Completed by: Huurak Aelita, student of 11 "a" class

Objective:

explore and acquaint with the life and work of one of the most famous and talented scientists of the 20th century - Andrei Nikolaevich Kolmogorov - a grandiose scientific figure, a talented organizer, an outstanding teacher and an extraordinary, highly developed personality.

Relevance:

at all times there have been and are people, undeniable bearers of moral values, among them scientists, writers, statesmen, people of labor, whose lives and deeds help us to believe in words about duty, honor, justice, on the implementation of the upbringing of the young generation on the example of the personality of an outstanding person.

INTRODUCTION

"Kolmogorov gave the people around him an incomparable, almost physical feeling of direct contact with a genius."

"Kolmogorov is a unique phenomenon of Russian culture, our national treasure."

V. A. Uspensky

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Municipal budgetary educational institution

secondary school with. Sosnovka

abstract

Topic:

ANDREI NIKOLAEVICH

KOLMOGOROV -

outstanding Russian mathematician of the 20th century"

Performed:

Huurak Aelita,

11 "a" class student

Supervisor:

Ondar F.S.-M.,

mathematics teacher MBOU secondary school

With. Sosnovka

Sosnovka - 2013

Objective:

explore and acquaint with the life and work of one of the most famous and talented scientists of the 20th century - Andrei Nikolaevich Kolmogorov - a grandiose scientific figure, a talented organizer, an outstanding teacher and an extraordinary, highly developed personality.

Relevance:

at all times there have been and are people, undeniable bearers of moral values, among them scientists, writers, statesmen, people of labor, whose lives and deeds help us to believe in words about duty, honor, justice, on the implementation of the upbringing of the young generation on the example of the personality of an outstanding person.

• Introduction…………………………………………..…p. 2
• The life path of Andrei Nikolaevich

Childhood……………………………………...……...p. 3

Kolmogorov's student years.

Formation in science……………………………….p. four

Scientific and pedagogical activity

A.N. Kolmogorov……………………………….….p. eight

• Conclusion………………………………………..…….page 14
• Literature………………………………………………p.15

INTRODUCTION

"Kolmogorov gave the people around him an incomparable, almost physical feeling of direct contact with a genius."

"Kolmogorov is a unique phenomenon of Russian culture, our national treasure."

V. A. Uspensky

April 25, 2013 marks the 110th anniversary of the birth of Andrei Nikolaevich Kolmogorov, a great scientist and mathematician.

In my essay, I want to talk about one of the most famous and talented scientists of the 20th century - Andrei Nikolaevich Kolmogorov - a grandiose scientific figure, a talented organizer, an outstanding teacher and an extraordinary, highly developed personality.

The great Russian scientist, one of the greatest mathematicians of the 20th century, worthily recognized by almost all authoritative world communities of scientists - 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 French and German Academy of Sciences academy of natural scientists "Leopoldina", a member of the International Academy of the History of Sciences and the national academies of Romania, Hungary and Poland, an honorary member of the Royal Statistical Society of Great Britain and the London Mathematical Society, an honorary member of the International Statistical Institute and the Mathematical Society of India, a foreign member of the American Philosophical and American Meteorological Society, winner 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 State and Lenin distance "Golden Star" Hero of Socialist Labor Academician Andrei Nikolaevich Kolmogorov always called himself "just a professor at Moscow University."

My goal is to explore the life and work of this truly brilliant man.

THE LIFE WAY OF ANDREI NIKOLAEVICH.

Childhood.

Andrei Nikolaevich Kolmogorov was born on April 25 (12), 1903 in Tambov. Andrei Nikolaevich's mother, Maria Yakovlevna Kolmogorova, died on her son's birthday, April 25, 1903. The name was given at will, expressed in advance by the mother: if a boy is born, name Andrei in honor of Andrei Bolkonsky, her favorite literary character from the novel by Leo Tolstoy. Andrei's father is Nikolai Matveevich Kataev, an agronomist and a bit of a novelist. While still a bachelor, he participated in the populist movement and at the beginning of the century was exiled to Yaroslavl, where he began working as a zemstvo statistician. There he met Maria Yakovlevna Kolmogorova, the daughter of a large landowner Ya. S. Kolmogorov. The acquaintance brought them closer. Maria agrees to become the wife of Nikolai Matveevich, against the will of her parents, and leaves her father's house. Since Maria and Nikolai were not married, the boy (Andrey) born to them was considered illegitimate and had no right to either a patronymic after his own father or his last name. And only after the October Revolution, under the new laws, he was able to get his mother's surname and father's patronymic. Andrey's sister, Vera Yakovlevna, who adopted the boy, took care of Andrei. Other sisters of Mary, especially Nadezhda Yakovlevna Kolmogorova, also took a great part in his upbringing. Andrei spent the first years of his life on his grandfather's estate - Tunoshna, located on the banks of one of the tributaries of the Volga not far from Yaroslavl. The aunts endowed the boy with love, affection, attention, and touching care for his intellectual and moral upbringing. Everyone tried to develop curiosity and interest in books, sciences, and nature in the child. 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 works of students - drawings, poems, stories. Andrey's "scientific works" also appeared in it - arithmetic problems invented by him. Here the boy published his first scientific work in mathematics at the age of five. True, it was only a well-known algebraic regularity, but the boy noticed it himself, without outside help!

