Andrei Nikolaevich Kolmogorov (1903-1987) is an outstanding scientist of the 20th century. The mathematician was born on April 25, 1903 in the provincial city of Tambov. The mother of the future academician, Maria Yakovlevna Kolmogorova, became very ill during childbirth and died, and his aunt V. Ya. Kolmogorova took the boy to live with her. All early years little Andryusha was in the grandfather's house in the village. Tunoshna, Yaroslavl region. Grandfather was a church father. The father of the mathematician, Kataev Nikolai Matveevich, had an agronomic education, but perished (1919) in the flames of the civil war, fighting on the Southern Front with the White Guard troops.
According to the scientist himself, he became interested in mathematics at the age of 6, discovering for himself "the joy of mathematical knowledge" in it. In that grandfather's village, his aunts set up a kind of school for a group of children and taught them in their own way. last word pedagogy. The father did not raise his son.
In 1910, the aunt took the boy to Moscow, where he studied at the educational institution of E.A. Repman, who became school after the revolutionary events. No. 23. Ten years later, at the end of it, he enters the Moscow State University for physics and mathematics. In addition to exact science, Kolmogorov is also seriously interested in history, at the same time studying at the mathematical department of KhTI. DI. Mendeleev. A student of Kolmogorov L.A. Bassalygo found and published the early historical works of his teacher.
According to the recollections of a former Soviet student, he was very prosperous, having received after a successfully passed exam "an opportunity every month for a pood of bread and 1 kg of butter."
In 1922, a very young boy receives worldwide recognition for having constructed a Fourier series that diverges almost everywhere. Subsequently, the scientist successfully teaches, is a professor at Moscow State University, and is friends with science, he directs the Institute of Mathematics and Mechanics at his native university. In 1935 he founded a new department of probability theory. He will manage it until 1966.
From 1922 to 1925 he was a teacher of mathematics, educates schoolchildren at the Potylikhinsky People's Commissariat of Education. He explains his work at the middle level by the great need for money, but he recalls it with pleasure and moral satisfaction, as he managed to instill in his science the interest and love of students.
Since 1924 he has been fond of probability theory. The debut on this topic is "On the convergence of series whose members are determined by chance" (together with A.Ya. Khinchin). N.N. Luzin was my favorite mentor all these years.
Among the works of that time is also "On the principle of" tertium non datur ". By 1927, the completion of work on the law of the repeated logarithm belongs. Not all of Kolmogrov's works were approved by his senior comrade N.N. Luzin, some were published a few years after their writing.
In 1929, Kolmogorov completed his postgraduate studies without defending a dissertation. The current order was introduced only in 1934. Since 1936, Andrei Nikolaevich has been enthusiastically working on the creation of the famous Soviet encyclopedias (BSE and ITU). Being at the head of the department of mathematics, he creates a large number of articles for this edition.
1939 brought A.N. Kolmogorov membership in the Union Academy, and until 1942 he worked as an academician-secretary of the department of physical and mathematical sciences. At the turn of the 30s-40s. he is fond of turbulence and, after the end of hostilities in the country, establishes from scratch the laboratory of atmospheric turbulence of the Institute of Theoretical Geophysics of the USSR Academy of Sciences. Before the most treacherous German attack (1940), he was awarded the Order of the Red Banner of Labor, and in 1941-1945. does not stand aside and develops a series of articles on the theory of shooting.
In 1942 Kolmogorov got married. Anna Dmitrievna Egorova, a former school friend from the gymnasium, becomes his chosen one. With her, he lived more than a dozen happy years. His wife survived him by only one year, dying in 1988.
In the 60s. he created a unique laboratory of probabilistic and statistical methods. Until 1976, Kolmogorov was its head. The idea of creating visited the scientist after his Indian trip, where he was greatly impressed by the work of the statistical institute. Such a laboratory was an innovation for the USSR. The great mathematician came up with an idea for a completely new specialty at that time - biometrics.
Attention is also paid to the state of teaching mathematics in the school of the era of socialism. In collaboration with P.S. Alexandrov created a wonderful "Algebra", which taught more than one generation of the USSR algebraic wisdom. Together with S.V. Fomin they release tutorial"Elements of the theory of functions..." (1st edition). Under him, a boarding school for physics and mathematics was founded at Moscow University; since 1989, the school has been named after Academician A.N. Kolmogorov. In addition, he edited the printed edition "Uspekhi matematicheskikh nauk" until his death, and through his efforts the youthful journal "Kvant" appeared.
Lives active scientific life, participating in mathematical conferences and congresses around the world. He was awarded the Stalin Prize by the government, repeatedly the Order of Lenin (7) and the medal "For Valiant Labor", the Prize to them. P.L. Chebyshev of the Academy of Sciences of the USSR, is an honorary member of the IMO, Hero of Socialist Labor, winner of the International Balzan Prize, The Wolf Foundation and many others. others
Venerable contemporaries remember Kolmogorov not only because he was an outstanding scientist, but also because he was a real person. He warmed many talented mathematicians under his wing and saved them from attacks and misunderstanding on the part of their superiors. He was also a talented administrator, under him his favorite faculty reached its highest peak. When moving to the Mathematical Institute. V.A.Steklov Academy of Sciences of the USSR, head of the Department of Mathematical Statistics and Information Theory.
On October 20, 1987, the genius Kolmogorov, who worthily occupies an honorable place among world-class scientists, passed away. The academician was buried at the Novodevichy cemetery.
(1903-1987) Russian mathematician
Andrei Nikolaevich Kolmogorov was born in 1903 in the city of Tambov. In the same year, his mother, Maria Yakovlevna, died, he was adopted and raised by his mother's sister, Vera Yakovlevna. Andrey treated her like a mother. Father, Nikolai Matveevich Kataev, was the son of a priest, received a higher agronomic education. The surname Andrey Nikolaevich took his mother's, since the father did not take any part in the upbringing of his son. So, according to his mother, Andrei Nikolaevich Kolmogorov had noble origin: his grandfather Yakov Stepanovich was an Uglich leader of the nobility. He had a large house in Yaroslavl and not far from Yaroslavl, the Tunoshna estate on the Tunoshonka river, in the place where it flows into the Volga. Andrei's childhood passed just in this estate.
In 1910, Vera Yakovlevna moved to Moscow with seven-year-old Andryusha. They lived on interest from the capital received from their father, but after the revolution, everything became more complicated. Vera Yakovlevna had to work in order not to die of hunger: she worked as a club manager, librarian, and clerk.
