# Andrei Nikolaevich Kolmogorov

# Andrei Nikolaevich Kolmogorov

**1903-1987**

**Russian Mathematician**

In discussing great mathematicians, the word "genius" is so often used that its effect sometimes seems blunted, yet in the case of Andrei Nikolaevich Kolmogorov the term is exceedingly apt. Though he is best known as the founder of probability theory, Kolmogorov contributed to virtually every area of mathematics as well as to fields ranging from physics to linguistics.

Kolmogorov's father, a Russian agriculturist named Nikolai Kataev, was killed in World War I, and his mother, Mariya Kolmogorova—who was not married to Nikolai—died giving birth to their son in the town of Tambov on April 25, 1903. Kolmogorov was raised by his mother's sister in the village of Tunoshna. He showed his brilliance at the age of five when he noted the pattern 1=1^{2}, 1+3=2^{2}, 1+3+5=3^{2}, and so on.

At age 17, Kolmogorov enrolled at Moscow University and worked his way through college as a secondary school teacher. As an undergraduate, he published a number of important papers, including one wherein he formulated the first known example of an integrable function with a Fourier series that diverged almost everywhere. He was only 19, and he soon improved on this work by extending his result to a series that divulged everywhere—work that quickly brought him to the attention of the international mathematics community.

After receiving his doctoral degree in 1925, Kolmogorov went to work as a research assistant at Moscow University and at the age of 28 became a full professor. In 1933, when he was just 30, he became director of the institute of mathematics at the university. He married Anna Egorova in 1942.

Kolmogorov published one of his most important works, "General Theory of Measure and Probability Theory," while he was still a research assistant. The paper, called the "New Testament" of mathematics by one of his admirers and often compared to Euclid's work for its foundational character, provided the framework for probability theory. Kolmogorov also contributed to the understanding of stochastic processes, which involve random variables. These achievements were not purely academic pursuits; during World War II, the Soviet military made use of his stochastic theory in planning its placement of barrage balloons in order to thwart Nazi bombing raids. As for probability theory, it led to progress in a number of areas, including Kolmogorov's own development of reaction-diffusion theory, the analysis of how events such as cultural changes spread through a group.

During the decades that followed, Kolmogorov worked tirelessly in mathematical studies and their applications to a wide array of fields. In 1939 he became one of the youngest full members of the Soviet Academy of Sciences and in 1946 he was chosen to direct the Turbulence Laboratory of the Academy Institute of Theoretical Geophysics. During the years 1970 to 1972, he sailed around the world to study the properties of ocean turbulence. He also is credited with being codeveloper of the Kolmogorov-Arnold-Moser (KAM) theorem for analysis of stability in dynamic systems.

The list of Kolmogorov's achievements and discoveries is seemingly endless. Among the ones in which he took the most pride was his solution of Hilbert's thirteenth problem, which involved the representation of functions of many variables in terms of a combination of functions possessing fewer variables. Kolmogorov, however, remained modest to the end, and, in line with his belief that a mathematician could no longer conduct valuable research after the age of 60, he retired in 1963, spending 20 years teaching high school. Long concerned with the state of mathematical education, he chaired the Academy of Sciences Commission on Mathematical Education and helped the Soviet Union move to the forefront in mathematics during the 1960s. Kolmogorov died in Moscow on October 20, 1987.

**JUDSON KNIGHT**

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**Andrei Nikolaevich Kolmogorov**