Ivan Matveevich Vinogradov
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Ivan Matveevich Vinogradov (Иван Матвеевич Виноградов: September 14, 1891–March 20, 1983) was a Russian mathematician, who was one of the creators of modern analytic number theory, and also the dominant figure in mathematics in the USSR. He was born in the Velikiye Luki district, Pskov Oblast. He graduated from the University of St. Petersburg, where in 1920 became a Professor. From 1934 he was a Director of the Steklov Institute of Mathematics, a position he held for the rest of his life, except for the five-year period (1941–1946) when the institute was directed by Academician Sobolev.
In analytic number theory, Vinogradov's method refers to his main problem-solving technique, applied to central questions involving the estimation of exponential sums. With its help, he tackled questions such as the ternary Goldbach problem, and the zero-free region for the Riemann zeta function. His own use of it was inimitable; in terms of later techniques, it is recognised as a prototype of the large sieve method in its application of bilinear forms, and also as an exploitation of combinatorial structure. In some cases his results resisted improvement for decades.
Complicity in aspects of the Soviet system
Vinogradov was a Communist Party official, as would be expected at the time from all highly placed administrators. Given his prominence, it is reasonable to conclude that he must have known of the repressive trends of the Soviet system, as they had an impact on the mathematical community of the USSR, continuing into the Brezhnev era, such as difficulties placed in the way of Jewish students wishing to continue research work after graduation, promotion of party hacks with inadequate research work, harassment of dissidents, limitation of foreign travel even in the cases of distinguished academicians, and abuses of position to take unearned credits and co-authorship in publications.
It is not clear, and may never be known in detail, if Vinogradov himself was subject to particular pressure from the KGB and other elements of the Soviet system to implement such policies. This being said, the evidence drawn from his behaviour and that of his associates, and from his rather overpowering personal character, has led many people to very unfavourable conclusions about his complicity.
Bibliography
- Selected Works, Berlin ; New York : Springer-Verlag, 1985, ISBN 0387127887
- Vinogradov, I.M. Elements of Number Theory. Mineola, NY: Dover Publications, 2003, ISBN 0486495302
- Vinogradov, I.M. Method of Trigonometrical Sums in the Theory of Numbers. Mineola, NY: Dover Publications, 2004, ISBN 0486438783