Editing Andrey Tikhonov (mathematician)

{{Short description|Soviet mathematician (1906–1993)}}
{{Infobox scientist
| name                    = Andrey Tikhonov
| image                   = Tychonoff.jpg
| image_size              = 200px
| caption                 = Tikhonov in 1975
| birth_date              = {{Birth date|1906|10|17|df=y}}
| birth_place             = [[Gzhatsk]], [[Russian Empire]]
| death_date              = {{death date and age|1993|10|7|1906|10|30|df=y}}
| death_place             = [[Moscow, Russia]]
| field                   = [[Mathematics]]
| work_institution        = [[Moscow State University]]
| alma_mater              = [[Moscow State University]]
| doctoral_advisor        = [[Pavel Alexandrov]]
| doctoral_students       = [[Alexander Andreevich Samarskii|Aleksandr Andreyevich Samarskiĭ]]<br>[[Alexei Georgievich Sveshnikov]]
| known_for               = Important contributions to [[topology]], [[functional analysis]], [[mathematical physics]], [[ill-posed problem]]s; 
*[[Tychonoff space]]s, 
*[[Tychonoff's theorem]], 
*[[Tikhonov regularization]], 
*[[Tikhonov's theorem (dynamical systems)]], 
*[[magnetotellurics]] geophysical method.
| prizes                  = 
| footnotes               = 
}}
'''Andrey Nikolayevich Tikhonov''' ({{langx|ru|Андре́й Никола́евич Ти́хонов}}; 17 October 1906 &ndash; 7 October 1993) was a leading [[USSR|Soviet Russian]]  [[mathematician]] and [[geophysicist]] known for important contributions to [[topology]], [[functional analysis]], [[mathematical physics]], and [[ill-posed problem]]s. He was also one of the inventors of the [[magnetotellurics]] method in geophysics. Other transliterations of his surname include "Tychonoff", "Tychonov", "Tihonov", "Tichonov".

== Biography ==
Born in [[Gzhatsk]], he studied at the [[Moscow State University]] where he received a Ph.D. in 1927 under the direction of [[Pavel Sergeevich Alexandrov]].<ref>{{MathGenealogy|id=58042|name=Andrei Nikolaevich Tikhonov}}</ref> 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 [[academician|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 [[topology]], [[functional analysis]], [[mathematical physics]], and certain classes of [[ill-posed problem]]s. [[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 theorems|metrization theorem]] he proved in 1926, and the [[Tychonoff's theorem]], which states that every product of arbitrarily many [[Compact space|compact]] [[topological space]]s is again [[Compact space|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]]<ref>{{cite journal|author=A. Tychonoff|title=Théorèmes d'unicité pour l'équation de la chaleur|journal=[[Matematicheskii Sbornik]]|volume=42 | issue = 2 |pages=199–216|year=1935|url= http://mi.mathnet.ru/eng/msb6410}}</ref> and studied [[Volterra integral equation]]s.

He founded the theory of [[asymptotic analysis]] for differential equations with small parameter in the leading derivative.<ref>{{cite journal |author=A. N. Tikhonov |title=Systems of Differential Equations Containing Small Parameters in the Derivatives |journal=Mathematical Sbornik |volume=31 |issue=73 |page=3 |year=1952 |url=http://mi.mathnet.ru/eng/msb5548}}</ref>

== Organizer work ==
Tikhonov played the leading role in founding the [[MSU Faculty of Computational Mathematics and Cybernetics|Faculty of Computational Mathematics and Cybernetics]] of [[Moscow State University]] and served as its first dean during the period of 1970–1990.

