Andrey Nikolayevich Tikhonov (russian: Андре́й Никола́евич Ти́хонов; October 17, 1906 – October 7, 1993) was a leading

Soviet Russian The Russian Soviet Federative Socialist Republic, Russian SFSR or RSFSR ( rus, Российская Советская Федеративная Социалистическая Республика, Rossíyskaya Sovétskaya Federatívnaya Soci ...

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

geophysicist Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' som ...

known for important contributions to

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

, and

ill-posed problem The mathematical term well-posed problem stems from a definition given by 20th-century French mathematician Jacques Hadamard. He believed that mathematical models of physical phenomena should have the properties that: # a solution exists, # the sol ...

s. He was also one of the inventors of the

magnetotellurics Magnetotellurics (MT) is an electromagnetic geophysical method for inferring the earth's subsurface electrical conductivity from measurements of natural geomagnetic and geoelectric field variation at the Earth's surface. Investigation depth ...

method in geophysics. Other transliterations of his surname include "Tychonoff", "Tychonov", "Tihonov", "Tichonov."

Biography

Born in

Gzhatsk Gagarin (russian: Гага́рин), known until 1968 as Gzhatsk (), is a town and the administrative centre of Gagarinsky District of Smolensk Oblast, Russia, located on the Gzhat River, northeast of Smolensk, the administrative centre of t ...

, he studied at the

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 ...

where he received a Ph.D. in 1927 under the direction of

Pavel Sergeevich Alexandrov Pavel Sergeyevich Alexandrov (russian: Па́вел Серге́евич Алекса́ндров), sometimes romanized ''Paul Alexandroff'' (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote about three hundred papers, ma ...

. In 1933 he was appointed as a professor at Moscow State University. He became a corresponding member of the

USSR Academy of Sciences 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 ...

on 29 January 1939 and a full member of the USSR Academy of Sciences on 1 July 1966.

Research work

Tikhonov worked in a number of different fields in mathematics. He made important contributions to

, and certain classes of

Tikhonov regularization Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. Also ...

, one of the most widely used methods to solve ill-posed

inverse problem An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the ...

s, is named in his honor. He is best known for his work on topology, including the

metrization theorem In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological space (X, \mathcal) is said to be metrizable if there is a metric d : X \times X \to , \infty ...

he proved in 1926, and the

Tychonoff's theorem In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named after Andrey Nikolayevich Tikhonov (whose surname sometimes is trans ...

, which states that every product of arbitrarily many

compact Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to: * Interstate compact * Blood compact, an ancient ritual of the Philippines * Compact government, a type of colonial rule utilized in British ...

topological space In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points ...

s is again

. In his honor,

completely regular In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are kinds of topological spaces. These conditions are examples of separation axioms. A Tychonoff space refers to any completely regular space that is ...

topological spaces are also named ''

Tychonoff space In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are kinds of topological spaces. These conditions are examples of separation axioms. A Tychonoff space refers to any completely regular space that is ...

s''. In mathematical physics, he proved the fundamental

uniqueness theorem In mathematics, a uniqueness theorem, also called a unicity theorem, is a theorem asserting the uniqueness of an object satisfying certain conditions, or the equivalence of all objects satisfying the said conditions. Examples of uniqueness theorems ...

s for the

heat equation In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat equation was first developed by Joseph Fourier in 1822 for t ...

and studied

Volterra integral equation In mathematics, the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and the second kind. A linear Volterra equation of the first kind is : f(t) = \int_a^t K(t,s)\,x(s ...

s. He founded the theory of asymptotic analysis for differential equations with small parameter in the leading derivative.

Organizer work

Tikhonov played the leading role in founding the Faculty of Computational Mathematics and Cybernetics of

and served as its first dean during the period of 1970–1990. Tikhonov board

Awards

Tikhonov received numerous honors and awards for his work, including the Lenin Prize (1966) and the

Hero of Socialist Labor The Hero of Socialist Labour (russian: links=no, Герой Социалистического Труда, Geroy Sotsialisticheskogo Truda) was an honorific title in the Soviet Union and other Warsaw Pact countries from 1938 to 1991. It repre ...

(1954, 1986).

Publications

Books

* A.G. Sveshnikov, A.N. Tikhonov, ''The Theory of Functions of a Complex Variable'',

Mir Publishers Mir Publishers (russian: Издательство "Мир") was a major publishing house in the Soviet Union which continues to exist in modern Russian Federation. It was established in 1946 by a decree of the USSR Council of Ministers and has hea ...

, English translation, 1978. * A.N. Tikhonov, V.Y. Arsenin, ''Solutions of Ill-Posed Problems'', Winston, New York, 1977. . * A.N. Tikhonov, A.V. Goncharsky, ''Ill-posed Problems in the Natural Sciences'', Oxford University Press, Oxford, 1987. . * * A.N. Tikhonov, A.V. Goncharsky, V.V. Stepanov, A.G. Yagola, ''Numerical Methods for the Solution of Ill-Posed Problems'', Kluwer, Dordrecht, 1995. . * A.N. Tikhonov, A.S. Leonov, A.G. Yagola. ''Nonlinear Ill-Posed Problems'', Chapman and Hall, London, Weinheim, New York, Tokyo, Melbourne, Madras, V. 1–2, 1998. .

Papers

* * *

References

External links

* {{DEFAULTSORT:Tikhonov, Andrey Nikolayevich 1906 births 1993 deaths Soviet mathematicians Topologists Full Members of the USSR Academy of Sciences Full Members of the Russian Academy of Sciences Moscow State University alumni Heroes of Socialist Labour Members of the German Academy of Sciences at Berlin Soviet inventors Moscow State University faculty