one of the most important mathematicians of the 20th century. Kolmogorov made ​​major contributions in the areas of probability theory and topology, it is regarded as the founder of algorithmic complexity theory. His most famous achievement was the mathematical axiomatization of probability theory.

As a student ( and published ) worked he also has logic and Fourier series, later on the application of probability theory in turbulence and classical mechanics.

Life and work

Kolmogorov's mother died at his birth on April 25 in the Russian Tambov - the mother was on the way from the Crimea to Tunoshna near Yaroslavl, where her father Yakov Stepanovich Kolmogorov lived ( he was from the nobility and was before the revolution landowners ). His father Nikolai Katayev was the son of a priest and a farmer, who returned after the Russian Revolution from exile and had a job at the Ministry of Agriculture, but in 1919 fell into civil war. The parents were not married and his father did not care about his son, so he was raised by his mother 's sister, Vera Jakowlena in Tunoshna. She and her sisters organized a small school by then progressive educational ideas, which also visited Kolmogorov. After moving (1910 ) to Moscow and a visit to a private, after the Revolution public school (organized by Yevgenia RepMan and Vera Fedorova ) he graduated in 1920 from the school, worked for a while as a conductor on the railroad, and then attended the University of Moscow and parallel to the Mendeleev Institute. Besides mathematics he studied Russian history and metallurgy.

1922 Kolmogorov published the first results in set theory in 1923 to work in Fourier Analysis, which made ​​him internationally known ( see below), and he published eight papers on integration theory, Fourier analysis as well as on probability theory. After graduating in 1925 he began his ( "small" ) Promotion with Nikolai N. Lusin, which he finished in 1929.

1925 ( and again in 1932 ), he also dealt with the intuitionistic logic of Brouwer, which he sought to formalize.

On trips to the Volga and the Caucasus, he completed a lifelong friendship with PS Aleksandrov, with whom he undertook in 1930/31 study visits to Göttingen, Munich and Paris. In 1931 he was appointed a full professor at the University of Moscow. Kolmogorov later lived with Alexandrov together in a house, which both bought in 1935 Komarowka in Moscow and where they received many famous mathematicians. As Lusin 1946 recording Alexandrov rejected in the Academy of Sciences, there was an uproar as Kolmogorov Lusin publicly slapped, which penetrated to Stalin.

In 1923 he constructed a - integrable function whose Fourier series diverges almost everywhere ( and 1926 one whose Fourier series converges nowhere ), counter suspicions of his teacher Lusin, who suspected the pointwise convergence of Fourier series. For square-integrable functions ( class) is also suspected long that counter-examples would be found until Lennart Carleson proved 1966 Lusins ​​conjecture for this class.

In 1933 Kolmogorov textbook Basic concepts of probability theory in German at the Heidelberg Springer -Verlag, in which he presents his axiomatization of probability theory. In the same year he became director of the Mathematical Institute of the Moscow State University.

Kolmogorov, 1934, his work on cohomology (a term from topology ) and reached about the "big " promotion doctoral degrees in mathematics and physics. In 1939 he became a member of the Russian Academy of Sciences, and later a member of many similar institutions in Romania, England, Germany, USA, India, Holland, and France. He has received awards such as the Order of Soviet Socialist Studies ( 1940), the Stalin Prize (1941 ) and multiply the Order of Lenin. In 1942 he married his high school sweetheart Anna Dmitrievna Jegorownaja.

In 1941 he published two important articles for homogeneous turbulence of fluids. 1953/54, he described the KAM theory of dynamical systems, announced at the ICM 1954 in Amsterdam, where Kolmogorov held a plenary lecture ( General theory of dynamical systems and classical mechanics) and further developed by Kolmogorov's student Vladimir Arnold. In 1957, he sparked a called already by Hilbert generalization of Hilbert's 13th problem.

1955 Kolmogorov was honorary doctorate from the Sorbonne in Paris. In 1962 he was awarded the Balzan Prize for Mathematics in 1980 and the Wolf Prize. In 1964 he became a member of the Royal Society of London, 1968 Member of the French Academy of Sciences. Countless awards and international honorary doctorates followed.

