Aleksandr Yakovlevich Khinchin (, ), July 19, 1894 – November 18, 1959, was a

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

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 or probability calculus 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 expre ...

. Due to romanization conventions, his name is sometimes written as "Khinchin" and other times as "Khintchine".

Life and career

He was born in the village of Kondrovo, Kaluga Governorate,

Russian Empire The Russian Empire was an empire that spanned most of northern Eurasia from its establishment in November 1721 until the proclamation of the Russian Republic in September 1917. At its height in the late 19th century, it covered about , roughl ...

. While studying at

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

, 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 co ...

. Later he applied methods from the metric theory of functions to problems in probability theory and

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

. 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 Aleksandr Khinchin, A. Ya. Khinchin (1924). Another state ...

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 (also called a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose statistical properties, such as mean and variance, do not change over time. M ...

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 ...

s and established an important result for simple real

continued fraction A continued fraction is a mathematical expression that can be written as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple fraction or not, ...

s, discovering a property of such numbers that leads to what is now known as

Khinchin's constant In number theory, Khinchin's constant is a mathematical constant related to the simple continued fraction expansions of many real numbers. In particular Aleksandr Yakovlevich Khinchin proved that for almost all real numbers ''x'', the coefficients ...

. He also published several important works on

statistical physics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...

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

information theory Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by 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 th ...

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 ( ...

. 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. It united the country's leading scientists and was subordinated directly to the Council of Ministers of the Soviet Union (u ...

. He was awarded the

USSR State Prize The USSR State Prize () was one of the Soviet Union’s highest civilian honours, awarded from its establishment in September 1966 until the dissolution of the USSR in 1991. It recognised outstanding contributions in the fields of science, mathem ...

(1941), and the

Order of Lenin The Order of Lenin (, ) was an award named after Vladimir Lenin, the leader of the October Revolution. It was established by the Central Executive Committee on 6 April 1930. The order was the highest civilian decoration bestowed by the Soviet ...

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 is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

and

Leningrad Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...

, 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 Recipients of the Stalin Prize Moscow State University alumni Academic staff of Moscow State University Corresponding Members of the USSR Academy of Sciences 1894 births 1959 deaths Burials at Donskoye Cemetery Russian scientists

Life and career

See also

Bibliography

References

External links