In 1910, Vera Yakovlevna and Andrei moved to Moscow. They lived on interest from the capital received by inheritance. Andrey entered the Repman private gymnasium, which after the revolution was transformed into the twenty-third school of the second stage. He graduated from it in 1920. It didn't take long for me to decide to become a mathematician.
The time was hungry and anxious. The young man wanted to get not only knowledge, but also a profession, a craft. Here is how he later recalled this period of his life:Technique was then perceived as something more serious and necessary than pure science. Simultaneously with the mathematical department of the university (where everyone was accepted without exams), I entered the metallurgical department of the Mendeleev Institute (which required an entrance exam in mathematics). But soon interest in mathematics surpassed doubts about the relevance of the profession of mathematics.

Kolmogorov's student years. Becoming in science.

"Kolmogorov was not just a scientist, he was a deep thinker. For him, the process of constant search for a new result, method, idea was tantamount to life itself." B. V. Gnedenko

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 doubt here about 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. Decided to do both here and there. And a seventeen-year-old youth taps two routes along the Moscow bridges with the wooden soles of homemade shoes: to the university and to Mendeleevsky. Entering the Faculty of Physics and Mathematics of Moscow University in 1920, he finally connects his life with mathematics.

« 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 work withP. S. Urysona, P. S. Alexandrova, V. V. Stepanova andN. N. Luzina, who, apparently, should be considered par excellence 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 it.”.

Lectures by professor of Moscow UniversityNikolai Nikolaevich Luzin, according to contemporaries, were an outstanding phenomenon. 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 one's own strength, and through this feeling another came - an understanding of the need for full dedication to one's favorite 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's wrong..."The “why” question was followed by a short answer from the freshman. Satisfied Luzin nodded:“Well, come to the circle, report to us your thoughts in more detail”. "Although my achievement was quite childish, it made me famous in the Lusitania"- Andrey 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 Lusitania, should be regarded as conferring the honorary title of student. As a recognition of ability.

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 foundations of mathematical analysis and closely related research in mathematical logic attracted Kolmogorov's attention almost at the very beginning of his work.

Of particular importance for the application of mathematical methods to the natural sciences and practical sciences waslaw of large 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. ATThese 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 timeChebyshevwas, as it were, a Russian national science. Its success was multiplied by many Soviet mathematicians, but the modern form of probability theory was due toaxiomatizationsproposed by Andrey Nikolaevich inand finally in. Corresponding Member of the USSR Academy of Sciences Khinchin became the founder of a new branch of probability theory - the theory of random processes. Together with A.N. Kolmogorov, he is credited with the formation of probability theory as a modern branch of mathematics. Norbert Wiener noted: "... Khinchin and Kolmogorov, two of the most prominent Russian specialists in probability theory, worked for a long time in the same field as me. For more than twenty years we stepped on each other's heels: then they proved a theorem that I I was about to prove that I managed to reach the finish line a little bit ahead of them." Khinchin was one of the first to reveal the richest possibilities of probability theory as a method of investigating problems in technology and natural science.

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".

Scientific and pedagogical activity of A. N. Kolmogorov.

"Andrey Nikolaevich belonged to those incomparable geniuses who decorate life with the very fact of their existence. The mere consciousness that somewhere on Earth the heart of a person endowed with such a perfect mind and a selfless soul is beating, inspired, gave joy, gave strength to live protected from bad deeds and inspired for good deeds.

V. M. Tikhomirov

In 1930, Kolmogorov "falls out" a long journey - a business trip to Germany and France. In Göttingen, the mathematical Mecca of the beginning of the century, he met with many outstanding colleagues, and above all with Hilbert and Courant.
Returning to Moscow, Andrei Kolmogorov became a professor at Moscow State University. In 1931, his fundamental article "On Analytical Methods in Probability Theory" was published, and two years later - the main work of his life, the monograph "Basic Concepts of Probability Theory". These works made Kolmogorov a world leader in the field of probability theory. This was followed by work on random processes, turbulence, algebraic topology. The scientist introduced one of the central concepts into topology - cohomology.

AT Mr. Kolmogorov from 1933 to 1939 was the rector of the Institute of Mathematics and Mechanics of Moscow State University, for many years he headed the Department of Probability Theory and the Laboratory of Statistical Methods. ATKolmogorov was awarded the degree of Doctor of Physical and Mathematical Sciences, inyear he was elected a memberUSSR Academy of Sciences. Shortly before the startGreat Patriotic WarKolmogorov and Khinchin for their work on the theory of probability was awardedStalin Prize ().

Kolmogorov was elected Academician in 1939. At the end of the thirties, new directions appeared in the field of his scientific interests: the problems of turbulence. The war forces Kolmogorov to interrupt his research work and turn to defense topics. On June 23, 1941, an extended meeting of the Presidium was heldUSSR Academy of Sciences. The decision adopted at the meeting marks the beginning of the restructuring of the activities of scientific institutions. Now the main thing is the military theme: all forces, all knowledge - to victory. Soviet mathematicians, on instructions from the Main Artillery Directorate of the Army, are conducting complex work in the field of ballistics and mechanics. Kolmogorov, using his research on probability theory, gives a definition of the most advantageous dispersion of projectiles during firing.

