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- Soviet mathematician, popularizer of mathematics. He is the author of well-known school textbooks in mathematics for grades 5 and 6, which have served for more than forty years. The first textbooks were published in September 1970 (co-authored with K. I. Neshkov, S. I. Shvartsburd, A. D. Semushin, A. S. Chesnokov, T. F. Nechaeva). Studied at the 7th prof. Prof. Kovalensky ”in Krivoarbatsky Lane. Then he graduated from Moscow State University (1942); Doctor of physico-mathematical sciences (1950), professor (1951). Since 1943, he worked in various universities, since 1961 - at the Moscow Correspondence Pedagogical Institute. The first works, including the dissertation, were devoted to the theory of topological groups. Developing the character theory of Pontryagin, he established a connection between the character systems of zero-dimensional compact Abelian groups, also known as Vilenkin systems, with the class of orthonormal systems of piecewise constant functions. Since the 1950s, the systems introduced by Vilenkin have been actively studied in connection with their widespread use in the field of digital signal processing. Since the mid-1950s, he worked on the study of the theory of representations of Lie groups, where he obtained a number of results related to infinite-dimensional representations constructed by I. M. Gelfand and M. A. Naimark. He is the author of the monograph Special Functions and Theory of Representation of Groups (1965, 1991), which was then (together with A. U. Klimyk) transformed into Representations of Lie groups and special functions (1991–1993, 1995). He is the author of popular science books Tales of Sets, Combinatorics, and a number of school mathematics textbooks.
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