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Andrey Kolmogorov

Born April 25, 1903(1903-04-25)
Tambov, Imperial Russia
Died October 20, 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
Roland Dobrushin
Eugene B. Dynkin
Israil Gelfand
Leonid Levin
Per Martin-Löf
Yuri Prokhorov
Yakov G. Sinai
Albert N. Shiryaev
Anatoli G. Vitushkin
Known for probability theory, topology, intuitionistic logic, turbulence, classical mechanics, mathematical analysis
Notable awards USSR State Prize (1941)
Balzan prize (1963)
Lenin Prize (1965)
Wolf prize (1980)
Lobachevsky Prize (1987)
Signature
Andrey Kolmogorov's signature

Andrey Nikolaevich Kolmogorov (Russian: Андре́й Никола́евич Колмого́ров) (April 25, 1903 - October 20, 1987) was a Soviet mathematician who made major advances in different scientific fields (among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity). Events 1607 - Eighty Years' War: The Dutch fleet destroys the anchored Spanish fleet at Gibraltar. Year 1903 ( MCMIII) was a Common year starting on Thursday (link will display calendar of the Gregorian calendar or a Common year starting TambovSoborJPG|thumb|200px|right|Cathedral in Tambov]] Мост через Цну The Russian Empire ( Pre-reform Russian: Pоссійская Имперія Modern Russian: Российская Империя translit: Rossiyskaya Events 1740 - Maria Theresa takes the throne of Austria. France, Prussia, Bavaria and Saxony Year 1987 ( MCMLXXXVII) was a Common year starting on Thursday (link displays 1987 Gregorian calendar) Moscow (Москва́ romanised: Moskvá, IPA: see also other names) is the Capital and the largest city of The Union of Soviet Socialist Republics (USSR was a constitutionally Socialist state that existed in Eurasia from 1922 to 1991 Russia (Россия Rossiya) or the Russian Federation ( Rossiyskaya Federatsiya) is a transcontinental Country extending A mathematician is a person whose primary area of study and research is the field of Mathematics. Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval A doctorate is an Academic degree that indicates the highest level of academic achievement Nikolai Nikolaevich Luzin, (also spelled Lusin) Никола́й Никола́евич Лу́зин ( December 9, 1883, Irkutsk – January Vladimir Igorevich Arnol'd or Arnold (Влади́мир И́горевич Арно́льд born June 12, 1937 in Odessa, Ukrainian SSR Roland Lvovich Dobrushin ( Russian: Роланд Львович Добрушин ( July 20, 1929, St Petersburg – November 12, Eugene Borisovich Dynkin (Евгений Борисович Дынкин born May 11, 1924) is a Russian Mathematician. Israïl Moiseevich Gelfand (Израиль Моисеевич Гельфанд ישראל געלפֿאַנד (born on) is a Mathematician who has contributed substantially Leonid Anatolievich Levin (לאוניד אנטולייביץ לוין Леонид Анатольевич Левин born November Per Erik Rutger Martin-Löf (born 1942 is a Swedish Logician, Philosopher, and Mathematician. Yuri Vasilevich Prokhorov (Юрий Васильевич Прохоров b Yakov Grigorevich Sinai (Яков Григорьевич Синай born September 21 1935) is one of the most influential Mathematicians of the twentieth Al'bert Nikolayevich Shiryaev (Альберт Николаевич Ширяев born October 12, 1934, Shchyolkovo, Moscow Oblast, Russia Anatoli Georgievich Vitushkin (Russian Анато́лий Гео́ргиевич Виту́шкин ( June 25, 1931 - May 9, 2004) was Probability theory is the branch of Mathematics concerned with analysis of random phenomena Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of Intuitionistic logic, or constructivist logic, is the Symbolic logic system originally developed by Arend Heyting to provide a formal basis for Brouwer In Fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic Stochastic property changes Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects Analysis has its beginnings in the rigorous formulation of Calculus. The USSR State Prize (Госуда́рственная пре́мия СССР was the Soviet Union 's state honour The International Balzan Prize Foundation awards four annual monetary prizes to people or organisations who have made outstanding achievements in the fields of humanities natural The Lenin Prize ( Russian: Ленинская премия was one of the highest awards in the Soviet Union. Lobachevsky Medal ( Lobachevsky International Prize) is a medal awarded by Kazan State University in honor of Nikolai Ivanovich Lobachevsky, who was a professor Events 1607 - Eighty Years' War: The Dutch fleet destroys the anchored Spanish fleet at Gibraltar. Year 1903 ( MCMIII) was a Common year starting on Thursday (link will display calendar of the Gregorian calendar or a Common year starting Events 1740 - Maria Theresa takes the throne of Austria. France, Prussia, Bavaria and Saxony Year 1987 ( MCMLXXXVII) was a Common year starting on Thursday (link displays 1987 Gregorian calendar) A soviet (сове́т, "council" originally was a workers' local council in late Imperial Russia. A mathematician is a person whose primary area of study and research is the field of Mathematics. Probability theory is the branch of Mathematics concerned with analysis of random phenomena Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of Intuitionistic logic, or constructivist logic, is the Symbolic logic system originally developed by Arend Heyting to provide a formal basis for Brouwer In Fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic Stochastic property changes Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects Computational complexity theory, as a branch of the Theory of computation in Computer science, investigates the problems related to the amounts of resources Kolmogorov is widely considered to be one of the pre-eminent mathematicians of the 20th century.