In Moscow, Andrei studied at the private gymnasium E.A. Repman, which after the revolution became the 23rd secondary school. After school, 17-year-old Andrei Kolmogorov worked on the Moscow-Sverdlovsk railway. In the autumn of 1920, he entered the Moscow State University at the Faculty of Physics and Mathematics. In the third year of the university, Andrei Nikolaevich went to school after lectures and began working as a teacher of mathematics and physics. In his first year, Kolmogorov attended lectures by N.N. Luzin, at the seminar he solved the problem posed by the teacher. Upon learning of this, N.N. Luzin invited Andrei Kolmogorov to become his student.
During his student years, Kolmogorov's work made his name known in the mathematical world. After university, he became a graduate student of Luzin. Simultaneously with another student of Luzin, A.Ya. Khinchin works in the field of probability theory. As Andrei Kolmogorov later wrote in his autobiography, "probability theory is my main narrow specialty."
Since 1929, the friendship of two great mathematicians - Andrei Nikolaevich Kolmogorov and P.S. Alexandrova. They are not separated for the rest of their lives. In 1982, on the day of the death of Pavel Sergeyevich Aleksandrov, Kolmogorov said: “For me, these 52 years of our close and inseparable friendship were the basis for the fact that my whole life as a whole turned out to be full of happiness, and the basis of my well-being was the unceasing care on the part of Pavel Sergeyevich ".
In 1931 Andrei Kolmogorov became a professor at Moscow State University. And two years later, his main monograph "Basic Concepts of Probability Theory" was published.
In the autumn of 1942, Andrei Nikolayevich married Anna Dmitrievna Egorova, whom he knew from school.
Before the war, he worked in the field of random processes, turbulence, algebraic topology, and during the war, like all scientists, he helped military engineering science.
After the war, the next rise in the creativity of the already world-famous scientist is associated with his work on celestial mechanics, Hilbert's problems, dynamical systems, and information theory. He becomes a professor at the University of Paris and the University of Berlin. Humboldt. According to Academician P.S. Aleksandrov, “Andrei Nikolaevich Kolmogorov holds the first place among all Soviet mathematicians in terms of the number of foreign academies and scientific societies that have elected him as their member, as well as universities that have made him their honorary doctorate. Among them we find: the Paris Academy of Sciences, the Royal Society of London, the All-German Academy "Leopoldina", the National Academy of the USA, founded by W. Franklin American philosophical society, Paris, Berlin, Warsaw universities and others.
If you open the well-known monograph by Abraham and Marsden "The Foundations of Mechanics", then in the gallery of portraits of great mechanical scientists we find both a portrait of Archimedes and a portrait of Andrei Kolmogorov. Kolmogorov's name is known in the most various fields modern science: the theory of shooting, the theory of statistical methods for controlling mass production, etc. And the famous scientist Dmitry Sergeevich Likhachev agreed to be the editor of the collection of poems by Andrei Nikolayevich Kolmogorov (Andrey Nikolayevich was engaged in the theory of verse).
He was the editor of the mathematical section of the 1st edition of the Great Soviet Encyclopedia, deeply engaged in mathematical education in schools and universities. Among his students are the world famous researchers M.D. Millionshchikov, Yu.V. Prokhorov, B.V. Gnedenko, I.M. Gelfand and others.
He was called a man of the Renaissance, a man of antiquity. One of the main dimensions of the great scientist's creativity is the depth of research. “In everything I want to get to the very essence,” said Pasternak, and Kolmogorov penetrated in his research to the maximum depth of the issue, reached the essence of the problem. The genius of his research results is confirmed by the fact that over time they are used again and again, new grains of scientific truth are found in them. The fact is that the genius of Andrei Kolmogorov was ahead of his time. His pedagogical ideas are the ideas of the 21st century. He knew the school from the inside as a teacher and from the outside as a great mathematician and as the organizer of the boarding school at Moscow State University. Mikhail Vasilyevich Lomonosov.
Andrei Kolmogorov was simple and accessible, and at the blackboard, stained with chalk, and in a kayak with his student, and in the evening by the fire, where the students were always next to the academician. Let us add that Kolmogorov's school has no equal in the world.
He was a Hero of Socialist Labor and was awarded many orders and prizes.
E. N. Filinov
The creation and application of electronic digital computers was based on the powerful foundation of the developments of domestic mathematical schools, which made a significant contribution to world science. The rapid start of the nuclear and space programs, the implementation of which provided the USSR with strategic parity in the 1950s and 1960s, became possible thanks to the most important results obtained by mathematicians during the pre-war decade.
On the other hand, the development of mathematics itself, after the advent and the beginning of the use of computers for solving computational and non-computational problems, received new incentives.
Among many eminent representatives Moscow School of Mathematics played an outstanding role academician A.N. Kolmogorov, which owns fundamental results in most branches of mathematics.
Andrei Nikolaevich Kolmogorov was born on April 12 (25), 1903 in the city of Tambov. In 1925 he graduated University of Moscow. A.N. Kolmogorov belonged to the Moscow school of mathematics headed by Academician N.N. Luzin. The first student works of Andrei Nikolaevich were published in 1923-1925. in the journal Fundamenta mathematicae, which indicated their high scientific level.
In the rank of Professor A.N. Kolmogorov was approved in 1930, and received the degree of Doctor of Physical and Mathematical Sciences in 1935. In January 1939, A.N. Kolmogorov was elected a full member of the USSR Academy of Sciences in the Department of Mathematics and natural sciences(mathematics).
In set theory, continuing the work of N.N. Luzina, A.N. Kolmogorov laid the foundations for constructing systems of operations on sets, which he published in the Mathematical Collection back in 1928.
In the theory of functions, a student work in 1923, establishing the existence of an almost everywhere divergent Fourier series, made A.N. Kolmogorov known to the whole world.
In topology, A. N. Kolmogorov (in parallel with the American scientist J. W. Alexander) proposed the fundamental foundations of the theory of cohomology.
AN Kolmogorov's contribution to the general theory of dynamical systems and classical mechanics was characterized at the International Congress of Mathematicians in 1954 in Amsterdam as an important historical milestone in the development of science. In the field of the theory of dynamical systems, A.N. Kolmogorov discovered a new method that allows one to describe perturbations of conditionally periodic motions, which is considered one of the greatest achievements of mathematics in the 20th century. The Kolmogorov-Arnold-Moser (KAM) method plays important role in nonlinear mechanics.
