Physicist Pyotr Kapitsa is depicted in this black-and-white portrait, wearing a suit with an open-collared shirt and displaying a thoughtful expression. Known for his groundbreaking research in low-temperature physics and his discovery of superfluidity in helium, Kapitsa made significant contributions to the field of condensed matter physics.
Physicist Pyotr Kapitsa is depicted in this black-and-white portrait, wearing a suit with an open-collared shirt and displaying a thoughtful expression. Known for his groundbreaking research in low-temperature physics and his discovery of superfluidity in helium, Kapitsa made significant contributions to the field of condensed matter physics.

Andrey Nikolaevich Kolmogorov

Historical

Historical

Apr 25, 1903

-

Oct 20, 1987

Physicist Pyotr Kapitsa is depicted in this black-and-white portrait, wearing a suit with an open-collared shirt and displaying a thoughtful expression. Known for his groundbreaking research in low-temperature physics and his discovery of superfluidity in helium, Kapitsa made significant contributions to the field of condensed matter physics.

Andrey Nikolaevich Kolmogorov

Historical

Historical

Apr 25, 1903

-

Oct 20, 1987

Biography

FAQ

Quotes

Biography

Andrey Kolmogorov was one of the most prominent Soviet mathematicians who introduced a new approach to probability theory and made significant contributions to several areas of mathematics, such as turbulence theory, topology, logic, and information theory. He was born in Tambov, Russia, and lost his mother during childbirth. His father also disappeared during political purges, and his aunts raised him. Kolmogorov started exhibiting signs of genius at the age of five, making patterns of numbers. His academic attainment at Moscow State University broadened his thought base, and by 1925, he had provided substantial contributions to mathematics, including set theory, trigonometric series, and probability.

In his scientific career, Kolmogorov met many famous mathematicians and joined the Moscow Mathematical Society. However, the key to his growth and fame came in 1933 when he published the "Foundations of the Theory of Probability," where he used axioms to formally present the probability theory, which he compared to how Euclid presented geometry. In the context of the political pressure of Stalin's Soviet Union, Kolmogorov successfully navigated between scientific discovery and political constraint and was involved in different controversies, including the "Luzin Affair."

Kolmogorov's research was wide-ranging. He made stochastic processes and turbulence, which were significant in physics, his specialty; at the same time, he also ventured into topology and classical mechanics. In his later years, he developed the algorithmic complexity theory, now called the Kolmogorov complexity, which gives the amount of resources needed to describe an object. Besides his outstanding mathematical achievements, Kolmogorov demonstrated great concern for developing gifted students and was actively involved in establishing special schools for talented youth in Moscow. He died in 1987 but made outstanding contributions to mathematics and education.

Quotes

"Each mathematician thinks he is more intelligent than others, and that's why none of them say it out loud – they are smart men."

"The most important is to teach a student how to think mathematically."

"Probability is the ultimate reality. Therefore, people cannot escape the fact that the world is random."

"Mathematics is a means of discovering the world's underlying patterns."

"It is worth mentioning that turbulence is classical physics's most important unsolved problem."

"Every piece I have done is based on my belief that nature is probabilistic."

"To understand is to perceive regularities."

"The interdependence of randomness and order is an essential aspect of life, which cannot be easily explained."

"An accurate mathematical theory captures the objective features of reality. In this sense, an accurate mathematical theory is a structural theory."

"Some wise man has said that the laws of probability were not given to us to believe in miracles but to avoid them."

"Every step in mathematics is a proof and discovery at the same time."

"Science is about explaining the complicated: 'What makes things go round is the attempt to reduce the complicated.'"

"It's also crucial to note the famous quote, 'The measure of intelligence is the ability to change.'"

"Probability is the theory where nothing is certain, yet everything can be explained."

"Mathematics is not just about solutions but also about posing the correct questions."

FAQ

What has Kolmogorov been most known for?

He is most well known for his work in probability theory and for establishing its modern axiomatic basis.

What can be considered Kolmogorov's significant contribution to the development of mathematics?

He is best known for creating probability theory in the axiomatic form, manifested in his work titled Theory of Probability, published in 1933.

Were there any political issues that Kolmogorov had to encounter at his workplace?

Yes, he survived Stalinist purges and participated in the "Luzin Affair," wherein he testified against his former teacher; it is still a matter of discussion whether he did this willingly.

What are Kolmogorov's equations?

The Kolmogorov equations are several mathematical formulas that define the changes of probabilities over time in the Markov processes.

What is Kolmogorov's complexity?

Kolmogorov complexity can be defined as the slightest description of an object regarding the resources used in the computation.