Together with the Mathematical Institute, Kolmogorov was evacuated to Kazan, but soon returned to Moscow to his duties as Academician-Secretary of the Physics and Mathematics Department of the Academy and to carry out defense work. He gets out to Kazan only from time to time, in addition, permission was required for this every time. Andrey Nikolaevich took up the theory of shooting in response to a request“give your opinion on the disagreements between the available methods for estimating the measure of accuracy from experimental data.”Kolmogorov himself notes that his work “Determination of the center of dispersion and a measure of accuracy from a limited number of observations”, submitted for publication on September 15, 1941, i.e. already three months after the start of the war, it claims mainly only methodological interest due to a critical comparison of various approaches. However, Andrei Nikolaevich, with his colleagues at the Mathematical Institute, the Faculty of Mechanics and Mathematics of the University, and direct practitioners from the Artillery Research Marine Institute, is developing a lot of theoretical and computational work on the effectiveness of firing systems. It ends with the appearance of a separate issue of "Proceedings of MIAN" (Andrei Nikolaevich called it "Shooting Collection"). At the same time, he teaches a course in the mathematical theory of shooting at the university, which he declares mandatory for students who have chosen the theory of probability as their specialty.

“Tomorrow is the longest day of the year and the anniversary of the start of the war,- writes to Kolmogorov Alexandrov in Kazan on June 21, 1942 -It is time for me to stop, for the most part, to be engaged in the experience of the ongoing world shock, to sum up some results of the first phase of this experience, to put myself in order and get down to business.

In September 1942, Kolmogorov married his classmate at the gymnasium Anna Dmitrievna Egorova, daughter of the famous historian, professor, corresponding member of the Academy of Sciences Dmitry Nikolaevich Egorov. Their marriage lasted 45 years.

In addition to academic affairs and work of a defensive nature, Andrei Nikolaevich also takes care of organizing the activities of the Faculty of Mechanics and Mathematics with the few forces that still remained in Moscow. He chairs the academic council of the faculty and the expert council of the Higher Attestation Commission, oversees mathematical journals (since the inception of Uspekhi Matematicheskikh Nauk, he has been in charge of this journal, and later organizes a number of new ones, in particular, the first “industry” mathematical journal, Theory of Probability and Its Applications) . He continues active work in his first Institute of Mathematics and Mechanics. During these first war years, when it would seem that it is difficult to allocate even an hour for proper mathematical creativity, Andrei Nikolaevich published articles that were destined to lay the foundations for the theory of turbulence, in which he became interested as early as the late 1930s.“A series of papers published in 1941,- W. Frish wrote in the book “Turbulence. Kolmogorov's legacy” (1998), -still exerts its influence on the study of turbulence. New advances often make it possible to see gems in classic works that were not seen before. This is also the case with these articles by Kolmogorov in 1941.”

In the same 1941, other fundamental works of Andrey Nikolaevich were published: “Stationary sequences in Hilbert space” and “Interpolation and extrapolation of stationary random sequences”. This year ended with the award to him (together with A.Ya. Khinchin) of the Stalin Prize for a series of works on the theory of random processes.

In 1943, forty-year-old Andrei Nikolaevich decided to keep a diary for the first time. On the first page there are two quotations from Goethe and a dedication in large, beautiful handwriting.

Dedicated to myself on my eightieth birthday with the wish to preserve by that time enough meaning at least to understand the writings of myself - forty years old - and judge them with sympathy, but also with severity.

“The experience is dear to everyone, and especially to those who remember and think about it in their declining years in the comforting confidence that no one will take this away from him.”

“Everything worthwhile has long been invented, you just have to not be afraid to try to re-invent it again.”

(Translations by B. Zakhoder.)

There is also a wonderful page in this diary, which Kolmogorov entitled:“A concrete plan on how to become a great person, if there is enough hunting and diligence for this”.

Time has shown that Andrey Nikolaevich fulfilled his entire plan and even died in the decade marked by only pass signs (Z). He did not publish the Complete Collection of his works, but managed to select those of them that were included in the three volumes of "Selected Works" published by his students. The matter did not reach only the very last point - writing memoirs of a life lived ...

Time has shown that he did much, much more than planned - he really became great, and everyone in the world recognized this.

The last war and the first post-war years can be associated with Kolmogorov's exceptional attention to the problems of probability theory and the ways of its development.

Andrei Nikolaevich talks about plans for further research and his mathematical duties in this way (this term itself"math responsibilities"- from his diary):

“Of course, these peculiar duties of a “leader” of a certain direction in probability theory must be carried out, since research in this direction must continue. I even thought of publishing shortly, in Russian and English, a short survey of problems in the theory of probability, which, in my opinion, deserve the attention of serious researchers. There are also some problems that, apparently, I will have to deal with.

But a long time ago (since 1936) I began a certain cycle of research, which arose from the problems of probability theory and dynamical systems, but turned out to be, in essence, the study of unitary representations of groups in a Hilbert space. This sounds somewhat elegant and “not classical”, but I am convinced that one of the central questions of the future “classical” mathematics is hidden here: very many problems of various styles lead exactly here.I am also very tempted by the homological topology into which I was immersed in 1934-36.With what of all this I can really cope, of course, it’s hard to say ... ”.

Now we can judge what“of all this, he really managed”and how much more was added to all this.

In 1946, he again returns to the questions that concern him. He organizes the laboratory of atmospheric turbulence at the Institute of Theoretical Geophysics of the USSR Academy of Sciences. In parallel with his work on this problem, Kolmogorov continues his successful work in many other areas of mathematics. The report "General Theory of Dynamical Systems and Classical Mechanics" read by him at the International Mathematical Congress in Amsterdam in 1954 became a world-class event.