Contents

Biography

Early life

Kolmogorov was born at Tambov in 1903. TambovSoborJPG|thumb|200px|right|Cathedral in Tambov]] Мост через Цну 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. Tunoshna (also Tunoshnoye, or Tunoschna) (Аэропорт Туношна is an airport in Yaroslavl Oblast, Russia located 18 km southeast Yaroslavl (Яросла́вль is a city in Russia, the administrative center of Yaroslavl Oblast, located north-east of Moscow. His father, an agronomist by trade, was deported from Saint-Petersburg for participation in the revolutionary movement. Agronomists (called Agrologists in Canada are scientists who specialize in Agronomy, which is the science of utilizing plants for food fuel feed and Saint Petersburg ( tr: Sankt-Peterburg,) is a city and a federal subject of Russia located on the Neva River He disappeared and was presumed to be killed in the Russian Civil War. The Russian Civil War (1917–1923 was a multi-party war that occurred within the former Russian Empire after the Russian provisional government collapsed

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. The term perpetual motion, taken literally refers to movement that goes on forever In 1910, his aunt adopted him and then they moved to Moscow, where he went to a gymnasium (the equivalent of a American high school), 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. Landholder or landowner is a holder of the Estate in land with considerable rights of ownership or simply put an owner of land Veliky Novgorod (Вели́кий Но́вгород is the foremost historic city of North-Western Russia and the administrative center of Novgorod [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). In Mathematics, a Fourier series decomposes a periodic function into a sum of simple oscillating functions

Maturity

In 1922 Kolmogorov constructed a Fourier series that diverges almost everywhere, gaining international recognition. In Mathematics, the question of whether the Fourier series of a Periodic function converges to the given function is researched by In Measure theory (a branch of Mathematical analysis) one says that a property holds almost everywhere if the set of elements for which the property does Around this time he decided to devote his life to mathematics. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In 1925 Kolmogorov graduated from Moscow State University, and began to study under the supervision of Nikolai Luzin. Nikolai Nikolaevich Luzin, (also spelled Lusin) Никола́й Никола́евич Лу́зин ( December 9, 1883, Irkutsk – January He made lifelong friends with Pavel Alexandrov who involved Kolmogorov in 1936 in an ugly political persecution of their mutual teacher, the so-called Luzin case or Luzin affair. Pavel Sergeyevich Alexandrov (Па́вел Серге́евич Алекса́ндров sometimes romanized Aleksandroff or Aleksandrov ( November 16 Nikolai Nikolaevich Luzin, (also spelled Lusin) Никола́й Никола́евич Лу́зин ( December 9, 1883, Irkutsk – January Nikolai Nikolaevich Luzin, (also spelled Lusin) Никола́й Никола́евич Лу́зин ( December 9, 1883, Irkutsk – January Kolmogorov (together with A. Khinchin) became interested in probability theory. Aleksandr Yakovlevich Khinchin ( Russian Алекса́ндр Я́ковлевич Хи́нчин French Alexandre Khintchine ( July 19, 1894 Probability theory is the branch of Mathematics concerned with analysis of random phenomena Also in 1925, he published his famous work in intuitionistic logic - On the principle of the excluded middle. Intuitionistic logic, or constructivist logic, is the Symbolic logic system originally developed by Arend Heyting to provide a formal basis for Brouwer In 1929 Kolmogorov earned his Doctor of Philosophy degree, Ph.D., at the Moscow State University. "PhD" redirects here for other uses see PhD (disambiguation.