In the theory of algorithms A.N. Kolmogorov owns the definition of the general concept of an algorithm and the creation of a theory of the complexity of constructive objects. Results related to discrete automata and finite algorithms were reported by A.N. Kolmogorov at the Fourth All-Union Mathematical Congress in 1963 and largely determined further development in this area. He continued the study of the Markov theory of normal algorithms, namely those algorithms that are to be implemented using digital computers.
In the theory of probability A.N. Kolmogorov was the recognized head of science throughout the world. In 1933 he wrote the work " Basic concepts of probability theory”, which was published in Berlin on German, and then translated into Russian in 1936. It determined the development of the theory of probability. Classical monograph by A.N. Kolmogorov " Theory of Probability and Mathematical Statistics”, in which he outlined the current state of this branch of mathematics, was published in 1986.
In mathematical logic A.N. Kolmogorov was one of the first to study intuitionistic logic as a subject of mathematical research. A.N. Kolmogorov had a great influence on the development of Russian schools of mathematical logic.
In the study of the famous Hilbert's thirteenth problem on superpositions, Andrei Nikolaevich established in 1956 the possibility of representing any continuous function (from arbitrarily a large number variables) as a superposition continuous functions three variables. At the same time, he put forward ideas that allowed his student IN AND. Arnold(then to a third-year student) to reduce the number of variables in this result from three to two and thereby finally solve Hilbert's 13th problem. At the same time, the answer turned out to be the opposite of that expected by D. Hilbert in 1900 when posing the problem. As you know, D. Hilbert proposed to prove that a specific continuous, even algebraic, function cannot be represented as a superposition of continuous functions of two variables. In 1957 A.N. Kolmogorov strengthened the result of V.I. Arnold, showing that any continuous function of an arbitrary number of variables can be represented as a superposition of continuous functions of one variable and the only function of two variables, the addition function.
Finally, A. N. Kolmogorov owns the most important results in information theory related to approaches to the definition of the concept of the amount of information and entropy and allowing to turn it into a rigorous mathematical science(and not just a technical discipline that studies the problems of information transmission). A.N. Kolmogorov together with I.M. Gelfand and A.M. Yaglom made a fundamental report at the Third All-Union Mathematical Congress in 1956 " The amount of information and entropy for continuous distributions ". Unlike Shannon's theory of information, which is based on the concept of probability, Kolmogorov's theory does not use this concept. On the contrary, it itself makes it possible to state in a new language the basic laws of probability theory and even to give a rigorous mathematical definition an individual random object (which the traditional probability theory is unable to do). The definition of the randomness of an individual object is given by A.N. Kolmogorov in terms of algorithms. In his famous article "On the logical foundations of information theory and probability theory" in 1969, A.N. Kolmogorov pointed out that:
- the basic concepts of information theory should and can be justified without resorting to the theory of probability and in such a way that the concepts of "entropy" and "amount of information" are applicable to individual objects;
- the concepts of information theory introduced in this way can form the basis of the concept of random, corresponding to the natural idea that randomness is the absence of regularity.
A.N. Kolmogorov was directly involved in solving a number of practical tasks. Thus, the Institute of Atmospheric Physics of the Russian Academy of Sciences grew out of a small laboratory of turbulence, created in 1946 on the initiative of A.N. Kolmogorov as part of the Institute of Theoretical Geophysics of the Academy of Sciences of the USSR and until 1949 headed by him. The director of the Institute of Oceanology of the USSR Academy of Sciences was a student of A.N. Kolmogorova Corresponding Member of the Academy of Sciences of the USSR A.S. Modin.
Back in 1936, on the initiative of A. N. Kolmogorov, his student began static processing of experimental data on the splitting of hybrids. This determined the application for many years. mathematical methods to solve the problems of genetics, both during the persecution of genetics in the 40s, and later, during really serious events in science associated with the discovery of the genetic code.
A. N. Kolmogorov was an example of a rare combination of mathematician and natural scientist, theorist and practitioner. At the same time he was a philosopher of science (philosophy of mathematics) and its popularizer.
Andrei Nikolaevich made an invaluable contribution to the methodology and history of mathematics, to the theory and practice of its teaching. On these topics, he published a number of brilliant articles, for example, in the collection Mathematics - Science and Profession, published in 1988 in the Kvant Library for Youth.
On Faculty of Mechanics and Mathematics, Moscow State University A.N. Kolmogorov headed the departments of probability theory (since 1935), mathematical statistics (since 1976), mathematical logic (since 1980). In 1954-1958. A.N. Kolmogorov was the dean of the Faculty of Mechanics and Mathematics of Moscow State University.
In 1963, on the initiative of A. N. Kolmogorov, Moscow State University established a physics and mathematics boarding school, where gifted children from all republics were accepted former USSR. Since 1989, this school has been named after him. For children and youth A.N. Kolmogorov together with a physicist Academician I.K. Kikoin organized the release of the popular Physics and Mathematics Journal "Kvant" .
Public lectures for a wide audience on the topics of cybernetics, which A.N. Kolmogorov read at the Polytechnic Museum, the Palace of Culture of Moscow State University in the early 60s, aroused great interest among specialists in various professions. In 1961 A.N. Kolmogorov published an article "Automata and Life" in the journal "Technology for Youth", in which he popularly outlined the content of his famous report at the methodological seminar of the Faculty of Mechanics and Mathematics of Moscow State University.
A.N. Kolmogorov, being a scientist of encyclopedic knowledge, played a decisive role in the formation of the mathematical sections of the Great Soviet Encyclopedia in the first (beginning in 1936) and in the second (since 1954) editions of the TSB. In addition to the article "Mathematics" and other mathematical articles written personally by A.N. Kolmogorov for the TSB, in 1958 he prepared for the TSB an article "Cybernetics", in which he outlined the fundamental concepts of this area, based on a thorough study of the theses on cybernetics, which were formulated by him in 1957 together with his students Vyach.Sun. Ivanov, M.K. Polivanov, V.A. Uspensky.
