Andrei N. Kolmogorov

Andrei N. Kolmogorov Winner of Wolf Prize in Mathematics - 1980
Andrei N. Kolmogorov


The Prize Committee unanimously decided to select as co-recipients of the Wolf Prize for mathematics for 1980:

Andrei N. Kolmogorov
Moscow State University
Moscow, U.S.S.R.

for deep and original discoveries in Fourier analysis, probability theory, ergodic theory and dynamical systems.

Henry Cartan
Universite de Paris
Paris, France

for pioneering work in algebraic topology, complex variables homological algebra and inspired leadership of a generation of mathematicians.

Both mathematicians are noteworthy for their breadth of interests and for the depth of the results they have obtained in the various fields of mathematics in which they have been active. Their interests were complementary and, taken together, span almost the whole range of mathematics.

Professor (Emeritus) Henri Cartan began his career in several complex variables when, along with Oka and Thullen, he laid the foundation for the general theory, culminating in the characterization of domains of holomorphy.

During the post-war period for about 15 years, Cartan was the leader of the famous Seminaire Cartan which, attracted mathematicians from allover the world. In this seminar he also turned to algebraic topology and soon made the seminar the center of new developments in this field. The new methods which were introduced by him and by others, formed the basis of an entirely new branch of mathematics, homological algebra, which
has grown beyond all expectation. In addition to the above, Cartan has contributed to various theories such as potential theory and harmonic analysis. He was one of the founding fathers of the Bourbaki Circle of French Mathematicians, who have definitely stamped the image of the present science of Mathematics.

The work of Professor Andrei N. Kolmogorov is characterized above all by great power. One of his first achievements was to give an example of an L1 function whose Fourier Series diverges everywhere. In addition the Kolmogorov-Seliverstov theorem remained for many years the deepest result on convergence of Fourier Series for L2 functions. However, it was his work in probability theory, which truly earned his reputation. In 1933 he wrote a fundamental book on the foundations of probability theory, which for the first time put probability theory on a completely secure footing, comparable to the rest of mathematics. He later introduced the critical concept of entropy, which enabled one to solve the famous isomorphism problem for Bernoulli shifts, and essentially revived the entire field of ergodic theory.

His interests include logic, approximation theory, and the theory of real variables, as well as many other subjects. His influence on students has also been very extensive.