In 1930, Kolmogorov went on his first long trip abroad, traveling to Göttingen and Munich, Germany, and then to Paris, France. Göttingen ( ˈgœtɪŋən, Low German: Chöttingen is a College town in Lower Saxony, Germany. Munich (München; Minga is the capital city of Bavaria, Germany. Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city 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 the world's leading living expert in this field. In Probability theory, the Probability P of some event E, denoted P(E is defined in such a way that P satisfies the 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. The Russian Academy of Sciences (Российская Академия Наук Rossi'iskaya Akade'miya Nau'k, shortened to PAH RAN) consists of the National 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. A stochastic process, or sometimes random process, is the counterpart to a deterministic process (or Deterministic system) in Probability theory. Cold War is the state of conflict tension and competition that existed between the United States and the Soviet Union (USSR and their respective allies from the [2]

In his study of stochastic processes (random processes), especially Markov processes, Komolgorov and the Briton Sydney Chapman independently developed the pivotal set of equations in the field, the Chapman-Kolmogorov equations. A Markov process, named after the Russian mathematician Andrey Markov, is a mathematical model for the random evolution of a memoryless system Sydney Chapman may refer to Sir Sydney Chapman (economist, (1871&ndash1951 British economist and civil servant Sydney Chapman (mathematician In Mathematics, specifically in Probability theory, and yet more specifically in the theory of Markovian Stochastic processes the Chapman - Kolmogorov

Kolmogorov (left) works on his talk (Tallinn, Estonian SSR, 1973)
Kolmogorov (left) works on his talk (Tallinn, Estonian SSR, 1973)
Kolmogorov works on his talk (Tallinn, Estonian SSR, 1973)
Kolmogorov works on his talk (Tallinn, Estonian SSR, 1973)

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. Tallinn (historically known by the German, Swedish and Danish name Reval or the Polish name Rewal, among other names The Estonian Soviet Socialist Republic (Eesti Nõukogude Sotsialistlik Vabariik Эстонская Советская Социалистическая Республика Estonskaya Tallinn (historically known by the German, Swedish and Danish name Reval or the Polish name Rewal, among other names The Estonian Soviet Socialist Republic (Eesti Nõukogude Sotsialistlik Vabariik Эстонская Советская Социалистическая Республика Estonskaya In Fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic Stochastic property changes In classical mechanics, he is best known for the Kolmogorov–Arnold–Moser theorem (first presented in 1954 at the International Congress of Mathematicians). Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects The Kolmogorov–Arnold–Moser theorem is a result in Dynamical systems about the persistence of quasi-periodic motions under small perturbations The International Congress of Mathematicians (ICM is the largest congress in the Mathematics community In 1957 he solved Hilbert's thirteenth problem (a joint work with his student V. I. Arnold). Hilbert's thirteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. Vladimir Igorevich Arnol'd or Arnold (Влади́мир И́горевич Арно́льд born June 12, 1937 in Odessa, Ukrainian SSR He was a founder of algorithmic complexity theory, often referred to as Kolmogorov complexity theory, which he began to develop around this time. In Algorithmic information theory (a subfield of Computer science) the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin In Algorithmic information theory (a subfield of Computer science) the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin

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. Probability is the likelihood or chance that something is the case or will happen Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. A stochastic process, or sometimes random process, is the counterpart to a deterministic process (or Deterministic system) in Probability theory. Mathematical logic is a subfield of Logic and Mathematics with close connections to Computer science and Philosophical logic.

In 1971, Kolmogorov joined an oceanographic expedition aboard the research vessel Dmitri Mendeleev. Oceanography (from the greek words Ωκεανός meaning Ocean and γράφω meaning to write also called oceanology or He wrote a number of articles for the Great Soviet Encyclopedia. The Great Soviet Encyclopedia ( Большая Советская Энциклопедия, or БСЭ; transliterated Bolshaya Sovetskaya Entsiklopediya In his later years he devoted much of his effort to the mathematical and philosophical relationship between probability theory in abstract and applied areas. Probability theory is the branch of Mathematics concerned with analysis of random phenomena [3]

Andrey Kolmogorov passed away in Moscow in 1987.