In what other fields apart from mathematics did Kolmogorov work?

They include Nikolai Luzin and Pavel Alexandrov, who he studied under, and other mathematicians such as Aleksandr Khinchin and Paul Lévy.

Who were Kolmogorov's influences?

They include Nikolai Luzin and Pavel Alexandrov, who he studied under, and other mathematicians such as Aleksandr Khinchin and Paul Lévy.

What is the KAM theorem?

The KAM theorem, created by Vladimir Arnold, concerns the stability of motion trajectories and Newton's mechanics.

Which awards did Kolmogorov get during his lifetime?

He received the Stalin, Lenin, and Wolf awards, among many other international awards.

It is also essential to know how Kolmogorov contributed to education.

He spent a lot of effort creating curricula for gifted children, especially in mathematics. He made it a practice to teach many of the leading mathematicians in the future.

Biography

FAQ

Quotes

Biography

Andrey Kolmogorov was one of the most prominent Soviet mathematicians who introduced a new approach to probability theory and made significant contributions to several areas of mathematics, such as turbulence theory, topology, logic, and information theory. He was born in Tambov, Russia, and lost his mother during childbirth. His father also disappeared during political purges, and his aunts raised him. Kolmogorov started exhibiting signs of genius at the age of five, making patterns of numbers. His academic attainment at Moscow State University broadened his thought base, and by 1925, he had provided substantial contributions to mathematics, including set theory, trigonometric series, and probability.

In his scientific career, Kolmogorov met many famous mathematicians and joined the Moscow Mathematical Society. However, the key to his growth and fame came in 1933 when he published the "Foundations of the Theory of Probability," where he used axioms to formally present the probability theory, which he compared to how Euclid presented geometry. In the context of the political pressure of Stalin's Soviet Union, Kolmogorov successfully navigated between scientific discovery and political constraint and was involved in different controversies, including the "Luzin Affair."

Kolmogorov's research was wide-ranging. He made stochastic processes and turbulence, which were significant in physics, his specialty; at the same time, he also ventured into topology and classical mechanics. In his later years, he developed the algorithmic complexity theory, now called the Kolmogorov complexity, which gives the amount of resources needed to describe an object. Besides his outstanding mathematical achievements, Kolmogorov demonstrated great concern for developing gifted students and was actively involved in establishing special schools for talented youth in Moscow. He died in 1987 but made outstanding contributions to mathematics and education.

Quotes

"Each mathematician thinks he is more intelligent than others, and that's why none of them say it out loud – they are smart men."

"The most important is to teach a student how to think mathematically."

"Probability is the ultimate reality. Therefore, people cannot escape the fact that the world is random."

"Mathematics is a means of discovering the world's underlying patterns."

"It is worth mentioning that turbulence is classical physics's most important unsolved problem."

"Every piece I have done is based on my belief that nature is probabilistic."

"To understand is to perceive regularities."

"The interdependence of randomness and order is an essential aspect of life, which cannot be easily explained."

"An accurate mathematical theory captures the objective features of reality. In this sense, an accurate mathematical theory is a structural theory."

"Some wise man has said that the laws of probability were not given to us to believe in miracles but to avoid them."

"Every step in mathematics is a proof and discovery at the same time."

"Science is about explaining the complicated: 'What makes things go round is the attempt to reduce the complicated.'"

"It's also crucial to note the famous quote, 'The measure of intelligence is the ability to change.'"

"Probability is the theory where nothing is certain, yet everything can be explained."

"Mathematics is not just about solutions but also about posing the correct questions."

FAQ

What has Kolmogorov been most known for?

He is most well known for his work in probability theory and for establishing its modern axiomatic basis.

What can be considered Kolmogorov's significant contribution to the development of mathematics?

He is best known for creating probability theory in the axiomatic form, manifested in his work titled Theory of Probability, published in 1933.

Were there any political issues that Kolmogorov had to encounter at his workplace?

Yes, he survived Stalinist purges and participated in the "Luzin Affair," wherein he testified against his former teacher; it is still a matter of discussion whether he did this willingly.

What are Kolmogorov's equations?

The Kolmogorov equations are several mathematical formulas that define the changes of probabilities over time in the Markov processes.

What is Kolmogorov's complexity?

Kolmogorov complexity can be defined as the slightest description of an object regarding the resources used in the computation.

In what other fields apart from mathematics did Kolmogorov work?

They include Nikolai Luzin and Pavel Alexandrov, who he studied under, and other mathematicians such as Aleksandr Khinchin and Paul Lévy.

