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tion of modern probability theory he also gave fundamental contributions to the mathematics of topology intuitionistic logic turbulence classical mechanics functional analysis algorithmic information theory and computational complexity 7 2 8 biography edit early life edit andrey kolmogorov was born in tambov about 500 kilometers southeast of moscow in 1903 his unmarried mother maria yakovlevna kolmogorova died giving birth to him 9 andrey was raised by two of his aunts in tunoshna near yaroslavl at the estate of his grandfather a well to do nobleman little is known about andrey s father he was supposedly named nikolai matveyevich katayev and had been an agronomist katayev had been exiled from saint petersburg to the yaroslavl province after his participation in the revolutionary movement against the tsars he disappeared in 1919 and was presumed to have been killed in the russian civil war andrey kolmogorov was educated in his aunt vera s village school and his earliest literary efforts and mathematical papers were printed in the school journal the swallow of spring andrey at the age of five was the editor of the mathematical section of this journal kolmogorov s interest in mathematics was spurred when he noticed at the age of six the regularity in the sum of the series of odd numbers 1 1 2 1 3 2 2 1 3 5 3 2 displaystyle 1 1 2 1 3 2 2 1 3 5 3 2 etc 10 in 1910 his aunt adopted him and they moved to moscow where he graduated from high school in 1920 later that same year kolmogorov began to study at moscow state university and at the same time mendeleev moscow institute of chemistry and technology 11 kolmogorov writes about this time i arrived at moscow university with a fair knowledge of mathematics i knew in particular the beginning of set theory i studied many questions in articles in the encyclopedia of brockhaus and efron filling out for myself what was presented too concisely in these articles 12 kolmogorov gained a reputation for his wide ranging erudition while an undergraduate student in college he attended the seminars of the russian historian s v bakhrushin and he published his first research paper on the fifteenth and sixteenth centuries landholding practices in the novgorod republic 13 during the same period 1921 22 kolmogorov worked out and proved several results in set theory and in the theory of fourier series adulthood edit in 1922 kolmogorov gained international recognition for constructing a fourier series that diverges almost everywhere 14 15 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 3 he formed a lifelong close friendship with pavel alexandrov a fellow student of luzin indeed several researchers have concluded that the two friends were sexually involved 16 17 18 although neither acknowledged this openly kolmogorov together with aleksandr khinchin became interested in probability theory also in 1925 he published his work in intuitionistic logic on the principle of the excluded middle in which 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 from moscow state university in 1929 kolmogorov and alexandrov during a long travel stayed about a month in an island in lake sevan in armenia 19 in 1930 kolmogorov went on his first long trip abroad traveling to göttingen and munich and then to paris he had various scientific contacts in göttingen first with richard courant and his students working on limit theorems where diffusion processes proved to be the limits of discrete random processes then with hermann weyl in intuitionistic logic and lastly with edmund landau in function theory 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 state university in 1933 kolmogorov published his book foundations of the theory of probability laying the modern axiomatic foundations of probability theory and establishing his reputation as the world s leading expert in this field in 1935 kolmogorov became the first chairman of the department of probability theory at moscow state university around the same years 1936 kolmogorov contributed to the field of ecology and generalized the lotka volterra model of predator prey systems during the great purge in 1936 kolmogorov s doctoral advisor nikolai luzin became a high profile target of stalin s regime in what is now called the luzin affair kolmogorov and several other students of luzin testified against luzin accusing him of plagiarism nepotism and other forms of misconduct the hearings eventually concluded that he was a servant to fascistoid science and thus an enemy of the soviet people luzin lost his academic positions but curiously he was neither arrested nor expelled from the academy of sciences of the soviet