Kolmogorov headed the mathematical department of the Great and Small Soviet Encyclopedias for many years. Many biographical articles have been published from his pen. Andrey Nikolaevich was surprisingly able to accurately say the most important thing about his colleague. He applied a similar approach to solving mathematical problems: the more general an idea is, the simpler it should be.
Academician Kolmogorov embodied the rarest combination of mathematician and natural scientist, theoretician and practitioner. He embarked on many months of voyages on the research ship "Dmitry Mendeleev", educated students, wrote not only scientific, but also popular science works.

Differentiation of education, optional courses, a network of special classes - now such a system of education is recognized as one of the main directions in the development of the national school. But Andrei Nikolayevich had to break through the wall of misunderstanding of the reasonableness of such a system for about three decades. The program of the school course of mathematics. In the mid-1960s, Andrei Nikolaevich led the work to improve the entire system of school mathematical education in the country. He worked on the creation of a program in mathematics for about three years in several stages. As a result, the structure of the course and the main methodological principles for the coming period were determined. There is no doubt that the methodology of teaching mathematics has advanced greatly thanks to his works - articles, books, textbooks. The extraordinary value of the pedagogical and methodological creativity of Andrei Nikolaevich Kolmogorov is given by the fact that it reflects the broadest, most modern view of the content and methods of teaching mathematics at school, which belongs to a person who possessed a unique combination of qualities - mathematical genius, pedagogical talent, breadth of scientific aspirations, high intelligence.

Being the initiator of the creation in 1970 of the physico-mathematical journal for youth "Kvant", from the moment of its inception and until the end of his days he was the first deputy editor-in-chief and supervised the mathematical section of this journal. Andrei Nikolaevich was the founder and first head of the editorial board of mathematics and mechanics at the Foreign Literature Publishing House.

On the days of his 80th birthday, the seriously ill Andrei Nikolayevich, recalling the years he had lived, said: "My life was full of happiness!"

In recent years, Kolmogorov headed the Department of Mathematical Logic at Moscow State University and taught at the PhMS No. 18 at Moscow State University (now - the A.N. Kolmogorov SUNC).

In 1987, Andrei Nikolayevich was already seriously ill and could hardly speak due to Parkinson's disease. Kolmogorov died on October 20, 1987 in Moscow at the age of 84. He was buried at the Novodevichy cemetery.

At the entrance of building "L" of the Moscow University building, where he lived in apartment 10 for 34 years (from the date of the construction of the new building to the day of his death), on November 18, 1997, a bronze plaque appeared with the words forever inscribed on it: "In this house since 1953 From 1987 to 1987 lived the great scientist of Russia, mathematician, professor of Moscow University, Academician Andrey Nikolaevich Kolmogorov. This is a modest tribute from the university to its professor.

On May 19, 2008, a street named after the great scientist, teacher, humanist and patriot Andrei Nikolayevich Kolmogorov was solemnly opened in Yaroslavl. This happened on the first day of the sixth scientific Kolmogorov readings, which have already become traditional and the program of which contains both scientific research in many areas of mathematics, as well as in the theory and methods of teaching mathematics, in the history of mathematics and mathematical education. Opening of A.N. Kolmogorov was initiated (and supported by the city authorities) Yaroslavl State Pedagogical University. K.D. Ushinsky (V.V. Afanasiev, E.I. Smirnov, R.Z. Gushel and others) and the Moscow State University. M.V. Lomonosov (V.A. Sadovnichiy, V.M. Tikhomirov and others).

On the wall of one of the new houses of the street opened in Yaroslavl, a memorial plaque is attached, on which it is written: “The street is named after our fellow countryman, an outstanding mathematician, academician, Hero of Socialist Labor Andrey Nikolaevich Kolmogorov (25.IY.1903 - 20.X. 1987)».

A.N. Kolmogorov created one of the largest scientific schools in the country. The whole life of Andrei Nikolayevich was devoted to the search for truth and the cause of the Enlightenment. It is he who can rightly be called the Enlightener - a person who illuminated the life and scientific path of many, many.

CONCLUSION

“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 on him a greater boon.”

Albert Einstein

The 20th century is the century of the atom, electronics and cybernetics, the century of great space research and discoveries. All this became possible thanks to the progress of mathematical science. Only modern mathematical methods allow people to solve important technical problems and introduce automation into production. We appreciate the outstanding achievements of Russian mathematicians of the 20th century.

The rapidly increasing time distance allows us to better understand the scope of Andrei Nikolayevich Kolmogorov's personality, to appreciate his democracy, the depth of pedagogical thinking.

An ingenious Scientist, a great Enlightener, a wonderful Person - the name of Andrei Nikolaevich Kolmogorov is inscribed in golden letters in the galaxy of the greatest people on the planet.

“In any case, I have always lived guided by the thesis that TRUTH is the main thing, that our duty is to find and defend it, regardless of whether it is pleasant or unpleasant. In any case, in my conscious life I have always proceeded from such positions.

Andrey Nikolaevich Kolmogorov

Review of the work "Andrei Nikolaevich Kolmogorov - an outstanding Russian mathematician of the twentieth century." The work was done by a student of 11 "a" class Huurak Aelita.

A lot of work has been done to search for materials about A.N. Kolmogorov, an outstanding Russian mathematician: about his childhood, about his student years, about scientific and pedagogical activities, about his awards and achievements.

At all times there have been and are people, undeniable bearers of moral values, including scientists, writers, statesmen, people of labor, whose lives and deeds help us to believe in words about duty, honor, and justice. Book about Kolmogorov. Digest of articles. - M.: "FAZIS", "MIROS", 1999.

A.N. Shiryaev - "Life in search of truth (on the 100th anniversary of the birth of Andrei Nikolaevich Kolmogorov)". Journal "Nature", No. 4, 2003

Baltic State Fishing Fleet Academy

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 of elementary probability theory

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 Moscow State University (1931), Academician of the USSR Academy of Sciences (1939). Kolmogorov is one of the founders of modern probability theory, he obtained fundamental results in topology, mathematical logic, turbulence theory, algorithm complexity theory 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 works of students - drawings, poems, stories. Andrey's "scientific works" also appeared in it - arithmetic problems invented by him. Here the boy published his first scientific work in mathematics at the age of five. 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 the construction of the Kazan-Yekaterinburg railway. Simultaneously with work, I continued to study on my own, preparing to take an external student 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 phenomenon. 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 Nikolayevich 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 Lusitania, should be regarded as conferring the honorary title of 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 foundations of mathematical analysis and closely related research in mathematical logic attracted Kolmogorov's attention almost at the very beginning of his work. He took part in discussions between the two main opposing methodological schools at that time - formal-axiomatic (D. Hilbert) and intuitionistic (E.Ya. Brouwer and G. Weyl). 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 the natural sciences and practical sciences was the law of large 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. Since the time of Chebyshev, the science "about the case" has been, as it were, a Russian national science. Many Soviet mathematicians multiplied its successes, but the theory of probability received its modern form 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".

Andrey Nikolaevich Kolmogorov(April 25, 1903, Tambov - October 20, 1987, Moscow) - one of the most prominent mathematicians of the 20th century, a person with the broadest mathematical horizons. He is one of the main initiators of the founding of the Moscow boarding school FMS 18 (now - SASC MGU named after A.N. Kolmogorov). Andrei Nikolaevich is primarily known for his integral contribution to such areas of mathematics as topology, geometry, functional analysis, measure theory, the theory of differential equations, the theory of dynamical systems, information theory, classical mechanics and many others, in fact, he is the founder of the modern axiomatics of probability theory.

Andrei Nikolaevich was born on April 12 (25), 1903 in Tambov in the family of Nikolai Matveevich Kataev and Maria Yakovlevna Kolmogorova. His parents left him at an early age, so he was brought up in Yaroslavl by his mother's sisters. Even then, Kolmogorov showed amazing mathematical abilities.

In 1920, Andrei Nikolaevich entered the mathematical department of Moscow University. Having passed all the exams for the course in the very first months, Kolmogorov begins his scientific activity, gradually solving more and more complex problems. This is how Andrei Nikolayevich is noticed by the famous theorist of real analysis, Nikolai Nikolayevich Luzin, who became his scientific adviser. In 1922, Kolmogorov built a famous example of a Fourier series that diverges almost everywhere, which makes him world famous.

In the first half of the 20th century, many theoretically necessary questions of measure theory and real analysis were very popular; functional analysis and probability theory gradually arose. Many outstanding mathematicians such as David Hilbert, Richard Courant, A.Ya. Khinchin, in fact, N.N. Luzin, worked in this area. Andrei Nikolaevich did not stand aside either. Young Kolmogorov first obtained the law of large numbers, and in 1933 for the first time published the well-known work "Basic Concepts of Probability Theory", published in German. This work represented an exact axiomatic of the theory of probability that leading minds had been thinking about since the turn of the century.

In 1931, Kolmogorov became a professor at Moscow State University, from 1933 to 1939 he was director of the Institute of Mechanics of Moscow State University, founded and for many years headed the Department of Probability Theory of the Faculty of Mechanics and Mathematics and the Interfaculty Laboratory of Statistical Methods. The degree of Doctor of Physical and Mathematical Sciences Kolmogorov was awarded in 1935 without defending a dissertation. In 1939, the 35-year-old Kolmogorov was immediately elected a full member (omitting the title of corresponding member) of the Academy of Sciences of the USSR, a member of the Presidium of the Academy and, at the suggestion of O.Yu.

All this time, Andrey Nikolayevich has been engaged not only in theoretical problems, but also in practical ones. So, during the war, you can see the results associated with the dispersion of shells (necessary in such a difficult period for the homeland), after which he deals with issues of turbulence. In the 1950s and 1960s, along with the development of random processes as a separate discipline and the gradual exploration of space, Kolmogorov wrote many works related to these areas. In particular, Andrei Nikolaevich proves a number of facts from celestial mechanics, many results appear related to dynamical systems, the famous KAM theory. At the same time, the theory of algorithms and information theory were also developing, in connection with which Kolmogorov introduced the concept of the complexity of an algorithm and, in accordance with this, posed the problem of measuring complexity.

Approximately in the mid-1960s, a rethinking of the teaching system took place in the USSR. Specialized schools are being set up all over the country. In particular, in 1963 in Moscow (as well as in Kyiv, Novosibirsk and Leningrad) the Specialized Boarding School No. 18 of the Physics and Mathematics profile was founded (now the SUNC of Moscow State University named after A.N. Kolmogorov), one of the initiators of the creation which was made by Andrey Nikolaevich. While teaching at FMS 18 and Moscow University, in 1970, together with academician I.K. Kikoin, Kolmogorov created the Kvant magazine. At the end of his life, Andrei Nikolaevich focuses on teaching. Even at school, he put the development of creative thinking in the first place: “It is essential that here in the boarding school, schoolchildren come into contact with creative thought. This is our request, but in all subjects! .. The method of work is an imitation of scientific research, step by step to find, calculate something ... and not to give ready-made ... ".