Who were Kolmogorov's influences?

They include Nikolai Luzin and Pavel Alexandrov, who he studied under, and other mathematicians such as Aleksandr Khinchin and Paul Lévy.

What is the KAM theorem?

The KAM theorem, created by Vladimir Arnold, concerns the stability of motion trajectories and Newton's mechanics.

Which awards did Kolmogorov get during his lifetime?

He received the Stalin, Lenin, and Wolf awards, among many other international awards.

It is also essential to know how Kolmogorov contributed to education.

He spent a lot of effort creating curricula for gifted children, especially in mathematics. He made it a practice to teach many of the leading mathematicians in the future.

Biography

FAQ

Quotes

Biography

Andrey Kolmogorov was one of the most prominent Soviet mathematicians who introduced a new approach to probability theory and made significant contributions to several areas of mathematics, such as turbulence theory, topology, logic, and information theory. He was born in Tambov, Russia, and lost his mother during childbirth. His father also disappeared during political purges, and his aunts raised him. Kolmogorov started exhibiting signs of genius at the age of five, making patterns of numbers. His academic attainment at Moscow State University broadened his thought base, and by 1925, he had provided substantial contributions to mathematics, including set theory, trigonometric series, and probability.

In his scientific career, Kolmogorov met many famous mathematicians and joined the Moscow Mathematical Society. However, the key to his growth and fame came in 1933 when he published the "Foundations of the Theory of Probability," where he used axioms to formally present the probability theory, which he compared to how Euclid presented geometry. In the context of the political pressure of Stalin's Soviet Union, Kolmogorov successfully navigated between scientific discovery and political constraint and was involved in different controversies, including the "Luzin Affair."

Kolmogorov's research was wide-ranging. He made stochastic processes and turbulence, which were significant in physics, his specialty; at the same time, he also ventured into topology and classical mechanics. In his later years, he developed the algorithmic complexity theory, now called the Kolmogorov complexity, which gives the amount of resources needed to describe an object. Besides his outstanding mathematical achievements, Kolmogorov demonstrated great concern for developing gifted students and was actively involved in establishing special schools for talented youth in Moscow. He died in 1987 but made outstanding contributions to mathematics and education.

Quotes

"Each mathematician thinks he is more intelligent than others, and that's why none of them say it out loud – they are smart men."

"The most important is to teach a student how to think mathematically."

"Probability is the ultimate reality. Therefore, people cannot escape the fact that the world is random."

"Mathematics is a means of discovering the world's underlying patterns."

"It is worth mentioning that turbulence is classical physics's most important unsolved problem."

"Every piece I have done is based on my belief that nature is probabilistic."

"To understand is to perceive regularities."

"The interdependence of randomness and order is an essential aspect of life, which cannot be easily explained."

"An accurate mathematical theory captures the objective features of reality. In this sense, an accurate mathematical theory is a structural theory."

"Some wise man has said that the laws of probability were not given to us to believe in miracles but to avoid them."

"Every step in mathematics is a proof and discovery at the same time."

"Science is about explaining the complicated: 'What makes things go round is the attempt to reduce the complicated.'"

"It's also crucial to note the famous quote, 'The measure of intelligence is the ability to change.'"

"Probability is the theory where nothing is certain, yet everything can be explained."

"Mathematics is not just about solutions but also about posing the correct questions."

FAQ

What has Kolmogorov been most known for?

He is most well known for his work in probability theory and for establishing its modern axiomatic basis.

What can be considered Kolmogorov's significant contribution to the development of mathematics?

He is best known for creating probability theory in the axiomatic form, manifested in his work titled Theory of Probability, published in 1933.

Were there any political issues that Kolmogorov had to encounter at his workplace?

Yes, he survived Stalinist purges and participated in the "Luzin Affair," wherein he testified against his former teacher; it is still a matter of discussion whether he did this willingly.

What are Kolmogorov's equations?

The Kolmogorov equations are several mathematical formulas that define the changes of probabilities over time in the Markov processes.

What is Kolmogorov's complexity?

Kolmogorov complexity can be defined as the slightest description of an object regarding the resources used in the computation.

In what other fields apart from mathematics did Kolmogorov work?

They include Nikolai Luzin and Pavel Alexandrov, who he studied under, and other mathematicians such as Aleksandr Khinchin and Paul Lévy.

Who were Kolmogorov's influences?

They include Nikolai Luzin and Pavel Alexandrov, who he studied under, and other mathematicians such as Aleksandr Khinchin and Paul Lévy.

What is the KAM theorem?

