Chinese name: Cole Molokov
Place of birth: Russia
Place of birth: Russia
Gender:: Male
Nationality: Soviet Union
Date of birth:1April 25th, 903.
Date of death:1987 65438+1October 20th.
Occupation: Mathematician
Graduate School: Moscow University
Representative works: probability theory, algorithmic information theory, topology, etc.
character introduction
The life of the character
André Andrey Kolmogorov1903 On April 25th, André Andrey Kolmogorov was born in the Russian city of Tambov. His father, an agronomist and writer, worked in a government department and died in 19 19. His mother was born in a noble family, in his
19 10, he entered the preparatory class of a grammar school in Moscow, and soon showed a strong interest in all subjects: 14 years old, he began to teach himself advanced mathematics, learned a lot of mathematical knowledge, and mastered many mathematical ideas and methods.
1920 graduated from high school and entered Moscow university. He studied history first, then turned to mathematics, and decided to take mathematics as his lifelong career. He published a paper in his third year of college, which showed his outstanding mathematical ability and won an international reputation. 1925 After graduating from university, he became a graduate student.
1929 After graduation, he worked as an assistant researcher in the Institute of Mathematical Mechanics of Moscow University.
1935 obtained the first batch of doctoral degrees in the Soviet Union. 193 1, professor of Moscow university, guiding graduate students.
1933 served as the director of the Institute of Mathematical Mechanics of Moscow University, founded the teaching and research section of probability theory, mathematical statistics, mathematical logic and probability statistical methods, and taught mathematical analysis, ordinary differential equations, complex variable function theory, probability theory, mathematical logic and information theory successively.
1939 was elected as an academician of the former Soviet Academy of Sciences, a member of the presidium and the director of the Institute of Mathematics.
From 65438 to 0954, he was the head of the Department of Mathematical Mechanics of Moscow University.
1966 was elected as an academician of the former Soviet union institute of education.
1987 10 died in Moscow on 10, at the age of 84.
Hobbies and interests
Andre Andrey Kolmogorov loves life and has a wide range of interests, such as travel, skiing, poetry, art and architecture. He is very modest and never boasts of his achievements and honors. He is indifferent to fame and fortune and doesn't value money. He donated the prize money to the school library and didn't win the Wolf Prize of 654.38 million dollars. He is a scientific giant with noble moral character and lofty selfless dedication.
teacher
André Andrey Kolmogorov was the editor-in-chief of the mathematics subject in the Encyclopedia of the Soviet Union, and the editor-in-chief of the journal Achievements in Mathematical Science for a long time. He founded the academic magazine Probability Theory and its Application and the popular science magazine Quantum for middle school students. He attaches great importance to middle school mathematics education. Since the 1930s, he has been guiding the national middle school students' mathematical Olympic activities, compiling counseling books and giving lectures to students in person. A boarding school for physics and mathematics has been established, and a large number of outstanding middle school students have been trained.
He has served as the director of the Mathematics Department of the Science Education Committee of the Soviet Academy of Sciences and the director of the Mathematics Department of the Middle School Textbook Committee of the Ministry of Education, presided over the compilation of the middle school mathematics syllabus and textbooks, and engaged in teaching reform experiments. He published 488 academic papers (including cooperative articles) and 57 popular science articles in his life. He is a great educator. He loves students, is strict with them and has good guidance. There are 67 students who directly guide them. Most of them became world-class mathematicians, and 14 of them became academicians of the former Soviet Academy of Sciences.
Research scope
André Andrey Kolmogorov has profound knowledge of Russian ancient architecture, Russian poetry, world sculpture and painting. He regards poetic style as a field of his scientific research. He also loves music. Mozart's Symphony in G minor and Bach's Violin Concerto often accompany him and Aleksandrov (and often many friends) to spend quiet nights in Komalov.
Achievement honor
Stochastic mathematics
In stochastic mathematics-probability theory, stochastic process theory and mathematical statistics.