[[File:Tikhonov board.jpg|thumb|250px|Memorial board of A.N. Tikhonov on the MSU Second Humanities Building where the Faculty of Computational Mathematics and Cybernetics is located]]

== 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===
* {{cite book |first1=A. G. |last1=Sveshnikov |first2=A. N. |last2=Tikhonov |title=The Theory of Functions of a Complex Variable |publisher=[[Mir Publishers|Mir]] |year=1978}} (English translation.)
* {{cite book |first1=A. N. |last1=Tikhonov |first2=V. Y. |last2=Arsenin |title=Solutions of Ill-Posed Problems |publisher=Winston |location=New York |year=1977 |isbn=0-470-99124-0}}<ref name="Levine1979">{{cite journal|last1=Levine|first1=Howard A.|title=Book Review: Solutions of ill posed problems|journal=Bulletin of the American Mathematical Society|volume=1|issue=3|year=1979|pages=521–525|issn=0273-0979|doi=10.1090/S0273-0979-1979-14602-0|doi-access=free}}</ref>
* {{cite book |first1=A. N. |last1=Tikhonov |first2=A. V. |last2=Goncharsky |title=Ill-posed Problems in the Natural Sciences |publisher=Oxford University Press |location=Oxford |year=1987 |isbn=0-8285-3739-9}}
*{{cite book
 |last1=A. N. |first1=Tikhonov |author2-link=Alexander Andreevich Samarskii |first2=A. A. |last2=Samarskii |orig-year=1990 |year=2013 |title=Equations of Mathematical Physics |publisher=Dover |isbn=978-0-48-617336-8 |url=https://books.google.com/books?id=PTmoAAAAQBAJ
}} 
* {{cite book |first1=A. N. |last1=Tikhonov |first2=A. V. |last2=Goncharsky |first3=V. V. |last3=Stepanov |first4=A. G. |last4=Yagola |title=Numerical Methods for the Solution of Ill-Posed Problems |publisher=Kluwer |location=Dordrecht |year=1995 |isbn=0-7923-3583-X}}
* {{cite book |first1=A. N. |last1=Tikhonov |first2=A. S. |last2=Leonov |first3=A. G. |last3=Yagola |title=Nonlinear Ill-Posed Problems |publisher=Chapman and Hall |location=London, Weinheim, New York, Tokyo, Melbourne, Madras |volume=1–2 |year=1998 |isbn=0-412-78660-5}}

===Papers===
* {{cite journal|doi=10.1016/0041-5553(62)90005-8|title=Homogeneous difference schemes|year=1962|last1=Tikhonov|first1=A. N.|last2=Samarskii|first2=A. A.|journal=USSR Computational Mathematics and Mathematical Physics|volume=1|pages=5–67|citeseerx=10.1.1.714.1396}}
* {{cite journal |last1=Tikhonov |first1=A. N. |last2=Samarskii |first2=A. A. |year=1963 |title=Homogeneous difference schemes on non-uniform nets |journal=USSR Computational Mathematics and Mathematical Physics |volume=2 |issue=5 |pages=927–953 |doi=10.1016/0041-5553(63)90505-6 |url=http://www.samarskii.ru/articles/1963/1963_016.pdf}}
* {{cite journal |doi=10.1016/0041-5553(66)90003-6 |title=On the stability of the functional optimization problem|year=1966 |last1=Tikhonov |first1=A. N. |journal=USSR Computational Mathematics and Mathematical Physics |volume=6 |issue=4 |pages=28–33}}

==See also==

*[[Regularization (mathematics)|Regularization]]
*[[Stone–Čech compactification]]
*[[Tychonoff cube|Tikhonov cube]]
*[[von Mises distribution|Tikhonov distribution]]
*[[Tychonoff plank|Tikhonov plank]]
*[[Tychonoff space|Tikhonov space]]
*[[Tikhonov's theorem (dynamical systems)|Tikhonov's theorem on dynamical systems]]

==References==
{{Reflist}}

==External links==
*{{MacTutor Biography|id=Tikhonov}}

{{Authority control}}

{{DEFAULTSORT:Tikhonov, Andrey Nikolayevich}}
[[Category:1906 births]]
[[Category:1993 deaths]]
[[Category:Soviet mathematicians]]
[[Category:Topologists]]
[[Category:Full Members of the USSR Academy of Sciences]]
[[Category:Full Members of the Russian Academy of Sciences]]
[[Category:Moscow State University alumni]]
[[Category:Heroes of Socialist Labour]]
[[Category:Members of the German Academy of Sciences at Berlin]]
[[Category:Soviet inventors]]
[[Category:Academic staff of Moscow State University]]
[[Category:Russian scientists]]