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25.01.2008 Andrey Nikolaevich Kolmogorov
Category: Mathematics
(1903-1987)
Mathematician
A WORLD BUILT ON PROBABILITY
During his lifetime, he was called a titan of the Renaissance, a harmonious representative of antiquity, and Pushkin in mathematics.
The widest range of creative interests, the variety of mathematical fields in which Andrey Nikolaevich worked, made him an encyclopedist of this ancient science.
We can say that in the history of the XX century there is hardly a mathematician who would work so successfully in the field of set theory and measure theory, mathematical logic and topology.
He was born on April 25, 1903 in Tambov, where his mother, Maria Yakovlevna Kolmogorova, was delayed on the way from the Crimea.
She died in childbirth, and all the care of the baby was taken over by her own sister Vera Yakovlevna.
She replaced Andrey's mother, and he treated her as a mother until her death.
On his mother's side, Kolmogorov came from the nobility.
His grandfather Yakov Stepanovich Kolmogorov was a district leader of the nobility.
The Kolmogorovs owned the Tunoshna estate, located on the Tunoshonka River near its confluence with the Volga near Yaroslavl, and a large house in Yaroslavl itself.
Andrey's father, Nikolai Matveyevich Kataev, was the son of a priest.
He received a higher special education, becoming, as they said at the time, "a scientific agronomist".
After the revolution, he worked in the People's Commissariat of Agriculture.
His father did not take part in Andrey's upbringing.
In 1910, Vera Yakovlevna and Andrey moved to Moscow.
They lived on the interest from the capital received by inheritance.
Andrey entered the private gymnasium Repman, which after the revolution was transformed into the twenty third school of the second stage.
He graduated in 1920.
And I didnot immediately decide to become a mathematician.
It was a hungry and anxious time.
The young man wanted to get not only knowledge, but also a profession, a craft.
Here is how he himself later recalled this period of his life: "At that time, technology was perceived as something more serious and necessary than pure science.
Simultaneously with the mathematics department of the university (where everyone was admitted without exams) I entered the metallurgical faculty of the Mendeleev Institute (where an entrance exam in mathematics was required).
But soon the interest in mathematics exceeded the doubts about the relevance of the profession of mathematics."
Student Kolmogorov teaches his favorite subject at school, which provides him with a livelihood.
At the same time, he conducts his first research under the guidance of the famous mathematician N. Luzin.
At the beginning of 1922, Kolmogorov completed his work on set theory, and in the spring of the same year he built a Fourier series.
This brings the young mathematician worldwide fame.
In 1925, Andrey Nikolaevich graduated from the university and became a graduate student of Luzin.
In the same year, he began his famous research in the field of probability theory.
"In those years," Kolmogorov recalled, " the period of stay in graduate school was not strictly limited — there was, for example, a case when a young mathematician stayed in graduate school for seven years!
Since being in graduate school gave me complete freedom to indulge in scientific research without having other responsibilities, I also preferred not to force its completion."
Andrey Nikolaevich graduated from graduate school in 1929 and became a researcher at the Research Institute of Mathematics and Mechanics of Moscow State University.
At the same time, he heads the Department of Mathematics at the Liebknecht Pedagogical Institute.
A number of the highest creative achievements of the great mathematician belong to the 20s.
He creates a general theory of operations on sets, studies trigonometric series, writes several works on mathematical logic, turns probability theory into a strict and systematic mathematical discipline.
He creates a general theory of operations on sets, studies trigonometric series, writes several works on mathematical logic, turns probability theory into a strict and systematic mathematical discipline.
In 1930, Kolmogorov "falls" on a long road — a business trip to Germany and France.
In Göttingen — the mathematical Mecca of the turn of the century he meets with many outstanding colleagues, and above all with Hilbert and Courant.
Later, Andrey Nikolaevich very vividly described the conditions that Mecca provided for young mathematicians to work: "The Mathematical Institute represented exceptional facilities for scientific studies.
Young scientists were provided with a small separate room with a desk, two chairs and shelves for books and all sorts of papers, and they were also given a key to the library, where they could take any books without asking anyone, take them to their work room.
It was assumed, of course, that after passing the need, the books taken are immediately taken to the library and put there in their proper place."
Returning to Moscow, Andrey Kolmogorov becomes 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 luminary in the field of probability theory.
This was followed by work on random processes, turbulence, and algebraic topology.
The scientist introduced one of the central concepts into topology — cohomology.
A huge place in Kolmogorov's life was occupied by friendship with another outstanding mathematician — Pavel Sergeevich Alexandrov.
It began in the summer of 1929 and lasted for more than 53 years until the death of Alexandrov.
Andrey Nikolaevich wrote: "For me, these fifty three 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."
One of the main events of this great friendship dates back to 1935: Kolmogorov and Alexandrov acquired a part of a country house in the village of Komarovka on the picturesque bank of the Klyazma River.
It was in this house that their creative activity mainly took place.
During his life, Andrey Nikolaevich held many responsible administrative posts.
It is particularly worth noting that in 1935 he founded the Department of Probability Theory at the Moscow State University Faculty of Mechanics and Mathematics.
Kolmogorov was elected an academician in 1939.
At the end of the thirties, new directions appeared in the field of his scientific interests: problems of turbulence.
The war forces Kolmogorov to interrupt his research work and turn to defense topics, but in 1946 he again returns to the issues 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", which he read at the International Mathematical Congress in Amsterdam in 1954, became a world class event.
Ilya Prigozhy, the creator of the theory of dissipative structures and a Nobel laureate, describing the highest achievements of the XX century, wrote: "We are experiencing a revolution in this field of knowledge.
Thanks to the Soviet scientist Andrey Kolmogorov, dynamics has become one of the most actively developed areas in physics and mathematics.
What is this revolution? <...
> The concepts of instability, chaos, and the growth of the amplitude of fluctuations are of interest today to an increasing number of researchers in various fields: from mathematics to economics.
The famous "black Monday" (October 19, 1987), the day when the stock price fell first on the New York and then on other exchanges, will probably go down in the history of science, but not at all because the victims of exchange frauds lost part of their capital.
The fact is that from that day on, major American newspapers began publishing articles on the dynamics of chaos, and the concepts of "fluctuation", "amplitude growth" and "bifurcation" became as familiar as the "Big Bang"and" black holes".
Kolmogorov for many years headed the mathematical department of the Large and Small Soviet Encyclopedias.
Many biographical articles were published from his pen.
Andrey Nikolaevich was surprisingly able to say the most important thing about his colleague.
He applied a similar approach to solving mathematical problems: the more general the idea is, the simpler it should be.
Academician Kolmogorov embodied the rarest combination of a mathematician and a natural scientist, a theorist and a practitioner.
He embarked on many months of voyages on the research vessel "Dmitry Mendeleev", educated students, wrote not only scientific, but also popular scientific works.
In terms of the breadth of his interests, he really was a man of the Renaissance, embodied in the XX century.
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