View source for Ivan Vinogradov

{{Short description|Soviet mathematician (1891–1983)}}
{{Use dmy dates|date=June 2020}}
{{distinguish|text = the Russian mathematicians [[Alexandre Mikhailovich Vinogradov|Alexandre Vinogradov]] (of [[Vinogradov sequence]]) or [[Askold Vinogradov]] (of [[Bombieri–Vinogradov theorem]])}}
{{family name hatnote|Matveevich|Vinogradov|lang=Eastern Slavic}}
{{Infobox scientist
| name              = Ivan Vinogradov
| native_name       = Иван Виноградов
| native_name_lang  = ru
| image             = Виноградов Иван Матвеевич.jpg
| image_size        = 
| caption           = Vinogradov in 1944
| birth_date        = {{birth date|1891|09|14|df=y}}
| birth_place       = [[Velikoluksky District|Milolyub]] village, [[Velikoluksky Uyezd]], [[Pskov Governorate]], [[Russian Empire]]
| death_date        = {{death date and age|1983|03|20|1891|09|14|df=y}}
| death_place       = [[Moscow]], [[Soviet Union]]
| nationality       = [[Russians|Russian]]
| ethnicity         = 
| field             = [[Mathematics]]
| work_institutions = 
| alma_mater        = [[St. Petersburg State University]]
| doctoral_advisor  = [[J. V. Uspensky|James Victor Uspensky]]<ref>{{Cite web|url=http://www.genealogy.math.ndsu.nodak.edu/id.php?id=161844|title=Ivan Vinogradov - the Mathematics Genealogy Project}}</ref>
| doctoral_students = 
| known_for         = [[Analytic number theory]]
| prizes            = [[Fellow of the Royal Society]]<ref name="frs">{{Cite journal | last1 = Cassels | first1 = J. W. S. | last2 = Vaughan | first2 = R. C. | doi = 10.1098/rsbm.1985.0021 | title = Ivan Matveevich Vinogradov. 14 September 1891 – 20 March 1983 | journal = [[Biographical Memoirs of Fellows of the Royal Society]] | volume = 31 | pages = 613–631 | year = 1985 | jstor = 769938| doi-access = free }}</ref>
}}
'''Ivan Matveevich Vinogradov''' {{post-nominals|post-noms=[[Foreign Member of the Royal Society|ForMemRS]]}}<ref name="frs"/> ({{lang-rus|Ива́н Матве́евич Виногра́дов|p=ɪˈvan mɐtˈvʲejɪvʲɪtɕ vʲɪnɐˈɡradəf|a=Ru-Ivan_Matveyevich_Vinogradov.ogg}}; 14 September 1891 – 20 March 1983) was a [[USSR|Soviet]] [[mathematician]], who was one of the creators of modern [[analytic number theory]], and also a dominant figure in mathematics in the [[Soviet Union|USSR]]. He was born in the [[Velikiye Luki]] district, [[Pskov Oblast]]. He graduated from the [[Saint Petersburg State University|University of St. Petersburg]], 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&ndash;1946) when the institute was directed by Academician [[Sergei Sobolev]]. In 1941 he was awarded the [[USSR State Prize|Stalin Prize]]. He was elected to the [[American Philosophical Society]] in 1942.<ref>{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=Ivan+Vinogradov&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |access-date=2023-04-17 |website=search.amphilsoc.org}}</ref> In 1951 he became a foreign member of the Polish Academy of Sciences and Letters in Kraków.

==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 sum]]s.  In its most basic form, it is used to estimate sums over prime numbers, or [[Weyl sum]]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

:<math>S=\sum_{p\le P}\exp(2\pi i f(p)).</math>

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 form]]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 [[Divisor summatory function#Dirichlet's divisor problem|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 [[Quadratic residue#The Pólya–Vinogradov inequality|Pólya–Vinogradov inequality]] for character sums.

{{Expand section|date=June 2008}}

== Personality and career ==

Vinogradov served as director of the [[Steklov Institute of Mathematics|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 [[mathematician]]s. As the head of a leading mathematical institute, Vinogradov enjoyed significant influence in the [[Russian Academy of Sciences|Academy of Sciences]] and was regarded as an informal leader of [[Soviet Union|Soviet]] [[mathematician]]s, not always in a positive way: his anti-Semitic feelings led him to hinder the careers of many prominent Soviet mathematicians.<ref name="Frenkel">{{cite book|last1=Frenkel|first1=Edward|title=Love and Math: The Heart of Hidden Reality|year=2013|publisher=Basic Books|isbn=978-0-465-05074-1|url=https://archive.org/details/lovemathheartofh0000fren|url-access=registration}}</ref>

Although he was always faithful to the official line, he was never a member of the [[Communist Party of the USSR|Communist Party]] and his overall mindset was [[nationalism|nationalistic]] rather than [[communism|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 unmarried) 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.

==References==
{{reflist}}

==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==
* {{Internet Archive author |sname=Ivan Matveyevich Vinogradov |sopt=t}}
* {{MacTutor Biography|id=Vinogradov}}
* [http://www.museum.ru/M833 Vinogradov memorial] {{in lang|ru}}
* [http://www.imec.msu.ru/pages/05-03-17-5976848.html Memoirs of colleagues] {{Webarchive|url=https://web.archive.org/web/20140305124533/http://www.imec.msu.ru/pages/05-03-17-5976848.html |date=5 March 2014 }} {{in lang|ru}}
* [http://www.mi.ras.ru/~snovikov/Mat_60.doc DOC] [http://www.mi.ras.ru/~snovikov/991.pdf PDF] [http://www.mccme.ru/edu/index.php?ikey=n-rohlin Memoirs of his opponent academician Sergei Novikov] {{Webarchive|url=https://web.archive.org/web/20110515203948/http://www.mccme.ru/edu/index.php?ikey=n-rohlin |date=15 May 2011 }}
* [http://www.proza.ru/2009/10/18/120 Vinogradov in Abramtsevo, memoirs] {{Webarchive|url=https://web.archive.org/web/20110515203948/http://www.mccme.ru/edu/index.php?ikey=n-rohlin |date=15 May 2011 }} {{in lang|ru}}

{{Authority control}}

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