The main thesis of A.N. Kolmogorov was that cybernetics is not a science, but a scientific direction. As part of this direction, he considered mathematical linguistics, indicating that two understandings of this area of mathematics are possible. The first is the theory of abstract formation of language, close to mathematical logic and the theory of algorithms. The second is the application of mathematical methods in ordinary (traditional) linguistics. Contribution of A.N. Kolmogorov in the development of semiotics, as one of the components of the cybernetic direction, and at present - informatics, enriched both of the above approaches.
In world science, to celebrate achievements in areas that are not covered Nobel Prizes, the Balzan Prizes were established. In 1963 first award of the Balzan Prize in mathematics, and its winner was A.N. Kolmogorov. This was the highest assessment of the contribution of A.N. Kolmogorov to world science.
His name is in history Russian science next to names M.V. Lomonosov, DI. Mendeleev, I.V. Kurchatov, S.P. Queen, L.S. Pontryagin- scientists who glorified Russia with a feat of their lives. Article by V.A. Uspensky in the book "Essays on the History of Informatics in Russia" is called - " Andrey Nikolaevich Kolmogorov - the great scientist of Russia».
There are memoirs of his students and colleagues about the life and work of A. N. Kolmogorov:
- Kolmogorov in memoirs. Ed.-stat. A.N. Shiryaev. M., Nauka, 1993. 734 p.
- Novikov S.P. Memories of A. N. Kolmogorov. Uspekhi matematicheskikh nauk, 1988, vol. 43, no. 6. p. 35-36.
- Yanin V.L. Kolmogorov as a historian. Uspekhi matematicheskikh nauk, 1988, vol. 43, no. 6, p. 189-195.
Life in search of truth
To the 100th anniversary of the birth
Andrey Nikolaevich Kolmogorov
Corresponding Member of the Russian Academy of Sciences A.N. Shiryaev
A person who was destined to give the world at least one great creative idea does not need the praise of posterity. His work bestowed upon him a greater boon.
Albert Einstein
The great Russian scientist, one of the greatest mathematicians of the 20th century, worthily recognized by almost all authoritative scientific communities of the world, is a member of the US National Academy of Sciences and the American Academy of Arts and Sciences, a member of the Royal Netherlands Academy of Sciences and the Finnish Academy of Sciences, a member of the Academy of Sciences France and the German Academy of Naturalists “Leopoldina”, member of the International Academy of the History of Sciences and the national academies of Romania, Hungary and Poland, honorary member of the Royal Statistical Society of Great Britain and the London Mathematical Society, honorary member of the International Statistical Institute and the Mathematical Society of India, foreign member of the American Philosophical and American meteorological society; Laureate of the most honorable scientific awards: the P.L. Chebyshev and N.I. Lobachevsky Prizes of the USSR Academy of Sciences, the International Prize of the Balzan Foundation and the International Prize of the Wolf Foundation, as well as the Lenin and State Prizes, awarded seven Orders of Lenin and the gold medal of the Hero of Socialist Labor - Academician Andrey Nikolaevich Kolmogorov called himself "just a professor at Moscow University."
Andrey Nikolaevich Kolmogorov
(1903-1987)
The whole life of Andrey Nikolayevich is connected with the university, starting from 1920, when he joined the Faculty of Physics and Mathematics at the age of 17, and until his very last day - October 20, 1987, when he died. From the first scientific article “Report to the Mathematical Circle on the Quadrillage”, dated 1921, to “Selected Works”, for the first three volumes of which, published in 1985-1987, he himself selected the works. Between these two dates 65 years - a huge life. This life contained so many creative accomplishments that in the time that has passed since the day of his death, it is not even possible to come close to any complete description of them.
Obviously there is no possibility, and there is hardly a need, to try to present here the mathematical work of Kolmogorov. “Andrei Nikolaevich Kolmogorov occupies a unique place in modern mathematics, and in world science in general. In terms of the breadth and variety of his scientific studies, he resembles the classics of natural science of past centuries.- N.N. Bogolyubov, B.V. Gnedenko and S.L. Sobolev testify in their jubilee article to the 80th anniversary of Kolmogorov [ 1 ]. Works on the theory of trigonometric series, measure theory and set theory; research on the theory of differentiation and integration, approximation theory, constructive logic, topology, the theory of superpositions of functions and Hilbert's famous 13th problem; papers on classical mechanics, ergodic theory and the theory of turbulence, diffusion and models of population dynamics; works on the foundations of probability theory, limit theorems, general theory random processes, the theory of Markov, stationary and branching processes, mathematical statistics, automata theory and applications of mathematical methods in humanities(including works on the theory of verse and text statistics); research on the history and methodology of mathematics - this is an incomplete list of areas in which Kolmogorov obtained fundamental results, developed fundamentally important concepts that determined the face and development of many branches of mathematics in the 20th century. and other branches of science and knowledge. Andrei Nikolaevich devoted almost a third of his life to school mathematical education; he left a huge number of works on the content and methods of teaching mathematics in secondary schools. educational institutions, popular science articles for students and teachers and textbooks for secondary schools.
During the time that has passed since the death of Andrei Nikolaevich, three large collections of memoirs about him have been published (“Kolmogorov in his memoirs” [ 2 ], “The phenomenon is extraordinary. The book about Kolmogorov” [ 3 ], and “KOLMogorov in Perspective” [ 4 ]) and a huge number of other publications around the world. Suffice it to say that the section “About Kolmogorov” in his bibliography already contains more than 150 entries. This updated, updated and verified bibliography will be included in the first biobibliographic book of the jubilee edition of Kolmogorov, dedicated to the 100th anniversary of the birth of the great scientist. The book also includes a large essay on the life and work of Kolmogorov and some other materials for his biography. The second book publishes selected correspondence of Kolmogorov with a friend of his life and one of the first teachers, outstanding mathematician, topologist and geometer Pavel Sergeevich Aleksandrov. In the third book some diaries of Andrey Nikolaevich will be published for the first time.
Selected from letters and diaries for publication are those relating to the pre-war and war periods, already distant from us and our time, but so bright and full of creative accomplishments and friendship. These three books are common name“Kolmogorov” should go to the international anniversary conference “Kolmogorov and modern mathematics”, which will be held in Moscow under the auspices of Russian Academy Sciences and Moscow University from 16 to 21 June 2003
“The beginning was so far away, the first interest was so timid…”
Let us mentally move back 100 years ago, to April 1903, when the youngest of the six daughters of the leader of the Uglich nobility and honorary trustee of public schools in the Yaroslavl province, a wealthy landowner of liberal views, Yakov Stepanovich Kolmogorov, turned up in Tambov, on the way from the Crimea. There, in Tambov, Maria Yakovlevna gave birth to a son. She did not survive the birth, and an alarming telegram arrived at her father's house, at the Tunoshna estate near Yaroslavl:
VERY UNFAVORABLE. COME IMMEDIATELY.