union 20 21 the question of whether kolmogorov and others were coerced into testifying against their teacher remains a topic of considerable speculation among historians all parties involved refused to publicly discuss the case for the rest of their lives soviet russian mathematician semën samsonovich kutateladze concluded in 2013 after reviewing archival documents made available during the 1990s and other surviving testimonies that the students of luzin had initiated the accusations against luzin out of personal acrimony there was no definitive evidence that the students were coerced by the state nor was there any definitive evidence to support their allegations of academic misconduct 22 soviet historian of mathematics a p yushkevich surmised that unlike many of the other high profile persecutions of the era stalin did not personally initiate the persecution of luzin and instead eventually concluded that he was not a threat to the regime which would explain the unusually mild punishment relative to other contemporaries 23 in a 1938 paper kolmogorov established the basic theorems for smoothing and predicting stationary stochastic processes a paper that had major military applications during the cold war 24 in 1939 he was elected a full member academician of the ussr academy of sciences during world war ii kolmogorov contributed to the soviet war effort by applying statistical theory to artillery fire developing a scheme of stochastic distribution of barrage balloons intended to help protect moscow from german bombers during the battle of moscow 25 in his study of stochastic processes especially markov processes kolmogorov and the british mathematician sydney chapman independently developed a pivotal set of equations in the field that have been given the name of the chapman kolmogorov equations kolmogorov left delivers a talk at a soviet information theory symposium tallinn 1973 kolmogorov works on his talk tallinn 1973 later kolmogorov focused his research on turbulence beginning his publications in 1941 in classical mechanics he is best known for the kolmogorov arnold moser theorem first presented in 1954 at the international congress of mathematicians 7 in 1957 working jointly with his student vladimir arnold he solved a particular interpretation of hilbert s thirteenth problem around this time he also began to develop and has since been considered a founder of algorithmic complexity theory often referred to as kolmogorov complexity theory kolmogorov married anna dmitrievna egorova in 1942 he pursued a vigorous teaching routine throughout his life both at the university level and also with younger children as he was actively involved in developing a pedagogy for gifted children in literature music and mathematics at moscow state university kolmogorov occupied different positions including the heads of several departments probability statistics and random processes mathematical logic he also served as the dean of the moscow state university department 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 26 kolmogorov died in moscow in 1987 and his remains were buried in the novodevichy cemetery a quotation attributed to kolmogorov is translated into english every mathematician believes that he is ahead of the others the reason none state this belief in public is because they are intelligent people vladimir arnold once said kolmogorov poincaré gauss euler newton are only five lives separating us from the source of our science 27 awards and honours edit kolmogorov received numerous awards and honours both during and after his lifetime member of the russian academy of sciences 1 awarded the stalin prize in 1941 elected an honorary member of the american academy of arts and sciences in 1959 28 elected member of the american philosophical society in 1961 29 awarded the balzan prize in 1962 elected a foreign member of the royal netherlands academy of arts and sciences in 1963 30 elected a foreign member of the royal society formemrs in 1964 2 awarded the lenin prize in 1965 elected member of the united states national academy of sciences in 1967 31 awarded the wolf prize in 1980 awarded the lobachevsky prize in 1986 the following are named in kolmogorov s honour fisher kolmogorov equation johnson mehl avrami kolmogorov equation kolmogorov axioms kolmogorov equations also known as the fokker planck equations in the context of diffusion and in the forward case kolmogorov dimension upper box dimension kolmogorov arnold theorem kolmogorov arnold moser theorem kolmogorov continuity theorem kolmogorov s criterion kolmogorov extension theorem kolmogorov s three series theorem convergence of fourier series gnedenko kolmogorov