1924 When he was in the fourth year of college, he established a third-order theorem about independent random variables with the then Soviet mathematician Qin Xin.
In 1928, he obtained the necessary and sufficient conditions for the sequence of random variables to obey the law of large numbers.
In 1929, the law of iterated logarithm of independent and identically distributed random variable sequences is obtained.
In 1930, a very general sufficient condition of strong law of large numbers is obtained.
193 1 published the article "analysis method of probability theory", which laid the foundation of Markov process theory. Markov process is widely used in physics, chemistry, biology, engineering technology and economic management, and it is still one of the hot spots and focuses of mathematics research in the world today.
In 1932, the necessary and sufficient conditions for the infinitely separable distribution law of second-order moment random variables are obtained.
1933 published the book "Fundamentals of Probability Theory", which established the axiomatic conclusion of probability theory on the basis of measure theory and integral theory for the first time in the world. This is an epoch-making masterpiece, which wrote the most brilliant page of mathematics in the former Soviet Union in the history of science.
1935 put forward the concept of reversible symmetric Markov process and its necessary and sufficient conditions, which became an important model in statistical physics, queuing network, simulated annealing, artificial neural network and protein structure.
1936— 1937 gives the state distribution of countable Markov chains.
1939 defines and obtains the statistic of maximum deviation between empirical distribution and theoretical distribution and its distribution function. In 1930s-1940s, together with Qin Xin, he developed the theory of Markov process and stationary stochastic process, which was applied to the automatic control of artillery and industrial and agricultural production and played a neutral role in the Great Patriotic War.
194 1 year, he obtained the prediction and interpolation formulas of stationary random processes.
From 1955 to 1956, he and his student, the Soviet mathematician prokhorov, initiated the weak limit theory of the probability measure of the mean value in the function space. This theory and D-space theory introduced by Soviet mathematician A.B. Skorokhod are epoch-making achievements of weak limit theory.
In pure mathematics and mathematics of deterministic phenomena
192 1 When he was a sophomore, he began to study many complicated problems such as trigonometric series and operators on sets, which made him famous all over the world.
1922 defines the basic operations in set theory.
1925 proves that law of excluded middle is established in transfinite induction, constructs an intuitive calculus system, and proves a Chebyshev inequality in Hilbert transform. 1932 studies geometry from the viewpoint of topology and group theory.
The cohomology group constructed by 1936 and its operation.
1935 ——1936 introduced approximation measure, which initiated a new direction of approximation theory.
In 1937, the open mapping from one-dimensional compact set to two-dimensional compact set is given.
From 1934 to 1938, the concepts of linear topological space and its bounded set and convex set are defined, which promotes the development of functional analysis. In the mid-1950s, he established the KAM theory with the third-year university student V.I.Arnord and the German mathematician J.K. Morsel, and solved the basic problems in the dynamic system. He used information theory to study the ergodicity of systems, which became a new starting point for the development of power system theory.
From 1956 to 1957, he put forward the basic idea of solving problems, and his student Arnold completely solved Hilbert's 13 problem.
applied mathematics
In biology:
In 1937, he first constructed the stable solution of the nonlinear diffusion traveling wave;
1947 proposed the branching process and its extinction probability;
1939 verified Mendel's law of gene inheritance;
In metallography:
In 1937, the probability that a given point belongs to a crystal cluster and the average number of crystals in the process of random crystallization of metals are studied.
194 1 year, the prediction and interpolation formulas of stochastic processes are applied to natural phenomena such as radio engineering, automatic control of artillery, atmosphere and ocean. In fluid mechanics, the approximate formula of local isotropic turbulence was obtained in the 1940s.
Throughout his life, André Andrey Kolmogorov has made outstanding contributions to pure mathematics or applied mathematics, mathematics of deterministic phenomena or random mathematics, mathematics research and mathematics education.
Honorary awards
Because of his outstanding achievements, he enjoys a high reputation at home and abroad.
