Andrey Nikolayevich Tikhonov (; 17 October 1906 – 7 October 1993) was a leading Soviet Russian

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

geophysicist Geophysics () is a subject of natural science concerned with the physical processes and properties of Earth and its surrounding space environment, and the use of quantitative methods for their analysis. Geophysicists conduct investigations acros ...

known for important contributions to

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...

mathematical physics Mathematical physics is 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 the de ...

, and ill-posed problems. He was also one of the inventors of the

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

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

Biography

Born in Gzhatsk, he studied at the

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 ...

where he received a Ph.D. in 1927 under the direction of Pavel Sergeevich Alexandrov. In 1933 he was appointed as a professor at Moscow State University. He became a corresponding member of the USSR Academy of Sciences 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 ill-posed problems. Tikhonov regularization, 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, sound source reconstruction, source reconstruction in ac ...

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

, 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, a type of agreement used by U.S. states * Blood compact, an ancient ritual of the Philippines * Compact government, a t ...

topological space In mathematics, a topological space is, roughly speaking, a Geometry, geometrical space in which Closeness (mathematics), closeness is defined but cannot necessarily be measured by a numeric Distance (mathematics), distance. More specifically, a to ...

s is again

. In his honor, completely regular 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 is any completely regular space that is also a ...

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 (more specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quanti ...

and studied Volterra integral equations. He founded the theory of

asymptotic analysis In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing Limit (mathematics), limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very larg ...

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 (1954, 1986).

Publications

Books

* (English translation.) * * * * *

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 Academic staff of Moscow State University Russian scientists