# Andrey Nikolayevich Tikhonov

Andrei Nikolaevich Tikhonov (Russian: Андрей Николаевич Тихонов, scientific transliteration Andrei Nikolaevich Tikhonov, English transliteration Andrei Tikhonov; * 17 Oktoberjul / October 30 1906greg in Gzhatsk, .. † 7 November 1993, Moscow) was a Russian mathematician. Often the letters Tychonoff is used

He was born in Smolensk and studied from 1922 to 1927 at the Lomonosov University in Moscow. In 1925 he published his first mathematical work and before graduating he delivered his fundamental contribution to the product topology. In 1936 he completed his habilitation (Russian PhD ) on functional equations from Volterratyp with applications in mathematical physics (heat conduction ). In 1936 he became a professor at Moscow State University. He was at times Dean of the Faculty of Numerical Computing and Cybernetics and Deputy Director of the Institute of Applied Mathematics of the Soviet Academy of Sciences.

During his lifetime, he received numerous awards, including the 1966 Lenin Prize (together with Valentin Konstantinovich Ivanov, for work on ill-posed problems ) and membership in the Academy of Sciences of the USSR ( since 1939 as a corresponding member, and from 1966 as a full member ). In 1953 he was awarded the State Prize of the USSR.

Tikhonov worked in various areas of mathematics. He wrote important contributions to topology, functional analysis, ordinary and partial differential equations to mathematical physics and applied problems, for example, in geophysics and electrodynamics, for numerical mathematics and to certain classes of ill-posed problems. Best known is his work in topology, including a Metrisierbarkeitssatz and the set of Tychonoff, which states that each product space of any number of compact topological spaces is again compact. In his honor, completely regular topological spaces are also called Tikhonov - rooms, constructed in 1930 by him topological space is now called Tikhonov plank. In 1935 he proved a fixed point theorem named after him for continuous maps of compact convex subsets of locally convex spaces. In numerical mathematics, he developed the theory with Samarski homogeneous difference scheme.

In 1966 he was invited speaker at the International Congress of Mathematicians in Moscow ( About -solving methods not correctly set tasks ).

His doctoral counts Sergei Vasilievich Fomin.

## Writings

- AA Samarski: Differential Equations of Mathematical Physics, German VEB Verlag der Wissenschaften, Berlin 1959, English translation: Equations of Mathematical Physics, Dover 1963, 1990
- With AG Sveshnikov: The theory of functions of a complex variable, Moscow, MIR 1971