He is a foreign academician of more than 20 academies of science, including the United States, France, the Democratic Republic of Germany, the Netherlands, Poland and Finland.
Foreign member of the Royal Society; He is an honorary doctor of many universities, such as Paris University in France and Warsaw University in Poland.
1963 won the International Balm Award, 1975 won the Hungarian Medal, 1976 won the American Meteorological Society Medal, Helmholtz Medal of the Democratic Republic of Germany, and 1980 won the world's most famous Wolff Prize. In China, 194 1 won the national prize, 195 1 won the Chebyshev Prize of the Soviet Academy of Sciences, 1963 won the title of Soviet hero, 1965 won the Lenin Prize, and1946 won the Lenin Prize. From 1944 to 1979, he won seven medals of Lenin, Venus and Brave Labor in the Great Patriotic War; Received the October Revolution Medal from 1983; Won the Lobachevsky Prize from 1986.
Character experience
Early experience
André Andrey Kolmogorov was born on April 25th, 1903 in Tampov province, Russia, and died on October 20th, 1987/kloc-0. His grandfather was a priest and his father Kataev was an agronomist. After the October Revolution, he was exiled to China and served as the leader of a Ministry of Agriculture. He died in 19 19. My mother was born into a noble family and died in childbirth. Andre Andrey Kolmogorov spent his childhood in his grandfather's house, and his menstruation brought him up. Although he lost his maternal love after his birth, and never got his father's love, Andre Andrey Kolmogorov grew up in love. At an early age, menstruation taught him to love learning knowledge and nature. At the age of five or six, Andre Andrey Kolmogorov discovered the relationship between odd numbers and square numbers:1=12,1+3 = 2 2,1+3+5 = 3 2,1+3+. Grandfather's family runs a family magazine, Chun Yan, and young Andre Andrey Kolmogorov is in charge of the math column. He published his findings in a magazine.
At the age of six, he went to Moscow with his period, where he was considered to be the most progressive preparatory school. While studying, André Andrey Kolmogorov had a wide range of interests. He studies biology and physics seriously.
/kloc-When he was 0/4 years old, he learned advanced mathematics from an encyclopedia. He is also interested in chess, social issues and history.
1920 After graduating from high school, Andre Andrey Kolmogorov worked as a train conductor for a while; After work, he wrote a pamphlet about Newton's laws of mechanics. In the same year, Andrei Andrey Kolmogorov Love entered Moscow University to study. Besides mathematics, he also studied metallurgy and Russian history. He was particularly fascinated by history, and once wrote a paper on the property of landlords in Novgrad in the 6th century15-/kloc-0. Regarding this paper, his teacher, S.V.Bakhrushin, a famous historian, said: "You provided a proof in your paper, which may be enough in the mathematics you studied, but it is not enough for a historian. He needs at least five kinds of proof. " Perhaps the history professor's answer had an important influence on André Andrey Kolmogorov: he chose mathematics that only needed one kind of proof.
Break into the kingdom of mathematics
At Moscow University, André Andrey Kolmogorov listened to the class of the great mathematician Luzin (N.N. Luzin, 1883- 1950), and had a conversation with Luzin and Aleksandrov (P.S.Alexandrov,1896-1950). André Andrey Kolmogorov also took part in the discussion class of stepanov trigonometric series (1889-1950), which solved a problem raised by Luzin. Jin Lu admired him very much and offered to accept him as an apprentice.
Although Andre Andrey Kolmogorov is only a college student, he has made remarkable achievements: in February 1922, he published a paper on set operation, which popularized suslin's results; In June of the same year, he published a Fourier series that diverged almost everywhere (to 1926, and he further constructed a Fourier series that diverged everywhere). According to himself, he came up with this series on the train when he was a train conductor. Andre Andrey Kolmogorov became a shining star in the world of mathematics for a while. Almost at the same time, he became interested in many other fields in analysis, such as differential and integral problems, measure theory and so on.