Academician A.N. Kolmogorov died on October 20, 1987 in Moscow at the age of 84. He was buried at the Novodevichy cemetery.

Selected publications

• A.N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitrechnung, in Ergebnisse der Mathematik, Berlin. 1933.
• AN Kolmogorov, On operations on sets, Mat. Sat., 1928, 35:3-4
• AN Kolmogorov, General measure theory and probability calculus // Proceedings of the Communist Academy. Maths. - M.: 1929, v. 1. S. 8 - 21.
• A. N. Kolmogorov, On analytical methods in the theory of probability, Uspekhi Mat. Nauk, 1938:5, 5-41
• AN Kolmogorov, Basic concepts of probability theory. Ed. 2nd, M. Nauka, 1974, 120 p.
• AN Kolmogorov, Theory of information and theory of algorithms. - M.: Nauka, 1987. - 304 p.
• A. N. Kolmogorov, S. V. Fomin, Elements of the theory of functions and functional analysis. 4th ed. M. Science. 1976 544 p.
• AN Kolmogorov, Theory of Probability and Mathematical Statistics. M. Science 1986. 534s.
• A. N. Kolmogorov, “On the profession of a mathematician.” M., Publishing House of Moscow University, 1988, 32p.
• A. N. Kolmogorov, “Mathematics is a science and a profession.” M.: Nauka, 1988, 288 p.
• A. N. Kolmogorov, I. G. Zhurbenko, A. V. Prokhorov, "Introduction to Probability Theory". M.: Nauka, 1982, 160 p.

At the initiative of Abramov A.M. (graduated from the Faculty of Music School No. 18 at Moscow State University in 1964), Vavilova V.V. and Tikhomirov V.M. and with the support of the director of the Russian State Library A. I. Visly (graduated from the Faculty of Music School No. 18 at Moscow State University in 1975)thislibrariescompiled a list of publications about the life and work of A.N. Kolmogorov, since 1941.

Kolmogorov Andrey Nikolaevich (born Kataev, April 12 (25), 1903, Tambov - October 20, 1987, Moscow) - one of the greatest mathematicians of the twentieth century, academician (1939). Hero of Socialist Labor (1963). He spent his childhood in Yaroslavl.

He was born on April 12 (April 25, according to a new style), 1903 in Tambov, where his mother lingered on the way from the Crimea home to Yaroslavl Maria Yakovlevna Kolmogorova(1871-1903), daughter of the leader of the Uglich nobility, trustee of public schools in the Yaroslavl province Yakov Stepanovich Kolmogorov. In Tambov, she died in childbirth.

Father - Nikolai Matveevich Kataev (? - 1919), a graduate of the Moscow Agricultural Institute, an agronomist, belonged to the Right SR party, was exiled from St. Petersburg for participating in the revolutionary movement in the Yaroslavl province, where he met Maria Yakovlevna. My paternal grandfather was a village priest in the Vyatka province.

Uncle Andrei Kolmogorov - Ivan Matveevich Kataev(1875-1946) - graduate of Moscow University, historian, professor, doctor of historical sciences, author of works on archeography, national history, history of Moscow, essays on Russian history, author of a textbook on Russian history for secondary school in three parts (published in 1907 ). The son of Ivan Matveyevich - Ivan Ivanovich Kataev (1902 - 1937, shot), writer, cousin of Andrei Kolmogorov.

Until the age of seven, Andrei was brought up in Yaroslavl by his mother's sisters, who lived in a house on Ilyinskaya (Proboynaya) Street, the modern address is st. Soviet, 3. One of them, Vera Yakovlevna Kolmogorova, officially adopted Andrei. Aunts in their house organized a school for children of different ages who lived nearby, studied with them, a handwritten magazine “Spring Swallows” was published for the children. It published creative works of students - drawings, poems, stories. Andrey's "scientific works" - arithmetic problems invented by him, also appeared in the journal. Here the boy published his first work in mathematics at the age of five. Together with Andrey, Pyotr Savvich Kuznetsov, later a well-known Soviet linguist, spent his childhood in his grandfather's house.

In 1910 Vera Yakovlevna Kolmogorova moved with Andrey to Moscow to be assigned to the Repman private gymnasium, one of the few where boys and girls studied together. Andrey already in those years showed remarkable mathematical abilities. Kolmogorov did not have time to finish the gymnasium - a revolution happened. As he later recalled, In 1918-1920, life in Moscow was not easy. In schools, only the most persistent were seriously engaged. At this time, I had to leave for the construction of the Kazan-Yekaterinburg railway. Simultaneously with work, I continued to study on my own, preparing to take an external student for high school. Upon returning to Moscow, I experienced some disappointment: they issued me a certificate of graduation without even bothering to take an exam».

In 1920, Kolmogorov entered the mathematical department of Moscow University, where his teachers were the best mathematicians of that time. In the very first months, Andrei passed the exams for the course. In his student years, in addition to mathematics, Kolmogorov was seriously engaged in a seminar on ancient Russian history. Already in his second year at the university, Kolmogorov made a number of mathematical discoveries that brought him world fame. And further work put him among the leading mathematicians of the world.

