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 Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

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, structure, space, models, and change. History On ...

, 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 Diric ...

, and also a dominant figure in mathematics in the

USSR The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nationa ...

. 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-П ...

district,

Pskov Oblast Pskov Oblast (russian: Пско́вская о́бласть, ') is a federal subjects of Russia, federal subject of Russia (an oblast), located in the west of the country. Its administrative center is the types of inhabited localities in Russia, ...

. He graduated from the

University of St. Petersburg Saint Petersburg State University (SPBU; russian: Санкт-Петербургский государственный университет) is a public university, public research university in Saint Petersburg, Russia. Founded in 1724 by a de ...

, where in 1920 he 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 Prof Sergei Lvovich Sobolev (russian: Серге́й Льво́вич Со́болев) H FRSE (6 October 1908 – 3 January 1989) was a Soviet mathematician working in mathematical analysis and partial differential equations. Sobolev introduc ...

. In 1941 he was awarded the

Stalin Prize Stalin Prize may refer to: * The State Stalin Prize in science and engineering and in arts, awarded 1941 to 1954, later known as the USSR State Prize The USSR State Prize (russian: links=no, Государственная премия СССР, ...

. 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 typic ...

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 typ ...

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 number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that : Every odd number greater than 5 can be expressed as the sum of three primes. (A prime m ...

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 rep ...

), 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 \operatorname(s) > ...

. His own use of it was inimitable; in terms of later techniques, it is recognised as a prototype of the

large sieve method The large sieve is a method (or family of methods and related ideas) in analytic number theory. It is a type of sieve where up to half of all residue classes of numbers are removed, as opposed to small sieves such as the Selberg sieve wherein onl ...

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 linear i ...

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 Johann Peter Gustav Lejeune Dirichlet (; 13 February 1805 – 5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and ...

, 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 (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (ge ...

. This was an improvement on the work of

Georgy Voronoy Georgy Feodosevich Voronoy (russian: Георгий Феодосьевич Вороной; ukr, Георгій Феодосійович Вороний; 28 April 1868 – 20 November 1908) was an Russian Empire, Imperial Russian mathematician of U ...

. 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 An academy of sciences is a type of learned society or academy (as special scientific institution) dedicated to sciences that may or may not be state funded. Some state funded academies are tuned into national or royal (in case of the Unite ...

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 A communist party is a political party that seeks to realize the socio-economic goals of communism. The term ''communist party'' was popularized by the title of ''The Manifesto of the Communist Party'' (1848) by Karl Marx and Friedrich Engels. A ...

and his overall mindset was

nationalistic Nationalism is an idea and movement that holds that the nation should be congruent with the state. As a movement, nationalism tends to promote the interests of a particular nation (as in a group of people), Smith, Anthony. ''Nationalism: T ...

rather than

communist Communism (from Latin la, communis, lit=common, universal, label=none) is a far-left sociopolitical, philosophical, and economic ideology and current within the socialist movement whose goal is the establishment of a communist society, a s ...

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

Russian Orthodox Church , native_name_lang = ru , image = Moscow July 2011-7a.jpg , imagewidth = , alt = , caption = Cathedral of Christ the Saviour in Moscow, Russia , abbreviation = ROC , type ...

. 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 ( rus, дача, p=ˈdatɕə, a=ru-dacha.ogg) is a seasonal or year-round second home, often located in the exurbs of post-Soviet countries, including Russia. A cottage (, ') or shack serving as a family's main or only home, or an outbu ...

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

gardening Gardening is the practice of growing and cultivating plants as part of horticulture. In gardens, ornamental plants are often grown for their flowers, foliage, or overall appearance; useful plants, such as root vegetables, leaf vegetables, fruits ...

. He had friendly relations with the president of the

Russian Academy of Sciences The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across t ...

Mstislav Keldysh Mstislav Vsevolodovich Keldysh (russian: Мстисла́в Все́володович Ке́лдыш; – 24 June 1978) was a Soviet mathematician who worked as an engineer in the Soviet space program. He was the academician of the Academy o ...

and

Mikhail Lavrentyev Mikhail Alekseevich Lavrentyev (or Lavrentiev, russian: Михаи́л Алексе́евич Лавре́нтьев) (November 19, 1900 – October 15, 1980) was a Soviet Union, Soviet mathematician and hydrodynamics, hydrodynamicist. Early years ...

, 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 The ''Encyclopedia of Mathematics'' (also ''EOM'' and formerly ''Encyclopaedia of Mathematics'') is a large reference work in mathematics. Overview The 2002 version contains more than 8,000 entries covering most areas of mathematics at a graduat ...

External links

* *
Vinogradov memorial

DOCPDFS. P. Novikov">Memoirs of his opponent academician Sergei Novikov (mathematician), S. P. 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 Perm State University faculty Tomsk State University faculty Steklov Institute of Mathematics faculty 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 Stalin Prize winners Recipients of the USSR State Prize Lenin Prize winners Heroes of Socialist Labour Recipients of the Order of Lenin Recipients of the Lomonosov Gold Medal