1925, graduated from André Andrey Kolmogorov University and became a graduate student in Jin Lu. This year, Andre Andrey Kolmogorov published eight papers written during his college years! In every paper, he introduced new concepts, new ideas and new methods. His first paper on probability theory was published this year. This paper was completed in cooperation with Qin Xin (A.Y.Khinchin, 1894- 1959), which included the theorem of trigonometric series and the inequality about the partial sum of independent random variables, and later became the basis of martingale inequality and stochastic analysis. He proved a Chebyshev inequality of Hilbert transform, which later became the pillar of harmonic analysis.
In 1928, he obtained the necessary and sufficient conditions for the sequence of independent random variables to satisfy the law of large numbers; In the second year, the broad conditions of the law of iterated logarithm were discovered. In addition, his work also includes differential and integral operations and some generalizations of intuitionistic logic.
1929 In the summer, André Andrey Kolmogorov and Aleksandrov sailed from yaroslavl, crossed the Caucasus mountains along the Volga River, and finally arrived at Sevan Lake in Armenia, where they settled on an island. There, while enjoying swimming and sunbathing, Aleksandrov wore sunglasses and a Panama hat and wrote a book on topology in the sun. This book cooperated with hopf (H.Hopf,1894-1971) and became a classic as soon as it came out. André Andrey Kolmogorov studied continuous state and continuous time Markov processes in the shade of trees. André Andrey Kolmogorov's achievement is published in 193 1, which is the origin of diffusion theory.
The lifelong friendship between the two began with this long trip. Aleksandrov later recalled: "1979 is the 50th anniversary of my friendship with André Andrey Kolmogorov. Throughout the half century, this friendship has never stopped, and there has never been a quarrel. There has never been any misunderstanding between us on any issues, no matter how important these issues are to our life and our philosophy; Even if there are differences on a certain issue, we fully understand and sympathize with each other's views. " Andre Andrey Kolmogorov regards this friendship as the reason for his happy life!
/kloc-in the summer of 0/930, André Andrey Kolmogorov and Aleksandrov made another long trip. This time they went to Berlin, G? ttingen, Munich and Paris. Andre Andrey Kolmogorov met Hilbert (D. Hilbert, 1862- 1943), Courand (R. Courand, 1888- 1972) and Landau (E. Landau,/kloc- 1885- 1955), Karatai audrey (Karatai audrey, 1873- 1950), Fréchet (Fréchet,1878-/kloc-0). 187 1- 1956)、Levi (P.Lévy， 18486- 197 1)、Lebesgue (H.Lebesgue， 1875-66)。 The period of 1930 is the second creative peak of Andre Andrey Kolmogorov's mathematical career. During this period, he published more than 80 papers, involving probability theory, projective geometry, mathematical statistics, real variable function theory, topology, approximation theory, differential equations, mathematical logic, biological mathematics, philosophy, mathematical history and mathematical methodology.
193 1, André Andrey Kolmogorov was hired as a professor by Moscow University.
1933 published "Fundamentals of Probability Theory", a classic work of probability theory. This book bases probability theory on strict axioms for the first time, solves the probability part of Hilbert's sixth question, marks the beginning of a new stage of probability theory development, and has epoch-making significance. In the same year, André Andrey Kolmogorov published an important paper "Analytical Methods in Probability Theory", which laid the foundation of Markov random process theory. Since then, Markov process theory has become a powerful scientific tool. In topology, Andre Andrey Kolmogorov is one of the founders of linear topological space theory; He and the famous American mathematician J.W. Alexander (1888- 197 1) independently introduced the concept of cohomology group at the same time.
In 1934, Andre Andrey Kolmogorov studied the cohomology of chain, winding, homology and finite cell complex. In the paper published in 1936, Andre Andrey Kolmogorov defined the concept of cohomology group of any locally compact topological space. 1935, at the Moscow International Topology Conference, André Andrey Kolmogorov defined the cohomology ring.