The KAM theorem, created by Vladimir Arnold, concerns the stability of motion trajectories and Newton's mechanics.

Which awards did Kolmogorov get during his lifetime?

He received the Stalin, Lenin, and Wolf awards, among many other international awards.

It is also essential to know how Kolmogorov contributed to education.

He spent a lot of effort creating curricula for gifted children, especially in mathematics. He made it a practice to teach many of the leading mathematicians in the future.

Life and achievements

Early life

Andrey Kolmogorov was born in Tambov, Russia, on April 25, 1903, under unfortunate circumstances, as his mother died while giving birth to him. His father was an agronomist involved in politics and was killed during the Russian Civil War, and Kolmogorov was brought up by his aunts, particularly his aunt, Vera Yakovlevna. By age five, Kolmogorov was already proving himself to be a mathematical prodigy. Before he reached five years old, he made his first mathematical discovery, in which he discovered that the sum of odd numbers has a pattern.

Kolmogorov's early education started in a village school, but when he was a teenager, he moved to Moscow, where his education began in the true sense of the term. After completing his education, he joined Moscow State University in 1920, studying various subjects, including mathematics and history. During his undergraduate years, he produced a paper on the structure of landholding in Novgorod in the 15th and 16th centuries. His early work on Newton's laws of mechanics and set theory formed a basis for a very productive mathematical career. Already by 1922, he was able to achieve the feat of constructing a Fourier series that almost everywhere diverges.

While his interests were broad at the beginning of his studies, Kolmogorov became captivated by mathematics and probability theory. His first contact with Moscow's outstanding mathematicians, such as Luzin, Egorov, and Stepanov, significantly determined his academic course. By 1925, Kolmogorov had finished his education at MSU and had already gained recognition as one of the world's leading mathematicians, having published a paper on probability theory that was to change the course of the subject.

Legacy

Kolmogorov's contribution to modern mathematics is beyond doubt and versatile, as he has contributed to several fields, including probability theory, turbulence, and complexity theory. The book Probability Calculus with Elementary Theory of Probability, written by Khinchin in 1933, is still considered the basis for the further development of the probability theory as it is considered today. His work went beyond theoretical mathematics and into practical applications, especially in physics, and his work on the theory of turbulence is still felt to date.

Later, in the 1940s, Kolmogorov segregated his attention towards algorithmic complexity, where he proposed that the length of the shortest description of the object could define the measure of the complexity of an object. Since then, this concept has been developed into what is now known as Kolmogorov complexity, a central concept in computer science and information theory. His work in dynamical systems, especially the KAM theorem that he did with Vladimir Arnold and Jürgen Moser, has been used to analyze the stability of orbits in celestial mechanics.

Kolmogorov was also an excellent teacher and spent a lot of time teaching and training young generations of mathematicians. He also worked to establish a program for gifted children in education, trying to encourage mathematical giftedness and interest in literature, music, and science. Kolmogorov's passion for teaching revolutionized the Russian educational system.

For his accomplishments, Kolmogorov was awarded many high-ranking honors, such as the Lenin Prize, the Stalin Prize, and the Wolf Prize in Mathematics. His contributions to mathematics, physics, and computer science remain widely popular, making him one of the most influential mathematicians of the twentieth century.

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Milestone moments

Apr 1, 1922

Kolmogorov Develops a Fourier Series
In 1923 19, Kolmogorov produced a Fourier series developed to diverge almost everywhere.

This made him receive international recognition at a very young age in his career.

His work provided an example of an unexpected outcome shocking the field specialists in mathematical analysis.

This could start Kolmogorov's interest in probability and set theory.

Jun 12, 1931

Kolmogorov was appointed as a professor at the Moscow State University
By 28, Kolmogorov was appointed a professor at Moscow State University.

This position signified the start of his academic career in teaching and research.

His appointment was due to his work in probability theory and, more specifically, his paper on Markov processes.

Kolmogorov was an excellent teacher, with many students in his class, many of whom became famous mathematicians.

Jul 15, 1933

Publication of "Foundations of the Theory of Probability"
This year, Kolmogorov published his most important work, the Foundations of the Theory of Probability.

This monograph provided the modern axiomatic framework for probability theory, which changed the course of the subject.

It made Kolmogorov the world's leading authority on probability and introduced the critical formulae of the topic, including conditional expectation.

Jul 22, 1941

Pioneering Work in Turbulence
Kolmogorov published two papers that are the basis for the statistical theory of turbulence.

These papers brought to light scaling laws for turbulence, which are still significant in fluid dynamics.

His work in turbulence is widely regarded as one of the most significant accomplishments in classical physics.

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