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 nation ...

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 ...

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 ...

Life and career

He was born in the village of Kondrovo,

Kaluga Governorate Kaluga Governorate (1796–1929) was a List of governorates of the Russian Empire, governorate of the Russian Empire and the Russian Soviet Federative Socialist Republic, Russian SFSR. Its capital was Kaluga. Administrative division Kaluga Go ...

Russian Empire The Russian Empire was an empire and the final period of the 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 the Great Northern War. ...

. 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 In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include conv ...

. 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, "Mat ...

. 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 In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Con ...

and laying a foundation for the theory of such processes. Khinchin made significant contributions to the metric theory of

Diophantine approximation In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by r ...

s and established an important result for simple real

continued fraction In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer ...

s, 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 approxim ...

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

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 The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991, uniting the country's leading scientists, subordinated directly to the Council of Ministers of the Soviet Union (until 1946 ...

. 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, ...

(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 millio ...

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