In addition to his scientific work, Kolmogorov was very involved for the promotion of gifted children, opened under his initiative at Moscow University, a boarding school with a focus on mathematics and physics. He was until his death scientifically active.

Kolmogorov had many disciples. His doctoral include Vladimir Arnold, Eugene Dynkin, Israel Gelfand, Boris Gnedenko, Vladimir Mikhailovich Tikhomirov, Vladimir Andreyevich Uspensky, Roland Lvovitch Dobrushin, Per Martin- Löf, Anatoly Ivanovich Maltsev, Robert Adolfovich Minlos, Sergei Mikhailovich Nikolsky, Albert Nikolaevich Shiryaev, Yakov Grigorjewitsch Sinai, Grigory Barenblatt Isaakowitsch, Vladimir Abramovich Rokhlin, Anatoly Georgijewitsch Wituschkin, Akiva Moissejewitsch Jaglom, Leonid Levin.

Writings

Books:

• Selected Works ( Izbrannye Trudy ), Volume 1 to 4 ( Volume 4 into two volumes), Moscow, Nauka, 2005, 2007 ( Russian edition ), editor Vladimir Mikhailovich Tikhomirov, Albert Nikolaevich Shiryaev
• Selected Works, 3 volumes Dordrecht, Kluwer, 1991, 1992, 1993 ( English Edition)
• Basic concepts of probability theory, Berlin, Springer 1933, 1973
• With Sergei Vasilievich Fomin: Real functions and functional analysis, Berlin, German Academic Publishers, 1975 ( English edition: Elements of the theory of functions and functional analysis, Dover 1999)
• Introductory Real Analysis with Fomin, Prentice- Hall 1970
• Boris Gnedenko limit distribution of sums of independent random variables, Akademie Verlag, 1959 ( English edition: Limit distributions for sums of random variables, Addison -Wesley 1954, 1968)
• Publisher: Mathematics of the 19th Century, 3 vols, 1992 Birkhäuser, 1998
• Alexander Danilovich Aleksandrov, Mikhail Alekseevich Lavrentiev: A general view of mathematics, 4 volumes, American Mathematical Society 1962, 1963
• Posts: Herbert Goering (Editor) anthology of the statistical theory of turbulence. The most important Soviet work on the turbulence problem, Akademie Verlag 1958
• Kolmogorov translated the Book of What is Mathematics? by Richard Courant and Herbert Robbins into Russian.

Some online reach work:

• Une série de Fourier - Lebesgue divergent presque partout (PDF, 219 kB), Fundamenta Mathematicae Vol 4, 1923, p 32
• About the analytical methods in probability theory, Mathematische Annalen, Vol 104, 1931, p 415
• On the interpretation of intuitionistic logic, mathematical journal, Volume 35, 1932, p 58
• About the totals are due to the coincidence of certain independent variables, Mathematische Annalen, Vol 99, 1928, p 309, note here Math Annalen, Volume 102, 1930, p 484
• On the theory of Markov chains, Annals of Mathematical, Volume 112, 1936, p.155
• About the law of the iterated logarithm, Mathematische Annalen, Vol 101, 1929, p.126
• For the reversibility of the statistical laws of nature, Mathematische Annalen, Vol 113, 1937, p 766
• On the theory of continuous random processes, Mathematische Annalen, Vol 108, 1933, p.149
• For a topological group theoretical foundation of geometry, News of the Göttingen Academy of Sciences, 1930, p.208
• Contributions to measure theory, Mathematische Annalen, Vol 107, 1933, p 351
• Studies on the integral term, Mathematische Annalen, Vol 103, 1930, p 654
• About the compactness of the function quantities at the convergence in the mean, news of the Göttingen Academy of Sciences, 1931, p.60
• Dmitri Jewgenjewitsch Menshov: Sur la convergence de fonctions orthogonal, Math Journal, Volume 26, 1927, p 432