Alexander Yakovlevich Chinchin
Aleksandr Khinchin (often in French Khintchine and English Aleksandr Jakovlevich Khinchin , Russian Александр Яковлевич Хинчин , scientific transliteration : Aleksandr Jakovlevic Chinčin * July 7 ^{. Jul} / 19th July 1894 ^{greg.} In Kondyrjowo in today's Kaluga oblast ; † 18 November 1959 in Moscow ) was a Soviet mathematician . His main field of work was stochastics . A sentence on the weak law of large numbers is named after him. He is referred to in the literature (among others) as one of the founders of probability theory in the Soviet Union. He also wrote some important papers on the history of mathematics.
Stations of teaching and research
He completed a secondary school in Kaluga and then went to a private school in Zurich to deepen his education from 1906 to 1907 . Then he went to Moscow to a high school. He began studying mathematics at Moscow University in 1911. In the research group around the mathematician Nikolai Nikolajewitsch Lusin he began his first independent investigations into the theory of real functions. After his studies, which he finished in 1916, he worked at a polytechnic institute in Moscow and was then appointed professor at the Faculty of Mathematics and Physics in Ivanovo-Voznesensk .
When he was offered a chair in mathematics in 1922, he returned to Moscow. Before that, he had already worked at a research institute at the Moscow State University. In 1939 the Academy of Sciences of the USSR appointed him a corresponding member. In the thirties he became the section head for the methodology of teaching in the People's Commissariat for Education of the RSFSR . From the mid-1940s he was also a member of the Presidium of the Soviet Academy of Educational Sciences for further years.
He received the State Prize of the USSR , the Order of Lenin , the Order of the Red Banner of Labor , the Stalin Prize and Badges of Honor of the Soviet Union .
Research work
Following on from the work of Arnaud Denjoy on a generalized integration method , he began to formulate the conditions for an asymptotic derivative to be formed at almost all points in a defined interval of a measurable function . Thereafter, Chinchin concentrated on studies in the field of number theory , such as the properties of irrational numbers . He investigated problems of the theory of Diophantine approximation and specially developed (parallel to Kurt Mahler ) so-called transfer theorems for results between related approximation problems .
He dealt with the application of metric function theory in the field of probability theory. In particular, he looked at the connection between sums of independent random variables and infinitely divisible distributions and showed the Lévy-Khinchin formula there . He was able to show, for example, that with a suitable choice of constants, the sum of standardized , independent and identically distributed distributions always converges to a normal distribution ( central limit theorem ).
He founded the metric theory of continued fractions by showing in 1935 that in almost all real numbers the geometric mean of the denominators of their continued fractions converges to the Chinchin constant .
According to him Chintschins weak law of large numbers named, a formulation of the weak law of large numbers .
At the same time as Andrei Nikolajewitsch Kolmogorow , he showed some basics for the description of random processes that were needed for the construction and function of technical, automatic systems and their work processes. This work led him to the field of classical quantum physics , where he was able to prove some connections with analytical methods. With the prerequisites for the individual ergodic set developed by George David Birkhoff at the same time , Chintschin succeeded in showing that in test procedures it is sufficient to consider only one stationary process if the mean value and the associated scatter of experimental values have to be estimated. He also turned to the field of information theory , the foundations of which were created by Claude Elwood Shannon . The Wiener-Chintschin theorem is named after him and Norbert Wiener .
Alexander Gelfond , Dmitri Abramowitsch Raikow and Boris Gnedenko were among his doctoral students .
See also
Fonts (selection)
- Sur la loi des grandes nombres , Comptes Rendus de l'Academie des Sciences, Paris, Volume 188, 1929, p. 477
- Continued Fractions , Mineola, NY: Dover Publications, 1997, ISBN 0-486-69630-8 (first published in Moscow , 1935)
- Three Pearls of Number Theory , Mineola, NY: Dover Publications, 1998, ISBN 0-486-40026-3 (first published in Moscow and Leningrad , 1947)
- Mathematical Foundations of Quantum Statistics , Mineola, NY: Dover Publications, 1998, ISBN 0-486-40025-5 (first published in Moscow and Leningrad, 1951)
German translations of the writings of AJ Chintschin:
- Asymptotic laws of probability , Berlin 1933
- Drei Perlen der Numberentheorie , Berlin 1951 (The book deals with Van der Waerden's theorem on arithmetic progressions, the proof of the Landau - Schnirelmann conjecture by Henry Mann , and the elementary proof of Waring's problem (previously proven by David Hilbert) by Juri Linnik )
- Encyclopedia of Elementary Mathematics with PS Alexandroff and AI Markuschewitsch , Berlin 1954. 5 volumes (= university books for mathematics , vol. 7-11).
- Mathematical foundations of statistical mechanics with Hans-Joachim Rossberg, Berlin 1956
- Mathematical foundations of quantum statistics , Berlin 1956
- E-entropy and e-capacity of quantities in functional spaces with AN Kolmogorov and Wladimir Michailowitsch Tichomirow , Berlin 1960
- Information and information stability of random variables and processes with MS Pinsker , Berlin 1963
- General formulation of Shannon's law of information theory with RL Dobruschin , Berlin 1963
- Work on information theory with DK Faddeev , AN Kolmogorov, Alfréd Rényi and J. Balatoni, Berlin 1967
- Elementary introduction to probability theory with BW Gnedenko , Berlin 1982
Web links
- John J. O'Connor, Edmund F. Robertson : Alexander Jakowlewitsch Chintschin. In: MacTutor History of Mathematics archive .
- Chinchin's résumé on math.ru (Russian)
- Literature by and about Alexander Jakowlewitsch Chintschin in the catalog of the German National Library
- Obituary ( by Boris Wladimirowitsch Gnedenko in: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (1960), Vol. 2, contains list of publications)
personal data | |
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SURNAME | Chinchin, Alexander Jakowlewitsch |
ALTERNATIVE NAMES | Aleksandr Yakovlevich Khintchine; Александр Яковлевич Хинчин |
BRIEF DESCRIPTION | Soviet mathematician |
DATE OF BIRTH | July 19, 1894 |
PLACE OF BIRTH | Kondyrjowo |
DATE OF DEATH | November 18, 1959 |
Place of death | Moscow |