Volodymyrska St, 60, Kyiv, 01033
In 1912 Chebotaryov entered the department of physics and mathematics at Kiev University. After graduating from the university in 1916, he taught and did research.
Chebotaryov became fascinated by mathematics while still in the lower grades of the Gymnasium. His mother was a strong influence on his education and her lack of knowledge of mathematics seems to have been one of the main reasons that Nikolai went in that direction. Ill health disrupted his education and he spent the winter of 1910-11 in Italy with his mother recovering from pneumonia.
In 1912 he entered the department of physics and mathematics at Kyiv University. Beginning in his second year at Kyiv, Chebotaryov participated in a seminar given by D. A. Grave which included O. Y. Schmidt, B. N. Delaunay, A. M. Ostrowski and others. Chebotaryov’s scientific interests took definite shape in this group. After graduating from the university in 1916, he taught and did research.
From 1921 to 1927 Chebotaryov taught at Odessa, where he prepared a paper on Frobenius’ problem; he defended this paper as a doctoral dissertation in Kyiv in 1927. In that year he was appointed a professor at Kazan University. In January 1928, he assumed his post at the university, where he spent the rest of his life and where he founded his own school of algebra.
Chebotaryov’s main works deal with the algebra of polynomials and fields (Galois’s theory); the problem of resolvents (first raised by Felix Klein and David Hilbert) - that is, the problem of the transformation of a given algebraic equation with variable coefficients to an equation whose coefficients depend on the least possible number of parameters (1931 and later); the distribution of the roots of an equation on the plane (1923 and later); and the theory of algebraic numbers.
In 1923 he published a complete solution to Frobenius’ problem concerning the existence of an infinite set of prime numbers belonging to a given class of substitutions of Galois’s group of a given normal algebraic field. This problem generalized Dirichlet’s famous theorem concerning primes among natural numbers in arithmetic progressions. The method applied was utilized by E. Artin in 1927 in proving his generalized law of reciprocity.
In 1934 Chebotaryov, applying the methods of Galois’s theory, made significant advances toward a solution of the question - first posed by the ancient Greeks - of the possible number of lunes that are bounded by two circular arcs so chosen that the ratio of their angular measures is a rational number and that can be squared using only a compass and a straightedge. One of Chebotaryov’s disciples, A. V. Dorodnov, completed the investigation of this famous problem in 1947. He also did work on the theory of Lie groups, in geometry (translation surfaces), and in the history of mathematics.
In 1929 Chebotaryov was elected a corresponding member of the Academy of Sciences of the Union of Soviet Socialist Republics, and in 1943 the title Honored Scientist of the Russian Soviet Federated Socialist Republic was conferred upon him. For his work on the theory of resolvents, he was posthumously awarded the State Prize in 1948.