Ivan Matveevich Vinogradov (Иван Матвеевич Виноградов: 14 September 1891–20 March 1983) (not to be confused with Askold Ivanovich Vinogradov of the Bombieri-Vinogradov theorem) was a Soviet mathematician, who was one of the creators of modern analytic number theory, and also a 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 Sergei Sobolev. In 1941 he was awarded the Stalin Prize.

Mathematical contributions

In analytic number theory, Vinogradov's method refers to his main problem-solving technique, applied to central questions involving the estimation of exponential sums. In its most basic form, it is used to estimate sums over prime numbers, or Weyl sums. It is a reduction from a complicated sum to a number of smaller sums which are then simplified. The canonical form for prime number sums is

With the help of this method, Vinogradov tackled questions such as the ternary Goldbach problem in 1937 (using Vinogradov's theorem), 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.

He also used this technique on the Dirichlet divisor problem, allowing him to estimate the number of integer points under an arbitrary curve. This was an improvement on the work of Georgy Voronoy.

In 1918 Vinogradov proved the Pólya–Vinogradov inequality for character sums.

Personality and career

Vinogradov served as director of the Mathematical Institute for an ample 49 years. For his long service he was twice awarded the order of The Hero of the Socialist Labour. The house where he was born was converted into his memorial – a unique honor among Russian mathematicians. As the head of a leading mathematical institute, Vinogradov enjoyed significant influence in the Academy of Sciences and was regarded as an informal leader of Soviet mathematicians.

His long monopoly of power caused growing protest which eventually took the form of organised opposition among academics. He was accused of biased handling of personnel issues and – although never officially - of antisemitism. His opponents, mostly prominent physicists, stated that after his first outstanding discoveries in number theory he never came up with any new significant results. However, he was still supported by most mathematicians in the Academy of Sciences and relied on the backing of its leadership. In 1977 he was re-elected as director of the institute only with great difficulty. During the secret vote at the general assembly of the Academy of Sciences more than 1/3 of the ballots were cast against him. However, it was not enough for his removal.

Although he was always faithful to the official line, he was never a member of the Communist Party and his overall mindset was nationalistic rather than communist. This can at least partly be attributed to his origins: his father was a priest of the Russian Orthodox Church. Vinogradov was enormously strong: in some recollections it is stated that he could lift a chair with a person sitting on it by holding the leg of the chair in his hands. He was never married and was very attached to his dacha in Abramtsevo, where he spent all his weekends and vacations (together with his sister Nadezhda, also a lonely bachelor) enjoying flower gardening. He had friendly relations with the president of the Russian Academy of Sciences Mstislav Keldysh and Mikhail Lavrentyev, both mathematicians whose careers started in his institute.

Bibliography

* Selected Works, Berlin; New York: Springer-Verlag, 1985, ISBN 0-387-12788-7.
* Vinogradov, I. M. Elements of Number Theory. Mineola, NY: Dover Publications, 2003, ISBN 0-486-49530-2.
* Vinogradov, I. M. Method of Trigonometrical Sums in the Theory of Numbers. Mineola, NY: Dover Publications, 2004, ISBN 0-486-43878-3.
* Vinogradov I. M. (Ed.) Matematicheskaya entsiklopediya. Moscow: Sov. Entsiklopediya 1977. Now translated as the Encyclopaedia of Mathematics.

External links

* O'Connor, John J.; Robertson, Edmund F., "Ivan Matveyevich Vinogradov", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Vinogradov.html .
* Vinogradov memorial (in Russian)
* Memoirs of colleagues (in Russian)
* [1][2]Memoirs of his opponent academician S. P. Novikov
* Vinogradov in Abramtsevo, memoirs (in Russian)