This telegram, handwritten on a letterhead, is still kept in the Kolmogorov house. The eldest of the daughters, Sofya Yakovlevna, left for the little one, and at the age of ten he was brought to his grandfather's house and named Andrei (as if in honor of Prince Andrei Bolkonsky, his mother's favorite literary hero). His aunts took care of the baby, and later one of them, Vera Yakovlevna, adopted him and lived with him all her life until her death in 1951. Andrey's only uncle, Stepan Yakovlevich Kolmogorov, became Andrei's godfather. The boy's parents were not married, and at baptism, according to the rules of that time, he had to receive, by the name of his godfather, the patronymic Stepanovich and the surname Stepanov. But here it was allowed to deviate from the rules: Andrei received his mother's surname - Kolmogorov, and his father's patronymic - Nikolaevich.
Andrei Nikolaevich's father, Nikolai Matveevich Kataev, an agronomist by training, who graduated from the Petrovsko-Razumovsky Agricultural Institute (now the Timiryazev Academy), ended up in Yaroslavl in exile for participating in a populist organization, worked as a zemstvo statistician. He was practically excluded from participation in the upbringing of his little son by the aunts who fussed around him, although, as his recently found letters testify, he was very sad about this and did not give up hope of becoming closer to him over time. But time decreed differently - Nikolai Matveevich died in civil war, in 1919
Now it is impossible to judge what was left to Andrei Nikolayevich by his father and what by his mother. However, in the Certificate of graduation from Maria Yakovlevna Kolmogorova in 1893 from the Yaroslavl gymnasium we read: “...with honors and special success in the chosen special subject - mathematics”. And Andrei Nikolaevich dreamed of becoming an agronomist, or rather a forester, from childhood.
Yakov Stepanovich Kolmogorov had a house in Yaroslavl on Proboynaya Street, which he inherited from his father Stepan Petrovich, who, according to Andrei Nikolaevich, "got rich and received the nobility thanks to personal enterprise." The Calendar of the Yaroslavl province for 1877 says: “Breaking street. From Ilyinskaya Square to Semyonovskaya Square there is a government building of the Offices. Next to the house of Stepan Petrovich Kolmogorov. From the correspondence of Andrey Nikolayevich with the author of the Guide to historical and cultural monuments of Yaroslavl, we learn that Proboynaya Street was renamed Sovetskaya, the Regional Executive Committee was located in the building of the Offices, and on the Kolmogorov house there was a memorial plaque in memory of the outstanding Russian theater figure F.G. Volkov (1729-1763 ), who founded the first Russian professional troupe in Yaroslavl in 1750. How the house came into the possession of the Kolmogorovs, Andrei Nikolaevich did not know, and the Yaroslavl local historian could not explain to him. “I used to visit the city house for several days or weeks (my aunt Varvara Yakovlevna ran the household there). In addition to the city house in Yaroslavl, Yakov Stepanovich also owned a house in Uglich and a country house in Tunoshna, eighteen miles from Yaroslavl down the Volga. In this country house I spent my early childhood” *.
* We take this and other quotes from the statements of A.N. Kolmogorov from various published [2 ] - [ 9 ] or handwritten sources, without always referring to the exact address.
The Kolmogorov sisters were free-thinking women with high social ideals. An underground hectograph was located in the Tunoshesk house, and, as Andrei Nikolayevich said, even he managed to take part in the revolutionary movement as an infant - during the next search, illegal literature was saved, being placed under his cradle. “The gendarmes entered, but did not dare to lift me up. They also knew, of course, that these wicked young women were, after all, the daughters of the local marshal of the nobility, so they had challenging tasks”, Andrey Nikolayevich concluded, chuckling.
Estate in Tunoshna,
where he spent his childhood.
The only surviving
photograph of father and mother.
With aunt Vera Yakovlevna (1863-1951),
adopted Andrei Nikolaevich.
The Joy of Mathematical Discovery
In the Tunoshno house of Andrey Nikolaevich's aunt “arranged a small school in which they studied with a dozen children different ages according to the latest recipes of the time”(later in Tunoshna “at the expense of Varvara Yakovlevna Kolmogorova, the school building was rebuilt from hollow bricks, which was then a technical novelty”). The school “published” the magazine “Spring Swallows”, in which A.N. “published” arithmetic problems invented by him. Among them were, for example: “There is a button with four holes. To secure it, it is enough to stretch the thread through at least two holes. How many ways can you fasten a button?
In the article “How I Became a Mathematician”, from where we quoted these lines, we read:
“I knew the joy of a mathematical discovery early, when I noticed a regularity at the age of five or six:
1 = 1 2
1 + 3 = 2 2
1 + 3 + 5 = 3 2
1 + 3 + 5 + 7 = 4 2 , and so on".
In Moscow, where in 1910 Andrei Nikolayevich arrived with Vera Yakovlevna to receive an education, he is assigned to the private gymnasium E.A. for studying. Andrei Nikolaevich recalled:
“The classes in the gymnasium were small (15-20 students). A significant part of the teachers were themselves fond of science. Sometimes they were university teachers, our geography teacher herself participated in interesting expeditions. Many students competed with each other self-study additional material, sometimes even with insidious plans to shame less experienced teachers with their knowledge. An experiment was being made to introduce into the tradition of public defense by graduating students of their graduation essay. In mathematics, I was one of the first in my class, but the first more serious scientific hobbies in school for me were first biology, and then Russian history.
“In childhood, dreams of future activities are legitimately intertwined with play. At the age of 11 or 12, I spent a lot of work collecting detailed information about the uninhabited islands of the southern oceans, as I was going to recruit people from different countries and organize some kind of ideal state on these islands, for which he even wrote a constitution. A navy was also provided to protect against possible encroachments on our freedom. But at the age of 13-14, such activities would already be foolishness. In addition, the year 1917 came, and all of us, schoolmates, suddenly became adults.
The first serious plan for future life and work was the intention to engage in forestry - to become a forester, plant forests, grow them and protect them. Of course, I was also fascinated by the romance of life in the forest.
