Russian mathematician known for his contributions to analytic number theory, especially his partial solution of the Goldbach conjecture (Goldbach, Christian) (proposed in 1742), that every integer greater than two can be expressed as the sum of three prime numbers.

In 1914 Vinogradov graduated from the University of St. Petersburg (renamed the Leningrad State University in 1924 and the St. Petersburg State University (Saint Petersburg State University) in 1991). From 1918 to 1920 he taught at Perm State University—founded in 1916, originally as a branch of the University of St. Petersburg—and was then appointed professor of mathematics at St. Petersburg. From 1925 he also served as head of the department of number theory there. He became director of the V.A. Steklov Institute of Mathematics, Moscow, in 1932 and, in 1934, professor of mathematics at Moscow State University. Because of his profound contributions to analytic number theory Vinogradov became one of the leaders of Soviet mathematics, serving as a member of the International Mathematical Association when it met at Saint Andrews, Scotland, in 1958 and heading the Soviet delegation to the International Congress of Mathematicians (ICM)—the governing body that awards the Fields Medal—in Edinburgh that year. When the Russian Academy of Sciences (Sciences, Academy of) adopted a new constitution in 1963, he was elected a member. In 1966, when the Soviet Union hosted the ICM in Moscow, he was selected to give one of the invited hour-long addresses.

Vinogradov's most famous result was his proof (1937; “Some theorems concerning the theory of prime numbers”) that every sufficiently large odd integer can be expressed as the sum of three odd primes, which constituted a partial solution of Goldbach's conjecture. Among his other published works are The Method of Trigonometrical Sums in the Theory of Numbers, trans. and rev. by K.F. Roth (1954; originally published in Russian, 1947), and An Introduction to the Theory of Numbers (1955; reissued 1961; trans. from Russian 6th ed., 1952). A collection of his work in Russian is Izbrannye trudy (1952, reissued 1955).