In 1931, Kolmogorov became a professor at Moscow State University, from 1933 to 1939 he was director of the Institute of Mathematics and Mechanics of Moscow State University, founded and for many years headed the Department of Probability Theory of the Faculty of Mechanics and Mathematics and the Interfaculty Laboratory of Statistical Methods. The degree of Doctor of Physical and Mathematical Sciences Kolmogorov was awarded in 1935 without defending a dissertation.

In 1939, at the age of 35, Kolmogorov was immediately elected a full member (omitting the title of corresponding member) of the USSR Academy of Sciences, a member of the Presidium of the Academy and, at the suggestion of O. Yu. Schmidt, Academician-Secretary of the Department of Physical and Mathematical Sciences of the USSR Academy of Sciences.

Shortly before the start of the Great Patriotic War, Kolmogorov and Khinchin were awarded the Stalin Prize (1941) for their work on the theory of random processes.

On June 23, 1941, an expanded meeting of the Presidium of the USSR Academy of Sciences was held, at which a decision was made to restructure the activities of scientific institutions on military topics. Soviet mathematicians, on the instructions of the Main Artillery Directorate of the Red Army, carried out complex work in the field of ballistics and mechanics. Kolmogorov, using his research on probability theory, gave a definition of the most advantageous dispersion of projectiles during firing.

In September 1942, Kolmogorov married his classmate at the gymnasium, Anna Dmitrievna Egorova, daughter of the famous historian, professor, corresponding member of the Academy of Sciences, Dmitry Nikolaevich Egorov. Their marriage lasted 45 years. Kolmogorov did not have his own children; his stepson, O. S. Ivashev-Musatov, was brought up in the family.

Back in the late thirties, Kolmogorov began to investigate the problems of turbulence. In 1946, he returned to these questions by organizing an atmospheric turbulence laboratory at the Institute of Theoretical Geophysics of the USSR Academy of Sciences. In parallel with his work on this problem, Kolmogorov continued his successful work in many areas of mathematics. Together with S. V. Fomin, he wrote the textbook "Elements of the Theory of Functions and Functional Analysis", which went through seven editions (7th ed. - M .: Fizmatlit, 2012). The textbook has been translated into English, French, German, Spanish, Japanese, Dari, Czech.

In the mid-1960s, on the instructions of the Ministry of Education of the USSR, under the leadership of A. N. Kolmogorov, programs were developed and new textbooks in mathematics for secondary school were created: a textbook on geometry, a textbook on algebra and the basics of analysis. In 1963, Kolmogorov was one of the initiators of the creation of a boarding school at Moscow State University and began teaching there himself.

In March 1966, he signed a letter from 13 figures of Soviet science, literature and art to the Presidium of the Central Committee of the CPSU against the rehabilitation of I.V. Stalin.

In 1966, Kolmogorov was elected a full member of the Academy of Pedagogical Sciences of the USSR. In 1970, together with academician I. K. Kikoin, he created the journal Kvant.

In recent years, Kolmogorov headed the Department of Mathematical Logic at Moscow State University and taught at the PhMS No. 18 at Moscow State University.

Kolmogorov's life interests were not limited to pure mathematics: he was fascinated by philosophical problems, the history of science, painting, literature, and music.

Awards and prizes: Hero of Socialist Labor (1963), seven Orders of Lenin (1944, 1945, 1953, 1961, 1963, 1973, 1975), Order of the October Revolution (1983), Order of the Red Banner of Labor (1940), Stalin Prize (1941, together with A. Ya. Khinchin), Lenin Prize (1965, together with V. I. Arnold), other awards

A.N. Kolmogorov was a member of the US National Academy of Sciences (1967), the Royal Society of London (1964), the Leopoldina German Academy of Natural Sciences (1959), the French (Paris) Academy of Sciences (1968), the American Academy of Arts and Sciences (1959), the Hungarian Academy of Sciences (1965), Polish Academy of Sciences (1956), Royal Netherlands Academy of Sciences (1963), Academy of Sciences of the GDR (1977), Finnish Academy of Sciences (1985), Romanian Academy, London Mathematical Society (1962), Indian Mathematical Society (1962), American Philosophical Society (1961); honorary doctorate from the University of Paris (1955), Stockholm University (1960), Indian Statistical Institute in Calcutta (1962).

In 2003, in Yaroslavl, a memorial plaque was erected on the house where Andrei Kolmogorov lived in 1903-1910, and in 2008, a street in the Yaroslavl Sokol microdistrict was named after him.

ANDREY NIKOLAEVICH KOLMOGOROV

According to the apt expression of one scientist, a mathematician is one who knows how to find analogies between statements. The best mathematician - who establishes analogy proofs. The stronger one can notice the analogies of theories. But there are those who see analogies between analogies. Andrey Nikolaevich Kolmogorov, one of the best, if not the best mathematician of the twentieth century, belongs to these rare representatives of the latter.

Andrei Nikolaevich Kolmogorov was born on April 12 (25), 1903 in Tambov. 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 works of students - drawings, poems, stories. Andrey's "scientific works" also appeared in it - arithmetic problems invented by him. Here the boy published his first scientific work in mathematics at the age of five. 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 under the threat of closing all the time.

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 Nikolaevich recalled. - In schools, only the most persistent were seriously engaged. At this time, I had to leave for the construction of the Kazan-Yekaterinburg railway. Simultaneously with work, I continued to study on my own, preparing to take an external student 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.