By this time, my abilities for mathematics had already manifested themselves to a large extent. I solved difficult problems, and in theory I went much further than school programs. He studied higher mathematics under articles in encyclopedic dictionary Brockhaus and Efron, which is not too easy, since these articles were not of an educational nature, but rather of a reference. But the well-formed idea of becoming a mathematician, a researcher, of making serious discoveries in mathematics oneself, of advancing mathematical science, did not come all at once. Most likely at sixteen.”
If the revolutionary events of 1905 fell on very early age Andrei Nikolaevich, then both revolutions of 1917 found him already 14 years old. We do not know for certain how young Kolmogorov reacted to these shocks - we only know that it was at this age that he began to advance independently in mathematics and came to the university with quite significant knowledge. At the same time, he entered the mathematical department of the Chemical-Technological Institute. D.I. Mendeleev. “Technology was then perceived as something more serious and necessary than pure science”, This is how he explains his move. The training went off without a hitch. “Having passed the exams for the first year in the very first months, I received the right to 16 kilograms of bread and 1 kilogram of butter per month, which, according to the ideas of that time, already meant complete material well-being. I had clothes, and I made my own wooden-soled shoes.”
“In my first student years, besides mathematics, I studied most seriously in a seminar on ancient Russian history by Professor S.V. Bakhrushin.” In this seminar in 1920, Kolmogorov made his first scientific report on land relations in Novgorod based on an analysis of cadastres of the 15th-16th centuries. “using some techniques of mathematical theory”. For a long time it was believed that the manuscripts of Kolmogorov's first works on history had not been preserved. Found recently, they were published by his student L.A. Bassalygo [ 10 ]. “If Andrei Nikolayevich’s work had been published soon after it was written, our knowledge today would be much more complete and, most importantly, more accurate… History has lost a brilliant researcher, mathematics has acquired him forever”,- this is how the historian academician V.L. Yanin evaluates this work today in the introduction to its publication.
In the country of the Lusitania
Andrey Nikolaevich makes the final choice in favor of mathematics. He becomes a student of N.N. Luzin, one of the Lusitania. Here is how another “Lusitan”, Pavel Sergeevich Alexandrov, describes his first meetings with Luzin:
“I first met Nikolai Nikolayevich Luzin when I was a second-year student. The impression of this meeting was, one might say, amazing, and I will remember it for the rest of my life. Turning to him after a lecture for advice on how I should continue to study mathematics, I was, first of all, struck by attentiveness and, I can’t find another word, respect for the interlocutor, no matter how strange it sounds when it comes to the conversation of the already famous, although still a young scientist, with an 18-year-old student. After listening to me, Luzin, with skillfully posed questions, very soon figured out the nature of my mathematical inclinations and immediately outlined in an accessible form the main directions that he could suggest to me for further studies; he himself persuaded me to choose one of these directions, and all this was done very subtly, without any pressure and - as I can now say - very correctly. At the same time I became a student of Luzin, and this was in the era of his highest creative upsurge. Luzin then lived completely alone in furnished rooms, he lived only by science. I remember his phrase, said in one of our many meetings: “I think day and night on Zermelo’s axiom (there is such a famous axiom in mathematics, which was then - and many years later - at the center of research on the logical foundations of mathematics). If only someone knew what this thing was!” [11 ].
First Aleksandrov's entry, and then Kolmogorov's, into Lusitania (as Luzin's students called their country) occurred at a time in which Nikolai Nikolayevich received all his most significant results. “In him during these years, what can be called an inspired attitude to science was clearly manifested, and his students not only learned mathematics from him, but also received a lesson in what a real scientist is, as well as what a professor can and should be. university. It became visibly clear to them that science and the introduction of new young people to it are two sides of the same activity - the activity of a scientist,- we will continue the quote of Alexandrov.
“The opportunity to communicate with N.N. Luzin, to tell him the results that were not yet fully completed was very important”, Kolmogorov echoes him. Among the short-lived but bright teachers of the young Kolmogorov, one more "Lusitanian" should be mentioned, PS Uryson, whose lectures Andrei Nikolaevich listened to in the very first courses. “At one of Uryson's lectures, Andrey Nikolaevich noticed an error in the complex constructions of Pavel Samuilovich in his proof of the theorem on the dimension of a three-dimensional space. Uryson corrected this mistake the very next day, but the sharpness of mathematical perception shown by the eighteen-year-old student Kolmogorov made a great impression on him.- testifies Pavel Sergeevich. Andrei Nikolaevich writes: “Moscow mathematics of that time was rich in bright and talented individuals, but P.S. Uryson, even against this background, stood out for his universality of interests, combined with purposefulness in choosing the subject of his own studies, the distinctness of setting problems, a clear assessment of his own and other people's achievements, combined with goodwill in applied to very small achievements.”
These words, spoken by Kolmogorov about his teacher who died very early and absurdly (while swimming in a storm), any of his students could say about him.
By 1929, students and graduate school were behind. Kolmogorov has already authored more than two dozen papers, among which are outstanding ones: the most famous result in the field of trigonometric series is an example of a Fourier-Lebesgue series that diverges almost everywhere; the first article on the theory of probability “On the convergence of series whose members are determined by chance” (together with another student of Luzin - A.Ya. Khinchin); the first work on intuitionistic logic "On the principle of "tertium non datur"". Andrey Nikolaevich said about this work: “The work was conceived by me as an introductory part of a broader idea. The construction of models of various branches of classical mathematics within the framework of intuitionistic mathematics should have served to substantiate their consistency.” In the autumn of 1929, Kolmogorov became a research fellow at the Institute of Mathematics at Moscow University (this Institute united mathematicians, separating them from the physicists of the then general Faculty of Physics and Mathematics).
In just two years, Andrei Nikolayevich became a professor, and two more years later, he became the director (!) of this Institute. And then every two years, some serious step: in 1935, Kolmogorov founded the department of probability theory at the university (and became its head), then opened and also headed the department of probability theory at the V.A. Steklov Mathematical Institute of the USSR Academy of Sciences and , finally, in 1939 he was elected (bypassing the corresponding member) a full member of the Academy of Sciences, a member of the presidium and academician-secretary of the Department of Physical and Mathematical Sciences.
