Ivan Matveyevich Vinogradov
Encyclopedia
Ivan Matveevich Vinogradov (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 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. In 1941 he was awarded the Stalin Prize
.
, 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 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.
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 Academy of Sciences
and was regarded as an informal leader of Soviet
mathematician
s.
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 physicist
s, 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 mathematician
s 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 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.
Askold Ivanovich Vinogradov
Askold Ivanovich Vinogradov was a Russian mathematician working in number theory. A major result he proved was the Bombieri–Vinogradov theorem.-External links:*...
of the Bombieri-Vinogradov theorem) was a Soviet mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, who was one of the creators of modern analytic number theory
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 Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic...
, and also a dominant figure in mathematics in the USSR
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
. He was born in the Velikiye Luki
Velikiye Luki
Velikiye Luki is a town on the meandering Lovat River in the southern part of Pskov Oblast, Russia. It is the second largest town in Pskov Oblast; population: The town is served by the Velikiye Luki Airport....
district, Pskov Oblast
Pskov Oblast
Pskov Oblast is a federal subject of Russia . Pskov Oblast borders the countries of Estonia and Latvia, as well as Belarus. It is the westernmost federal subject of contiguous Russia . Its major cities are the administrative center Pskov and Velikiye Luki . Area: 55,300 km²...
. He graduated from the University of St. Petersburg
Saint Petersburg State University
Saint Petersburg State University is a Russian federal state-owned higher education institution based in Saint Petersburg and one of the oldest and largest universities in Russia....
, where in 1920 he became a Professor. From 1934 he was a Director of the Steklov Institute of Mathematics
Steklov Institute of Mathematics
Steklov Institute of Mathematics or Steklov Mathematical Institute is a research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. It was established April 24, 1934 by the decision of the General Assembly of the Academy of Sciences of the USSR in...
, 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
USSR State Prize
The USSR State Prize was the Soviet Union's state honour. It was established on September 9, 1966. After the breakup of the Soviet Union, the prize was followed up by the State Prize of the Russian Federation....
.
Mathematical contributions
In analytic number theoryAnalytic 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 Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic...
, Vinogradov's method refers to his main problem-solving technique, applied to central questions involving the estimation of exponential sum
Exponential sum
In mathematics, an exponential sum may be a finite Fourier series , or other finite sum formed using the exponential function, usually expressed by means of the functione = \exp.\,...
s. 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
Vinogradov's theorem
In number theory, Vinogradov's theorem 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 conjecture, which would imply the existence of such a representation for all odd integers greater than five. It is named after...
), 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
Curve
In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...
. This was an improvement on the work of Georgy Voronoy
Georgy Voronoy
Georgy Feodosevich Voronoy was a Russian Empire mathematician of Ukrainian origin. Among other things, he defined the Voronoi diagram.Voronoy was born in the village of Zhuravky, district of Pyriatin, in Poltava Governorate of the Russian Empire .From 1889, Voronoy studied at Saint Petersburg...
.
In 1918 Vinogradov proved the Pólya–Vinogradov inequality for character sums.
Personality and career
Vinogradov served as director of the Mathematical InstituteSteklov Institute of Mathematics
Steklov Institute of Mathematics or Steklov Mathematical Institute is a research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. It was established April 24, 1934 by the decision of the General Assembly of the Academy of Sciences of the USSR in...
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
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s. As the head of a leading mathematical institute, Vinogradov enjoyed significant influence in the Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
and was regarded as an informal leader of Soviet
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s.
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 physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
s, stated that after his first outstanding discoveries in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
he never came up with any new significant results. However, he was still supported by most mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s in the Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
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
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
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
Nationalism
Nationalism is a political ideology that involves a strong identification of a group of individuals with a political entity defined in national terms, i.e. a nation. In the 'modernist' image of the nation, it is nationalism that creates national identity. There are various definitions for what...
rather than communist
Communism
Communism is a social, political and economic ideology that aims at the establishment of a classless, moneyless, revolutionary and stateless socialist society structured upon common ownership of the means of production...
. This can at least partly be attributed to his origins: his father was a priest of the Russian Orthodox Church
Russian Orthodox Church
The Russian Orthodox Church or, alternatively, the Moscow Patriarchate The ROC is often said to be the largest of the Eastern Orthodox churches in the world; including all the autocephalous churches under its umbrella, its adherents number over 150 million worldwide—about half of the 300 million...
. 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
Dacha
Dacha is a Russian word for seasonal or year-round second homes often located in the exurbs of Soviet and post-Soviet cities. Cottages or shacks serving as family's main or only home are not considered dachas, although many purpose-built dachas are recently being converted for year-round residence...
in Abramtsevo, where he spent all his weekends and vacations (together with his sister Nadezhda, also unmarried) enjoying flower gardening
Gardening
Gardening is the practice of growing and cultivating plants. Ornamental plants are normally grown for their flowers, foliage, or overall appearance; useful plants are grown for consumption , for their dyes, or for medicinal or cosmetic use...
. He had friendly relations with the president of the Russian Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
Mstislav Keldysh
Mstislav Keldysh
Mstislav Vsevolodovich Keldysh was a Soviet scientist in the field of mathematics and mechanics, academician of the USSR Academy of Sciences , President of the USSR Academy of Sciences , three times Hero of Socialist Labor , fellow of the Royal Society of Edinburgh . He was one of the key figures...
and Mikhail Lavrentyev
Mikhail Lavrentyev
Mikhail Alekseevich Lavrentyev or Lavrentiev was an outstanding Soviet mathematician and hydrodynamicist.-Biography:...
, both mathematicians whose careers started in his institute.