Andrey Nikolayevich Tychonoff
Encyclopedia
Andrey Nikolayevich Tikhonov ' onMouseout='HidePop("84081")' href="/topics/Moscow">Moscow
) was a Soviet and Russia
n mathematician
known for important contributions to topology
, functional analysis
, mathematical physics
, and ill-posed problems. He was also inventor of magnetotellurics
method in geology. Tikhonov originally published in German, whence the transliteration. His surname is also transliterated as "Tychonoff".
, he studied at the Moscow State University
where he received Ph.D. in 1927 under 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.
, functional analysis
, mathematical physics
, and certain classes of ill-posed problems. Tikhonov regularization
, one of the most widely used methods to solve ill-posed inverse problem
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
, which states that every product of arbitrarily many compact
topological space
s is again compact
. In his honor, completely regular topological spaces are also named Tychonoff space
s.
In mathematical physics, he proved the fundamental uniqueness theorem
s for the heat equation
and studied Volterra integral equation
s.
In asymptotical analysis, he founded the theory of asymptotic analysis for differential equations with small parameter in the leading derivative.
and served as its first dean during the period of 1970–1990.
(1966) and the Hero of Socialist Labor
(1954, 1986).
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
) was a Soviet and Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
known for important contributions to topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, functional analysis
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 and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
, and ill-posed problems. He was also inventor of magnetotellurics
Magnetotellurics
Magnetotellurics is an electromagnetic geophysical method of imaging the earth's subsurface by measuring natural variations of electrical and magnetic fields at the Earth's surface. Investigation depth ranges from 300m below ground by recording higher frequencies down to 10,000m or deeper with...
method in geology. Tikhonov originally published in German, whence the transliteration. His surname is also transliterated as "Tychonoff".
Biography
Born near SmolenskSmolensk
Smolensk is a city and the administrative center of Smolensk Oblast, Russia, located on the Dnieper River. Situated west-southwest of Moscow, this walled city was destroyed several times throughout its long history since it was on the invasion routes of both Napoleon and Hitler. Today, Smolensk...
, he studied at the Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
where he received Ph.D. in 1927 under direction of Pavel Sergeevich Alexandrov
Pavel Sergeevich Alexandrov
Pavel Sergeyevich Alexandrov , sometimes romanized Aleksandroff or Aleksandrov was a Soviet Russian mathematician...
. In 1933 he was appointed as a professor at Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
. He became a corresponding member of the USSR Academy of Sciences on 29 January 1939 and a full member
Academician
The title Academician denotes a Full Member of an art, literary, or scientific academy.In many countries, it is an honorary title. There also exists a lower-rank title, variously translated Corresponding Member or Associate Member, .-Eastern Europe and China:"Academician" may also be a functional...
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 topologyTopology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, functional analysis
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 and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
, and certain classes of ill-posed problems. Tikhonov regularization
Tikhonov regularization
Tikhonov regularization, named for Andrey Tikhonov, is the most commonly used method of regularization of ill-posed problems. In statistics, the method is known as ridge regression, and, with multiple independent discoveries, it is also variously known as the Tikhonov-Miller method, the...
, one of the most widely used methods to solve ill-posed inverse problem
Inverse problem
An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in...
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
Tychonoff's theorem
In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact. The theorem is named after Andrey Nikolayevich Tychonoff, who proved it first in 1930 for powers of the closed unit interval and in 1935 stated the full theorem along with the...
, which states that every product of arbitrarily many compact
Compact space
In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness property, which has many important implications not valid in general spaces...
topological space
Topological space
Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...
s is again compact
Compact space
In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness property, which has many important implications not valid in general spaces...
. In his honor, completely regular topological spaces are also named Tychonoff space
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....
s.
In mathematical physics, he proved the fundamental uniqueness theorem
Uniqueness theorem
The uniqueness theorem for Poisson's equation states that the equation has a unique gradient of the solution for a large class of boundary conditions...
s for the heat equation
Heat equation
The heat equation is an important partial differential equation which describes the distribution of heat in a given region over time...
and studied Volterra integral equation
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 = \int_a^t K\,x\,ds...
s.
In asymptotical analysis, 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 Faculty of Computational Mathematics and Cybernetics of Moscow State UniversityMoscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
and served as its first dean during the period of 1970–1990.
Awards
Tikhonov received numerous honors and awards for his work, including the Lenin PrizeLenin Prize
The Lenin Prize was one of the most prestigious awards of the USSR, presented to individuals for accomplishments relating to science, literature, arts, architecture, and technology. It was created on June 23, 1925 and was awarded until 1934. During the period from 1935 to 1956, the Lenin Prize was...
(1966) and the Hero of Socialist Labor
Hero of Socialist Labor
Hero of Socialist Labour was an honorary title in the Soviet Union and other Warsaw Pact countries. It was the highest degree of distinction for exceptional achievements in national economy and culture...
(1954, 1986).
Books
- A.G. Sveshnikov, A.N. Tikhonov, The Theory of Functions of a Complex Variable, Mir PublishersMir Publishers150px|rightMir Publishers 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 headquartered in Moscow, Russia since then...
, English translation, 1978. - A.N. Tikhonov, V.Y. Arsenin, Solutions of Ill-Posed Problems, Winston, New York, 1977. ISBN 0470991240.
- A.N. Tikhonov, A.V. Goncharsky, Ill-posed Problems in the Natural Sciences, Oxford University Press, Oxford, 1987. ISBN 0828537399.
- A.N. Tikhonov, A.A. Samarskii, Equations of Mathematical Physics, Dover Publications, 1990. ISBN 0486664228.
- A.N. Tikhonov, A.V. Goncharsky, V.V. Stepanov, A.G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems, Kluwer, Dordrecht, 1995. ISBN 079233583X.
- 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. ISBN 0412786605.