See also

Bibliography

A bibliography of his works appeared in The Annals of Probability, 17(3): 945--964 (July 1989). In Probability theory, the Probability P of some event E, denoted P(E is defined in such a way that P satisfies the The Kolmogorov backward equation (KBE and its adjoint the Kolmogorov forward equation (KFE are Partial differential equations (PDE that arise in the theory The Fokker–Planck equation describes the Time evolution of the Probability density function of the position of a particle and can be generalized to other observables In Fractal geometry, the Minkowski-Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the Fractal In Fractal geometry, the Minkowski-Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the Fractal In Algorithmic information theory (a subfield of Computer science) the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin In Mathematics, the Kolmogorov continuity theorem is a Theorem that guarantees that a Stochastic process that satisfies certain constrains on the moments In Mathematics, the Kolmogorov extension theorem (also known as Kolmogorov existence theorem) is a Theorem that guarantees that a suitably "consistent" In Probability theory, Kolmogorov's inequality is a so-called "maximal Inequality " that gives a bound on the probability that the Partial sums In Mathematics, the Landau-Kolmogorov inequality is an Inequality between different derivatives of a function In Mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, of Intuitionistic logic was proposed by L Kolmogorov microscales are the smallest scales in turbulent flow. In Topology and related branches of Mathematics, the T0 spaces or Kolmogorov spaces, named after Andrey Kolmogorov, form a broad class In Statistics, the Kolmogorov &ndash Smirnov test (also called the K-S test for brevity is a form of Minimum distance estimation used The Kolmogorov–Arnold–Moser theorem is a result in Dynamical systems about the persistence of quasi-periodic motions under small perturbations In Probability theory, Kolmogorov's zero-one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, called a In Mathematics, a reversible diffusion is a specific example of a reversible Stochastic process. Borel's paradox (sometimes known as the Borel-Kolmogorov paradox) is a Paradox of Probability theory relating to Conditional probability In Mathematics, specifically in Probability theory, and yet more specifically in the theory of Markovian Stochastic processes the Chapman - Kolmogorov Sydney Chapman may refer to Sir Sydney Chapman (economist, (1871&ndash1951 British economist and civil servant Sydney Chapman (mathematician In Algorithmic information theory (a subfield of Computer science) the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin Astronomical seeing refers to the blurring and twinkling of astronomical objects such as stars caused by Turbulence in the Earth's atmosphere

References

  1. ^ David Salsburg, The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century, New York, W. H. Freeman, 2001; pp. 137-50.
  2. ^ Salsburg, p. 139.
  3. ^ Salsburg, pp. 145-7.


External links

Persondata
NAME Kolmogorov, Andrey
ALTERNATIVE NAMES
SHORT DESCRIPTION Mathematician
DATE OF BIRTH April 25, 1903
PLACE OF BIRTH Tambov, Imperial Russia
DATE OF DEATH October 20, 1987
PLACE OF DEATH Moscow, USSR
The MacTutor History of Mathematics archive is an award-winning website maintained by John J A mathematician is a person whose primary area of study and research is the field of Mathematics. Events 1607 - Eighty Years' War: The Dutch fleet destroys the anchored Spanish fleet at Gibraltar. Year 1903 ( MCMIII) was a Common year starting on Thursday (link will display calendar of the Gregorian calendar or a Common year starting TambovSoborJPG|thumb|200px|right|Cathedral in Tambov]] Мост через Цну The Russian Empire ( Pre-reform Russian: Pоссійская Имперія Modern Russian: Российская Империя translit: Rossiyskaya Events 1740 - Maria Theresa takes the throne of Austria. France, Prussia, Bavaria and Saxony Year 1987 ( MCMLXXXVII) was a Common year starting on Thursday (link displays 1987 Gregorian calendar) Moscow (Москва́ romanised: Moskvá, IPA: see also other names) is the Capital and the largest city of The Union of Soviet Socialist Republics (USSR was a constitutionally Socialist state that existed in Eurasia from 1922 to 1991
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