Ivan Matveevich Vinogradov ( rus, Ива́н Матве́евич Виногра́дов, p=ɪˈvan mɐtˈvʲejɪvʲɪtɕ vʲɪnɐˈɡradəf, a=Ru-Ivan_Matveyevich_Vinogradov.ogg; 14 September 1891 – 20 March 1983) was a

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, who was one of the creators of modern

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dir ...

, and also a dominant figure in mathematics in the

USSR The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

. He was born in the

Velikiye Luki Velikiye Luki ( rus, Вели́кие Лу́ки, p=vʲɪˈlʲikʲɪjə ˈlukʲɪ; lit. ''great meanders''. Г. П. Смолицкая. "Топонимический словарь Центральной России". "Армада-� ...

district,

Pskov Oblast Pskov Oblast () is a federal subjects of Russia, federal subject of Russia (an oblast), located in the west of the country. Its administrative center is the Classification of inhabited localities in Russia, city of Pskov. As of the Russian Census ...

. He graduated from the University of St. Petersburg, where in 1920 he became a Professor. From 1934 he was a Director of the

Steklov Institute of Mathematics Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Stek ...

, 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. He was elected to the

American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...

in 1942. In 1951 he became a foreign member of the Polish Academy of Sciences and Letters in Kraków.

Mathematical contributions

, ''Vinogradov's method'' refers to his main problem-solving technique, applied to central questions involving the estimation of

exponential sum In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function :e(x) = \exp(2\pi ix).\, Therefore, a typi ...

s. In its most basic form, it is used to estimate sums over prime numbers, or

Weyl sum In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function :e(x) = \exp(2\pi ix).\, Therefore, a typic ...

s. 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 :

S=\sum_\exp(2\pi i f(p)).

With the help of this method, Vinogradov tackled questions such as the ternary Goldbach problem in 1937 (using

Vinogradov's theorem In number theory, Vinogradov's theorem is a result which implies that any sufficiently large odd integer can be written as a sum of three prime numbers. It is a weaker form of Goldbach's weak conjecture, which would imply the existence of such a re ...

), and the zero-free region for the

Riemann zeta function The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for and its analytic c ...

. 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 form In mathematics, a bilinear form is a bilinear map on a vector space (the elements of which are called '' vectors'') over a field ''K'' (the elements of which are called '' scalars''). In other words, a bilinear form is a function that is linea ...

s, 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 In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ...

. This was an improvement on the work of

Georgy Voronoy Georgy Feodosevich Voronyi (; ; 28 April 1868 – 20 November 1908) was an Imperial Russian mathematician of Ukrainians, Ukrainian descent noted for defining the Voronoi diagram. Biography Voronyi was born in the village of Zhuravka, Pyriatyn, in ...

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

Personality and career

Vinogradov served as director of the Mathematical Institute for 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 honour among Russian

s. 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

s, not always in a positive way: his anti-Semitic feelings led him to hinder the careers of many prominent Soviet mathematicians. 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 Communism () is a sociopolitical, philosophical, and economic ideology within the socialist movement, whose goal is the creation of a communist society, a socioeconomic order centered on common ownership of the means of production, di ...

. This can at least partly be attributed to his origins: his father was a priest of the

Russian Orthodox Church The Russian Orthodox Church (ROC; ;), also officially known as the Moscow Patriarchate (), is an autocephaly, autocephalous Eastern Orthodox Church, Eastern Orthodox Christian church. It has 194 dioceses inside Russia. The Primate (bishop), p ...

. 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 A dacha (Belarusian, Ukrainian language, Ukrainian and rus, дача, p=ˈdatɕə, a=ru-dacha.ogg) is a seasonal or year-round second home, often located in the exurbs of former Soviet Union, post-Soviet countries, including Russia. A cottage (, ...

in Abramtsevo, where he spent all his weekends and vacations (together with his sister Nadezhda, also unmarried) enjoying flower

gardening Gardening is the process of growing plants for their vegetables, fruits, flowers, herbs, and appearances within a designated space. Gardens fulfill a wide assortment of purposes, notably the production of Aesthetics, aesthetically pleasing area ...

. He had friendly relations with the president of the

Russian Academy of Sciences The Russian Academy of Sciences (RAS; ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such ...

Mstislav Keldysh Mstislav Vsevolodovich Keldysh (; – 24 June 1978) was a Soviet mathematician who worked as an engineer in the Soviet space program. He was the academician of the Academy of Sciences of the Soviet Union (1946), President of the Academy of Sc ...

and Mikhail Lavrentyev, both mathematicians whose careers started in his institute.

References

Bibliography

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

External links

* *
Vinogradov memorial

DOCPDFMemoirs of his opponent academician Sergei Novikov

Vinogradov in Abramtsevo, memoirs
{{DEFAULTSORT:Vinogradov, Ivan Matveyevich 1891 births 1983 deaths People from Velikoluksky District People from Velikoluksky Uyezd Soviet mathematicians Russian mathematicians Number theorists Saint Petersburg State University alumni Academic staff of Perm State University Academic staff of Tomsk State University Academic staff of the Steklov Institute of Mathematics Full Members of the USSR Academy of Sciences Members of the German Academy of Sciences at Berlin Foreign members of the Serbian Academy of Sciences and Arts Foreign members of the Royal Society Recipients of the Stalin Prize Recipients of the USSR State Prize Recipients of the Lenin Prize Heroes of Socialist Labour Recipients of the Order of Lenin Recipients of the Lomonosov Gold Medal Members of the American Philosophical Society Russian scientists