“Souls high freedom, which is called friendship "
And between the end of graduate school and the beginning of work, in the summer of 1929, a boat trip took place, which unexpectedly became a milestone in Kolmogorov's life. Pavel Sergeevich Alexandrov was invited on this journey along the Volga, where Andrei Nikolaevich and his school friend were going. “It is still not entirely clear to me how I decided to offer Pavel Sergeevich to be our partner. However, he immediately agreed ... From the day of departure - June 16 - Pavel Sergeevich and I calculate our friendship.
And further Andrei Nikolaevich testifies: “Probably, I would have become a mathematician on my own, but my human qualities were formed to a large extent under the influence of Pavel Sergeevich. He really was a most amazing person in terms of wealth and breadth of views. His knowledge of music, painting, his spiritual attitude towards people are extraordinary.”
Aleksandrov and Kolmogorov returned from this first journey with the firm intention of settling down together somewhere near Moscow, especially since not only the postgraduate graduate Andrei Nikolaevich, but also the professor of Moscow University Pavel Sergeevich did not have his own housing in Moscow - for many years , until the war, they occupied two rooms in the apartment of L.S. Neiman, the sister of P.S. Uryson, Aleksandrov's closest friend. For some time, the prospect of leaving together somewhere from Moscow was seriously considered - plans for resettlement to Kyiv or Tbilisi were closely discussed ...
The first joint home of Pavel Sergeevich and Andrei Nikolaevich and the first test of life in such a "mathematical commune" was a house in the village of Klyazma along the Northern Railway, which belonged to the Alexandrov family. Then half of the house was rented in the same village, Vera Yakovlevna led a simple household.
In June 1935, after a long search and legal difficulties, on shares with several buyers, a house was purchased on the banks of the Klyazma in the small village of Komarovka. This old house once belonged to the family of a famous philanthropist, textile industrialist S.V. Alekseev, father of K.S. Stanislavsky. Alekseev opened a free hospital in it at his own expense and named it Elisavetinskaya, after the wife, mother of the founder of the Moscow Art Theater. By 1935, the ownership had passed to Alekseev's daughter Anna Sergeevna. The hospital, of course, no longer existed, and the house was actually empty. “The house in Komarovka met all our needs, making it possible to place a large library and place our guests in separate rooms,” writes Kolmogorov. The guests - let's add from ourselves - were most often students of both.
With Pavel Sergeyevich Alexandrov.
Germany. 1931
Komarovsky house.
We read with interest in the letters of Pavel Sergeevich and Andrei Nikolaevich the history of the acquisition of the Komarovsky house. 1935th. Andrei Nikolaevich is 32 years old, Pavel Sergeevich is 40 years old. It is clear that all the worries and troubles associated with finding and buying (and later repairing) a suitable house were taken over by Aleksandrov. In general, he treated Kolmogorov's helplessness in everyday affairs with paternal condescension, and at crucial moments he took everything upon himself. The option of buying a decent house intended for demolition was considered (there were a lot of them for sale - it was expected that many small villages in the district would go under water with the approach of the Moscow-Volga Canal under construction), transporting it to the Klyazma. The house in Komarovka seemed just a feasible dream, although it cost so much that this feasibility was very illusory. But Alexandrov managed to put together a "cooperative of buyers", which bought the house on shares from the previous owners. The money for the first installment was lent by Mikhail Sergeevich, Aleksandrov's elder brother, a well-known Moscow surgeon. Subsequently, for many years, Alexandrov and Kolmogorov bought out shares belonging to other "buyers", until, finally, in 1950 they became the absolute masters of their dream.
For the rest of their lives, even after Andrei Nikolayevich and Pavel Sergeevich acquired comfortable Moscow housing (after the war, they were provided with apartments in the famous house of academicians at B. Kaluzhskaya, 13, and in 1953 they, together with Moscow University, moved to the Lenin Hills and settled in the professorial tower "L", in the neighboring apartments - No. 9 and 10), they spent part of the week, usually from Friday evening to Tuesday morning, in their Komarovsky house. In the diary of Andrei Nikolaevich there are calendars that he compiled for each month, and all the weeks in them began on Friday.
Life in Komarovka was not, of course, idle. Moreover, she was very organized. A drawing by Andrei Nikolaevich has been preserved (he was generally very fond of drawing with a pen, his letters and especially diaries resemble Pushkin's draft manuscripts), where the routine in the Komarovsky house is depicted in cheerful pictures - but he was executed quite seriously and immutably. In this Komarovo life there were many household worries, which could not be missing - firewood, stoves, repairs ... But this life was creative, and therefore free, free. Books and music, travel and sports activities, meetings and conversations with students and, of course, first of all, their own creativity - mathematics.
Baltic state academy fishing fleet
Department of Higher Mathematics
in higher mathematics
Biography and works of Kolmogorov A.N.
Completed:
Krupnova A.S.
Kaliningrad 2008
Introduction
Main part
1. Biography
1.1 Early years
1.2 University
1.3 Professor
1.4 Post-war work
2. Works of Kolmagorov A.N.
2.1 Kolmogorov's axioms elementary theory probabilities
2.2 Kolmogorov's empirical deduction of axioms
2.3 Axiom of continuity and infinite probability spaces
2.4 Infinite probability spaces and "ideal events"
2.5 Kolmogorov duality
2.6 Gnoseological principle
2.7 Kolmogorov averages
2.8 Kolmogorov theorems
Conclusion.
List of used literature.
Introduction
I chose this topic because I am interested not only in the biography of the famous Soviet mathematician, but also in his works. This topic is quite extensive. In this essay, I will start with a review of the biography of A.N. Kolmogorov. Further we will consider the works of this great mathematician: axioms, theorems.
Main part
1. Biography
Andrei Nikolaevich Kolmogorov (April 12 (25), 1903, Tambov - October 20, 1987, Moscow) - an outstanding domestic mathematician, Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University(1931), Academician of the Academy of Sciences of the USSR (1939). Kolmogorov is one of the founders modern theory probabilities, he obtained fundamental results in topology, mathematical logic, the theory of turbulence, the theory of complexity of algorithms, and a number of other areas of mathematics and its applications.
