In 1940 Khinchin received the Order of the Badge of Honor.
In 1941 Khinchin received the Stalin Prize.
In 1944 and 1945 Khinchin received the Order of the Red Banner of Labor.
In 1953 Khinchin received the Order of Lenin.
Lomonosov Moscow State University, Moscow, Russia
From 1911 until 1916 Khinchin studied at the Faculty of Physics and Mathematics of Moscow University.
A photo of Khinchin.
Александр Яковлевич Хинчин
Khinchin's interest in mathematics was awakened in high school. He graduated from a technical high school in Moscow in 1911 and, from 1911 until 1916, studied at the Faculty of Physics and Mathematics of Moscow University. In 1916 he was retained by the university to prepare for professorship. In 1935 he received his Doctor of Science degree; his doctoral advisor was Nikolai Luzin.
From 1918 Khinchin taught at various colleges in Moscow and Ivanovo; in 1927 he became a professor at Moscow University. With A. N. Kolmogorov, Khinchin was one of the founders of the Moscow school of probability theory, one of the most influential in the twentieth century.
At the university, he became an active member of the group of gifted young mathematicians guided by N. Luzin, the passionate propagandist of the modern theory of functions. In this group, Khinchin began to work on the metric theory of functions. His first paper (1916), on a generalization of the Denjoy integral, began a series of works dealing with the properties of functions which remain after the removal of a set of density 0 at a given point (asymptotic derivative, asymptotic monotonicity).
After 1922 Khinchin turned to the theory of numbers and to probability theory. First, he studied metric problems of the theory of Diophanline approximations and of the theory of continuous fractions. These problems, which deal with properties true for almost all real numbers, are naturally connected with the asymptotic properties of functions mentioned above. Later Khinchin studied classical Diophantine approximations, which hold true for all numbers; in particular he established the so-called principle of transposition. Another topic of the theory of numbers was studied in his works on the density of sequences.
In 1923 Khinchin established the so-called law of the iterated logarithm, strengthening the results obtained by G. H. Hardy and John Littlewood on the frequency of zeros in the binary expansion of real numbers. In the probabilistic interpretation, this law improves the strengthened law of large numbers established by Borel. Probability theory proved to be an auspicious field for the application of the methods of the metric theory of functions, and Khinchin was drawn more and more into the problems of the summation of independent random variables. During the 1920s and 1930s, this classical branch of probability theory assumed its present form in the closely related works of Kolmogorov, P. Lévy, Khinchin, and others. Khinchin’s contribution included results on the applicability of the law of large numbers to equally distributed random variables with finite mathematical expectations, on the coincidence of the class of all limit distributions with the class of all infinitely divisible laws, on the convergence of series of random variables (jointly with Kolmogorov), and on the structure of stable laws (jointly with Lévy).
In a series of papers written between 1932 and 1934, Khinchin laid the foundation of the general theory of stationary random processes, revealed the spectral representation of their correlation functions, and generalized G. D. Birkhoff’s ergodic theorem, which is a strengthened law of large numbers for such processes.
In other works Khinchin dealt with the convergence of discrete Markov chains to continuous diffusion, with large deviations, with the arithmetic of distribution laws, and with the method of arbitrary functions. In the 1940s Khinchin’s interest shifted to statistical mechanics. With the aid of local limit theorems, he substantiated the possibility of replacing means in time by means in the phase space both for classical and quantum statistics. In the last years of his life, Khinchin studied information theory and queuing theory.
Khinchin also wrote several popular books on the theory of numbers and published articles devoted to pedagogic and philosophic questions of mathematics.
Khinchin was elected an associate member of the Soviet Academy of Sciences in 1939 and a member of the Academy of Pedagogical Sciences of the R.S.F.S.R. in 1944.
Khinchin's strong interests of his youth were poetry and the theater. He once sent his poems to Alexander Blok, and later received a letter from him where Blok approved of his work.
No information about Khinchin's family is available.