1935, Andrei Andrey Kolmogorov and Alexanderov bought an old mansion in a small village outside Moscow called komarov Ka. Much of their math work was done here. Many famous mathematicians have been to Komalov Card, including J. Hadamard (1865- 1963), Fréchet, Banach (S.Banach, 1892- 1945), hopf and K. Kuratowski. Graduate students from Moscow University often go together. In the evening, although the students are a little tired, they always return to Moscow happily with their math gains. Malcef (A.I.Malcev, 1909- 1967) and Gelfand (I.M.Gelfand, 19 13-) who later became academicians of the Soviet Academy of Sciences are two of them. Andre Andrey Kolmogorov's famous mathematician and doctoral student B.V.Gnedenko (19 12- 1995) recalled: "For all the students of André Andrey Kolmogorov, the years they studied under André Andrey Kolmogorov were unforgettable: the hardships in science and culture. Unforgettable is the outing on Sunday. Andre Andrey Kolmogorov invited all his students (graduate students or undergraduates) and other tutors' students. In these outings from 30 to 35 kilometers away to Porche, Kryazma and other places, we have been discussing the current problems of mathematics (and its application) and cultural progress, especially painting, architecture and literature. "
At the end of 1930, Andre Andrey Kolmogorov developed the theory of stationary stochastic processes, and the American mathematician Wiener (N.Wiener, 1894- 1964) later got the same result. Andre Andrey Kolmogorov also expanded his research field to planetary motion and air theory of turbulence. In the1940s, Andre Andrey Kolmogorov's interest turned to application.
194 1 year, he published two papers on turbulence of great significance, which became one of the most important contributions in the history of theory of turbulence. A famous result obtained by Andre Andrey Kolmogorov is the "two-thirds law": in turbulent flow, the square average of the velocity difference between two points with a distance of r is directly proportional to r2/3. During this period, in addition to mathematics, André Andrey Kolmogorov also made important contributions to genetics, ballistics, meteorology and metal crystallography. In the paper published in 1940, Andre Andrey Kolmogorov proved that the materials collected by the followers of lysenko (1898- 1976) supported Mendel's law. At that time, Mendel's law was criticized in the Soviet Union, and André Andrey Kolmogorov's paper reflected his scientific spirit of pursuing truth.
The period from 65438 to 0950 was the third creative peak of André Andrey Kolmogorov's academic career. The research fields in this period include classical mechanics, ergodic theory, function theory, information theory, algorithm theory and so on.
1953 and 1954, Andre Andrey Kolmogorov published two papers on dynamical systems and their applications in Hamiltonian dynamics, which marked the beginning of KAM (Kolmogorov-Arnold-Moser) theory. From 65438 to 0954, André Andrey Kolmogorov was invited to give an important report on "General Theory and Classical Mechanics of Dynamical Systems" at the International Congress of Mathematicians in Amsterdam. Later research proved his profound insight. During this period, Andre Andrey Kolmogorov also began to study automata theory and algorithm theory. He and his student V.A.Uspenskii established an important concept called "Andre Andrey Kolmogorov -Uspenskii machine". He also opposed it and supported the research of computing theory. Many Soviet computer scientists are students or students of André Andrey Kolmogorov.
In the middle and late 1950s, André Andrey Kolmogorov devoted himself to the research of information theory and ergodicity theory of dynamical systems. He introduced the important concept of entropy into the dynamic system theory, which opened up a vast new field and later led to the birth of chaos theory.
From 1958 to 1959, André Andrey Kolmogorov applied ergodic theory to a kind of turbulence phenomenon, which had a far-reaching impact on later work.
1957, Andre Andrey Kolmogorov and student Arnold completely solved Hilbert's 13 problem: there are continuous ternary functions, which cannot be expressed as the superposition of binary continuous functions. The answer is no: the continuous function of any number of variables can be expressed as the superposition of single-variable continuous functions.