1.1 Early years
Kolmogorov's mother, Maria Yakovlevna Kolmogorova (1871-1903), died in childbirth. Father - Nikolai Matveevich Kataev, an agronomist by education (graduated from the Petrovsky (Timiryazev) Academy), died in 1919 during the Denikin offensive. The boy was adopted and raised by his mother's sister, Vera Yakovlevna Kolmogorova. Andrei's aunts organized a school in their house for children of different ages who lived nearby, taught them - a dozen children - according to the recipes of the latest pedagogy. For the children, a handwritten magazine "Spring Swallows" was published. It published creative work students - drawings, poems, stories. Andrey's "scientific works" also appeared in it - arithmetic problems invented by him. Here, at the age of five, the boy published his first scientific work mathematics. True, it was only a well-known algebraic regularity, but the boy noticed it himself, without outside help!
At the age of seven, Kolmogorov was assigned to a private gymnasium. It was organized by a circle of Moscow progressive intelligentsia and was constantly under threat of closing.
Andrei already in those years showed remarkable mathematical abilities, but still it is too early to say that his further path has already been decided. There was also a passion for history and sociology. At one time he dreamed of becoming a forester. “In 1918-1920, life in Moscow was not easy,” Andrei Nikolayevich recalled. - In schools, only the most persistent were seriously engaged. At this time, I had to leave for construction railway Kazan-Yekaterinburg. Simultaneously with work, I continued to study on my own, preparing to take an external course for high school. Upon returning to Moscow, I experienced some disappointment: they gave me a certificate of graduation from school, without even bothering to take an exam.
1.2 University
When, in 1920, Andrei Kolmogorov began to think about entering an institute, an eternal question arose before him: what should he devote himself to, what business? He is attracted to the mathematical department of the university, but there is also a doubt: here is pure science, and technology is, perhaps, a more serious matter. Here, for example, is the metallurgical faculty of the Mendeleev Institute! A real man's business, moreover, promising. Andrey decides to do both here and there. But it soon becomes clear to him that pure science is also very relevant, and he makes a choice in its favor.
In 1920 he entered the mathematical department of Moscow University. “Having decided to engage in serious science, I, of course, strove to learn from the best mathematicians,” the scientist later recalled. - I was lucky to study with P.S. Uryson, P.S. Alexandrova, V.V. Stepanova and N.N. Luzin, who, apparently, should be considered primarily my teacher in mathematics. But they "found" me only in the sense that they evaluated the works I brought. It seems to me that a teenager or a young man should find the "purpose of life" for himself. The elders can only help.”
In the very first months, Andrei passed the exams for the course. And as a second-year student, he gets the right to a "stipend": "... I got the right to 16 kilograms of bread and 1 kilogram of butter per month, which, according to the ideas of that time, already meant complete material well-being." Now there is free time. It is given to attempts to solve already set mathematical problems.
The lectures of Nikolai Nikolaevich Luzin, a professor at Moscow University, were, according to contemporaries, an outstanding event. Luzin never had a prescribed form of presentation. And his lectures by no means could serve as a role model. He had a rare sense of audience. He, like a real actor, performing on the theater stage and perfectly feeling the reaction of the audience, had constant contact with students. The professor knew how to bring students into contact with his own mathematical thought, revealing the mysteries of his scientific laboratory. Invited to joint spiritual activity, to co-creation. And what a holiday it was when Luzin invited students to his home for the famous “Wednesdays”! Conversations over a cup of tea about scientific problems ... However, why necessarily about scientific ones? There were plenty of topics for conversation. He knew how to ignite the youth with the desire for a scientific achievement, instill faith in their own strengths, and through this feeling another came - an understanding of the need for full dedication to their beloved work.
Kolmogorov first attracted the attention of a professor at a lecture. Luzin, as always, led the classes, constantly addressing the audience with questions and assignments. And when he said: "Let's build a proof of the theorem based on the following assumption..." Andrey Kolmogorov raised his hand in the audience: "Professor, it is wrong..." The question "why" was followed by a short answer from the first-year student. Satisfied Luzin nodded: "Well, come to the circle, report to us your thoughts in more detail." “Although my achievement was rather childish, it made me famous in the Lusitania,” Andrei Nikolaevich recalled.
But a year later, the serious results obtained by the eighteen-year-old sophomore Andrei Kolmogorov attracted the real attention of the “patriarch”. With some solemnity, Nikolai Nikolaevich invites Kolmogorov to come on a certain day and hour of the week, intended for the students of his course. Such an invitation, according to the concepts of the Lusitania, should be regarded as an assignment honorary title student. As a recognition of ability.
Over time, Kolmogorov's attitude towards Luzin changed. Under the influence of Pavel Sergeevich Alexandrov, also a former student of Luzin, he took part in the political persecution of their common teacher, the so-called Luzin case, which almost ended in repressions against Luzin. With Aleksandrov himself, Kolmogorov was bound by friendly ties until the end of his life.
Kolmogorov's first publications were devoted to the problems of descriptive and metric theory of functions. The earliest of these appeared in 1923. Discussed in the mid-twenties everywhere, including in Moscow, questions of the grounds for mathematical analysis and closely related research in mathematical logic attracted the attention of Kolmogorov almost at the very beginning of his work. He took part in discussions between the two main opposed methodological schools at that time - formal-axiomatic (D. Hilbert) and intuitionistic (E.Ya. Brouwer and G. Weil). In doing so, he obtained a completely unexpected first-class result, proving in 1925 that all known sentences of classical formal logic, under a certain interpretation, turn into sentences of intuitionistic logic. Kolmogorov retained a deep interest in the philosophy of mathematics forever.
Of particular importance for the application of mathematical methods to natural science and practical sciences had a law big numbers. To find the necessary and sufficient conditions under which it takes place - that is what the desired result was. The leading mathematicians in many countries have been unsuccessfully trying to obtain it for decades. In 1926, these conditions were obtained by graduate student Kolmogorov.
Many years of close and fruitful cooperation connected him with A.Ya. Khinchin, who at that time began to develop problems in the theory of probability. It has become an area of joint activity of scientists. Science "about the case" since the time of Chebyshev was, as it were, Russian national science. Her success multiplied many Soviet mathematicians, but modern look The theory of probability received thanks to the axiomatization proposed by Andrei Nikolaevich in 1929 and finally in 1933.
Until the end of his days, Andrei Nikolaevich considered probability theory to be his main specialty, although the areas of mathematics in which he worked can be counted in a good two dozen. But then the path of Kolmogorov and his friends in science was just beginning. They worked hard, but did not lose their sense of humor. Partial differential equations were jokingly called "equations with unfortunate derivatives", such a special term as finite differences was changed into "different finitenesses", and probability theory - into "trouble theory".