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 PS Uryson, PS Alexandrov, VV Stepanov and NN Luzin, who, apparently, should be considered par excellence 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": sixteen kilograms of bread and a kilogram of butter per month - this is real 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 phenomenon. 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 “why” question was followed by a short answer from the freshman. 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 Nikolayevich 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 Nikolayevich 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 Lusitania, should be regarded as conferring the honorary title of student. As a recognition of ability.

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 foundations of mathematical analysis and closely related research in mathematical logic attracted Kolmogorov's attention almost at the very beginning of his work. He took part in discussions between the two main opposing methodological schools at that time - formal-axiomatic (D. Hilbert) and intuitionistic (L. E. Ya. Brower and G. Weil). In doing so, he got 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.

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.

Since the time of Chebyshev, the science "about the case" has been, as it were, a Russian national science. Her successes were multiplied by Soviet mathematicians.

Of particular importance for the application of mathematical methods to the natural sciences and practical sciences was the law of large numbers. To find the necessary and sufficient conditions under which it takes place - this 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.

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".

Norbert Wiener, the father of cybernetics, testified: “... Khinchin and Kolmogorov, two of the most prominent Russian specialists in probability theory, worked for a long time in the same field as me. For more than twenty years, we stepped on each other's heels: either they proved the theorem that I was about to prove, or I managed to reach the finish line a little earlier than them.

And one more confession of Wiener, which he once made to journalists: “For thirty years now, when I read the works of Academician Kolmogorov, I feel that these are my thoughts. This is always what I myself wanted to say.

In 1930, Kolmogorov became a professor at Moscow State University, from 1933 to 1939 he was rector of the Institute of Mathematics and Mechanics of Moscow State University, for many years he headed the Department of Probability Theory and the Laboratory of Statistical Methods. In 1935, Kolmogorov was awarded the degree of Doctor of Physical and Mathematical Sciences, in 1939 he was elected a member of the USSR Academy of Sciences. Shortly before the start of the Great Patriotic War, Kolmogorov and Khinchin were awarded the State Prize for their work on probability theory.

And on June 23, 1941, an expanded meeting of the Presidium of the USSR Academy of Sciences was held. The decision adopted at the meeting marks the beginning of the restructuring of the activities of scientific institutions. Now the main thing is the military theme: all forces, all knowledge - to victory. Soviet mathematicians, on instructions from the Main Artillery Directorate of the Army, are conducting complex work in the field of ballistics and mechanics. Kolmogorov, using his research on probability theory, gives a definition of the most advantageous dispersion of projectiles during firing.

The war is over, and Kolmogorov is returning to peaceful research. It is difficult to even briefly highlight Kolmogorov's contribution to other areas of mathematics - the general theory of operations on sets, integral theory, information theory, hydrodynamics, celestial mechanics, etc., all the way to linguistics. In all these disciplines, many of Kolmogorov's methods and theorems are, admittedly, classical, and the influence of his work, as well as the work of his numerous students, among whom there are many outstanding mathematicians, on the general course of the development of mathematics is extremely great.

When one of Kolmogorov's young colleagues was asked how he felt about his teacher, he replied: "Panic respect ... You know, Andrei Nikolaevich gives us so many of his brilliant ideas that they would be enough for hundreds of excellent developments."

A remarkable pattern: many of Kolmogorov's students, gaining independence, began to play a leading role in the chosen direction of research. And the academician proudly emphasizes that the most dear to him are students who have surpassed teachers in scientific research.

One can be surprised at Kolmogorov's asceticism, his ability to practice at the same time - and not without success! - many things at once. This is the management of the university laboratory of statistical methods of research, and the care of the physics and mathematics boarding school, the initiator of which Andrei Nikolayevich was the initiator of the creation of which Andrei Nikolaevich was, and the affairs of the Moscow Mathematical Society, and work on the editorial boards of Kvant, a magazine for schoolchildren, and Mathematics at School - methodical journal for teachers, and scientific and teaching activities, and the preparation of articles, brochures, books, textbooks. Kolmogorov never had to beg to speak at a student debate, to meet schoolchildren at a party. In fact, he was always surrounded by young people. He was very loved, his opinion was always listened to. Not only the authority of the world famous scientist played a role, but also the simplicity, attention, spiritual generosity that he radiated.

The circle of Andrei Nikolaevich's vital interests was not limited to pure mathematics, the unification of the individual sections of which into one whole he devoted his life to. He was fascinated by philosophical problems, and the history of science, and painting, and literature, and music.

Academician Kolmogorov is an honorary member of many foreign academies and scientific societies. In March 1963, the scientist was awarded the international Bolzano Prize, which is called the "Nobel Prize for Mathematicians" (the work of mathematicians was not specified in Nobel's will). In the same year, Andrei Nikolaevich was awarded the title of Hero of Socialist Labor. In 1965 he was awarded the Lenin Prize (together with V. I. Arnold). In recent years, Kolmogorov headed the Department of Mathematical Logic.

“I belong,” the scientist said, “to those extremely desperate cyberneticists who do not see any fundamental limitations in the cybernetic approach to the problem of life and believe that it is possible to analyze life in its entirety, including human consciousness, using the methods of cybernetics. Progress in understanding the mechanism of higher nervous activity, including the highest manifestations of human creativity, in my opinion, does not diminish anything in the value and beauty of human creative achievements.

From the book Encyclopedic Dictionary (B) author Brockhaus F. A.

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