/kloc-after the 1960s, Andre Andrey Kolmogorov founded two branches of calculus information theory (now called "Andre Andrey Kolmogorov's complexity theory") and calculus probability theory. Andre Andrey Kolmogorov's research covers almost all fields of mathematics except number theory. 1963 At the conference on probability statistics held in Tbilisi, American statistician J. Wolfowitz (1910-1981) said, "The special purpose of my coming to the Soviet Union is to determine whether André Andrey Kolmogorov is a person or a research institution."
Unique teaching and research methods
During his academic career of more than half a century, André Andrey Kolmogorov kept raising new questions, constructing new ideas and creating new methods, and maintained lasting vitality in the world mathematics stage, which was due to his healthy body to some extent. He loves physical exercise very much and is called "outdoor mathematician". He and Aleksandrov live in Komalov card four days a week (the other three days in the school apartment in the city). Physical exercise lasts a whole day: skiing, boating and hiking (the average distance is as long as 30 kilometers). On a sunny March day, they often wear ski shoes and shorts to exercise outdoors for four hours. Exercise is uninterrupted in the morning on weekdays, and you have to run again in winter 10 km. They also like to swim in the water when the river ice melts.
During the celebration of Andre Andrey Kolmogorov's 70th birthday, he organized a skiing trip. Andre Andrey Kolmogorov, wearing shorts and bare arms, is old and strong, leaving all the other participants behind! Many of his wonderful and key ideas are often born while walking in the Woods, swimming in the lake and skiing on the hillside.
During his visit to India on 1962, he even suggested that all universities and research institutes in India should be built on the coastline, so that teachers and students can swim first and then start serious discussions. Andre Andrey Kolmogorov is also a famous mathematics educator. He is particularly interested in the plan of providing special education for students with mathematical talent. He believes that some parents and teachers try to dig out children with mathematical talent from students aged 10 ~ 12, which will do harm to children. But when 14 ~ 16 years old, the situation changed. It is usually obvious whether children of this age are interested in mathematics. About half of them think that mathematical physics is of little use to them, and these students should take special simplified courses. The math education of the other half students can be carried out more effectively. When choosing a major in mathematics, these students should also test their adaptability to mathematics-calculation ability, geometric intuition ability and logical reasoning ability. André Andrey Kolmogorov founded the boarding school for mathematics at Moscow University. Over the years, he spent a lot of time in school, drawing up teaching syllabus, compiling teaching materials, giving lectures (up to 26 hours per week), leading students to explore on foot, teaching students music, art and literature, and seeking the natural development of children's personality. The students in his school are often among the best in the all-Soviet and international mathematical olympiads. But for those students who can't become mathematicians, he is not worried. No matter what occupation they end up in, he will be satisfied if they can keep their eyes open and curiosity. How lucky a student will be if he can enter Andre Andrey Kolmogorov's big family! As one of the most outstanding mathematicians in the 20th century, André Andrey Kolmogorov won many honors:
194 1 won the first Soviet state award;
1949 won the Chebyshev Prize of the Soviet Academy of Sciences;
1963 won the international bazin award; 1965 won the Lenin Prize; 1976 won the Helmholtz medal of the Democratic German Academy of Sciences;
He won the Wolf Prize with 1980 and the Lobachevsky Prize with 1986. He also won the Lenin Medal seven times before and after.
1939, André Andrey Kolmogorov was elected as an academician of the Soviet Academy of Sciences. It is also the Polish Academy of Sciences (1956), the Royal Statistical Society of London (1956), the Romanian Academy of Sciences (1957), the German Academy of Sciences (1959), the American Academy of Arts (1959), and the United States. Foreign academicians or honorary members such as the Royal Society of London (1964), Hungarian Academy of Sciences (1965), American National Academy of Sciences (1967), French Academy of Sciences (1968) and Finnish Academy of Sciences (1983). He was awarded honorary doctorates by the University of Paris (1955), Stockholm University (1960), Indian Institute of Statistics (1962), Warsaw University and Budapest University.