central limit theorem quasi arithmetic mean it is also called kolmogorov mean kolmogorov homology kolmogorov s inequality landau kolmogorov inequality kolmogorov integral brouwer heyting kolmogorov interpretation kolmogorov microscales kolmogorov s normability criterion fréchet kolmogorov theorem kolmogorov space kolmogorov complexity kolmogorov smirnov test wiener filter also known as wiener kolmogorov filtering theory wiener kolmogorov prediction kolmogorov automorphism kolmogorov s characterization of reversible diffusions borel kolmogorov paradox chapman kolmogorov equation hahn kolmogorov theorem johnson mehl avrami kolmogorov equation kolmogorov sinai entropy astronomical seeing described by kolmogorov s turbulence law kolmogorov structure function kolmogorov uspenskii machine model kolmogorov s zero one law kolmogorov zurbenko filter kolmogorov s two series theorem rao blackwell kolmogorov theorem khinchin kolmogorov theorem kolmogorov population model kolmogorov s strong law of large numbers bibliography edit 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 grundbegriffe der wahrscheinlichkeitsrechnung in german berlin julius springer 32 translation kolmogorov andrey 1956 foundations of the theory of probability 2nd ed new york chelsea isbn 978 0 8284 0023 7 archived from the original on 14 september 2018 retrieved 17 february 2016 cite book isbn date incompatibility help 33 1991 93 selected works of a n kolmogorov 3 vols tikhomirov v m ed volosov v m trans dordrecht kluwer academic publishers isbn 90 277 2796 1 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 mr 0178484 kolmogorov andrei n 1998 1963 on tables of random numbers theoretical computer science 207 2 387 395 doi 10 1016 s0304 3975 98 00075 9 mr 1643414 kolmogorov andrei n 2005 selected works in 6 volumes moscow in russian textbooks a n kolmogorov and b v gnedenko limit distributions for sums of independent random variables 1954 a n kolmogorov and s v fomin elements of the theory of functions and functional analysis publication 1999 publication 2012 kolmogorov andrey nikolaevich fomin sergei vasilyevich 1975 1970 introductory real analysis new york dover publications isbn 978 0 486 61226 3 references edit 1 2 youschkevitch a p 1983 a n kolmogorov historian and philosopher of mathematics on the occasion of his 80th birthday historia mathematica 10 4 383 395 doi 10 1016 0315 0860 83 90001 0 1 2 3 kendall d g 1991 andrei nikolaevich kolmogorov 25 april 1903 20 october 1987 biographical memoirs of fellows of the royal society 37 37 300 326 doi 10 1098 rsbm 1991 0015 s2cid 58080873 1 2 3 andrey kolmogorov at the mathematics genealogy project sufrin bernard 12 april 2026 sir tony hoare obituary the guardian academician andrei nikolaevich kolmogorov obituary russian mathematical surveys 43 1 1 9 1988 bibcode 1988rumas 43 1 doi 10 1070 rm1988v043n01abeh001555 s2cid 250857950 parthasarathy k r 1988 obituary andrei nikolaevich kolmogorov journal of applied probability 25 2 445 450 doi 10 1017 s0021900200041115 jstor 3214455 1 2 yaglom a m january 1994 a n kolmogorov as a fluid mechanician and founder of a school in turbulence research annual review of fluid mechanics 26 1 1 23 doi 10 1146 annurev fl 26 010194 000245 issn 0066 4189 o connor john j robertson edmund f andrey kolmogorov mactutor history of mathematics archive university of st andrews encyclopædia britannica online s v andrey nikolayevich kolmogorov accessed february 22 2013 tikhomirov v m 2001 andrei n kolmogorov wolf prize in mathematics v 2 world scientific pp 119 141 isbn 978 9812811769 андрей николаевич колмогоров curriculum vitae retrieved 19 june 2023 ams 2000 kolmogorov in perspective history of mathematics american mathematical society p 6 isbn 978 0821829189 salsburg david 2001 the lady tasting tea how statistics revolutionized science in the twentieth century new york w h freeman pp 137 50 isbn 978 0 7167 4106 0 kolmogorov a 1923 une série de fourier lebesgue divergente presque partout a fourier lebesgue series that diverges almost everywhere pdf fundamenta mathematicae in french 4 1 324 328 doi 10 4064 fm 4 1 324 328 v i arnold max dresden in brief archived from the original on 5 october 2013 graham loren r kantor jean michel 2009 naming infinity a true story of religious mysticism and mathematical creativity harvard university press p 185 isbn 978 0 674 03293 4 the police soon learned of kolmogorov and alexandrov s homosexual bond and they used that knowledge to obtain the behavior that they wished gessen masha 2011 perfect rigour a genius and the mathematical breakthrough of a lifetime icon books ltd p 17 kolmogorov alone among the top soviet mathematicians avoided being dra...