Person: Tikhonov, Andrei Nikolaevich
Andrey Nikolayevich Tikhonov was a Russian mathematician who worked in topology, functional analysis, mathematical physics, and ill-posed problems.
Mathematical Profile (Excerpt):
- The most common way, other than Andrei Nikolaevich Tikhonov, is to write it as Andrey Nikolayevich Tychonoff.
- Andrei Nikolaevich Tikhonov attended secondary school as a day pupil and entered the Moscow University in 1922, the year in which he completed his school education.
- By 1926 he had discovered the topological construction which is today named after him, the Tikhonov topology defined on the product of topological spaces.
- very well with what mistrust he met Tikhonov's proposed definition.
- Tikhonov certainly had given the right definition and this idea, which was counterintuitive to even as great a topologist as Aleksandrov, allowed Tikhonov to go on and prove such important topological results as the product of any set of compact topological spaces is compact.
- Few mathematicians have gained a worldwide reputation before they even start their research careers but this was essentially how it was for Tikhonov.
- His results on the Tikhonov topology of products were achieved before he graduated in 1927.
- Tikhonov, however, had equal talents for other areas of mathematics.
- Tikhonov's scientific work is characterised by magnificent achievements in very abstract fields of so-called pure mathematics, combined with deep investigations into the mathematical disciplines directly connected with practical requirements.
- Tikhonov's work led from topology to functional analysis with his famous fixed point theorem for continuous maps from convex compact subsets of locally convex topological spaces in 1935.
- These results are of importance in both topology and functional analysis and were applied by Tikhonov to solve problems in mathematical physics.
- After successfully defending his thesis, Tikhonov was appointed as a professor at Moscow University in 1936 and then, three years later, he was elected as a Corresponding Member of the USSR Academy of Sciences.
- The extremely deep investigations of Tikhonov into a number of general problems in mathematical physics grew out of his interest in geophysics and electrodynamics.
- Tikhonov's work on mathematical physics continued throughout the 1940s and he was awarded the State Prize for this work in 1953.
- One of the most outstanding achievemnets in computational mathematics is the theory of homogeneous difference schemes, which Tikhonov developed in collaboration with Samarskii....
- In the 1960s Tikhonov began to produce an important series of papers on ill-posed problems.
- Combining his computing skills with solving problems of this type, Tikhonov gave computer implementations of algorithms to compute the operators which he used in the solution of these problems.
- Tikhonov was awarded the Lenin Prize for his work on ill-posed problems in 1966.
- Tikhonov's wide interests throughout mathematics led him to hold a number of different chairs at Moscow University, in particular a chair in the Mathematical Physics Faculty and a chair of Computational Mathematics in the Engineering Mathematics Faculty.
- Tikhonov was appointed as Deputy Director of the Institute of Applied Mathematics of the USSR Academy of Sciences, a position he held for many years.
Born 30 October 1906, Gzhatska, Smolensk, Russia. Died 7 October 1993, Moscow, Russia.
View full biography at MacTutor
Tags relevant for this person:
Origin Russia, Topology
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive