Aleksandr Yakovlevich Khinchin (russian: Алекса́ндр Я́ковлевич Хи́нчин, french: Alexandre Khintchine; July 19, 1894 – November 18, 1959) was a

Soviet 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 national ...

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 ...

and one of the most significant contributors to the Soviet school of

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

Life and career

He was born in the village of Kondrovo,

Kaluga Governorate Kaluga Governorate (1796–1929) was a governorate of the Russian Empire and the Russian SFSR. Its capital was Kaluga. Administrative division Kaluga Governorate consisted of the following uyezds (administrative centres in parentheses): * B ...

Russian Empire The Russian Empire was an empire and the final period of the List of Russian monarchs, Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended th ...

. While studying at

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

, he became one of the first followers of the famous Luzin school. Khinchin graduated from the university in 1916 and six years later he became a full professor there, retaining that position until his death. Khinchin's early works focused on real analysis. Later he applied methods from the metric theory of functions to problems in probability theory and

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

. He became one of the founders of modern probability theory, discovering the

law of the iterated logarithm In probability theory, the law of the iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due to A. Ya. Khinchin (1924). Another statement was given by A ...

in 1924, achieving important results in the field of limit theorems, giving a definition of a stationary process and laying a foundation for the theory of such processes. Khinchin made significant contributions to the metric theory of Diophantine approximations and established an important result for simple real continued fractions, discovering a property of such numbers that leads to what is now known as

Khinchin's constant In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers ''x'', coefficients ''a'i'' of the continued fraction expansion of ''x'' have a finite geometric mean that is independent of the value of ''x'' and is kno ...

. He also published several important works on

statistical physics Statistical physics is a branch of physics that evolved from a foundation of statistical mechanics, which uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approxi ...

, where he used the methods of probability theory, and on

information theory Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...

queuing theory Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the ...

and

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

. In 1939 Khinchin was elected as a Correspondent Member of the Academy of Sciences of the USSR. He was awarded the Stalin Prize (1941), the

Order of Lenin The Order of Lenin (russian: Орден Ленина, Orden Lenina, ), named after the leader of the Russian October Revolution, was established by the Central Executive Committee on April 6, 1930. The order was the highest civilian decoration ...

, three other orders, and medals.

Bibliography

*''Sur la Loi des Grandes Nombres'', in ''Comptes Rendus de l'Académie des Sciences'', Paris, 1929 *''Asymptotische Gesetze der Wahrscheinlichkeitsrechnung'', Berlin: Julius Springer, 1933 *''Continued Fractions'', Mineola, N.Y. : Dover Publications, 1997, (first published in Moscow, 1935) *''Three Pearls of Number Theory'', Mineola, NY : Dover Publications, 1998, (first published in

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

and

Leningrad Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...

, 1947) *''Mathematical Foundations of Quantum Statistics'', Mineola, N.Y. : Dover Publications, 1998, (first published in Moscow and Leningrad, 1951; trans. in 1960 by Irwin Shapiro) *''Mathematical Foundations of Information Theory'', Dover Publications, 1957,

References

External links

* *
List of books by Khinchin provided by National Library of AustraliaA.Ya. Khinchin
a
Math-Net.Ru
{{DEFAULTSORT:Khinchin, Aleksandr Yakovlevich 20th-century Russian mathematicians Soviet mathematicians Number theorists Probability theorists Queueing theorists Stalin Prize winners Moscow State University alumni Moscow State University faculty Corresponding Members of the USSR Academy of Sciences 1894 births 1959 deaths Burials at Donskoye Cemetery

Life and career

See also

Bibliography

References

External links