Editing Teiji Takagi

{{Short description|Japanese mathematician}}
{{Infobox scientist
| name              = Teiji Takagi
| image             = Teiji Takagi photographed by Shigeru Tamura.jpg
| image_size        =
| caption           =
| birth_date        = {{Birth date|1875|04|21}}
| birth_place       = Kazuya village near [[Gifu, Gifu|Gifu]]
| death_date        = {{Death date and age|1960|02|28|1875|04|21}}
| death_place       = [[Tokyo]]
| nationality       = [[Japan]]ese
| fields            = [[Mathematics]]
| workplaces        = [[Tokyo Imperial University]]
| alma_mater        = Tokyo Imperial University
| doctoral_advisor  = [[David Hilbert]]
| doctoral_students = [[Shokichi Iyanaga]]<ref name=MathGen>{{MathGenealogy|id=55699}}</ref><br>[[Sigekatu Kuroda]]<ref name=MathGen/><br>[[Tadasi Nakayama]]<ref name=MathGen/><br>[[Kenjiro Shoda]]<ref name=MathGen/>
| known_for         = [[Takagi curve]]<br>[[Takagi existence theorem]]<br>[[Symmetric matrix#Complex symmetric matrices|Autonne–Takagi factorization]]
| awards            =
}}
'''Teiji Takagi''' (高木 貞治 ''Takagi Teiji'', April 21, 1875 – February 28, 1960) was a Japanese [[mathematician]], best known for proving the [[Takagi existence theorem]] in [[class field theory]]. The [[Blancmange curve]], the graph of a nowhere-differentiable but [[uniformly continuous]] function, is also called the Takagi curve after his work on it.

== Biography ==
He was born in the rural area of the [[Gifu Prefecture]], [[Japan]]. He began learning mathematics in middle school, reading texts in English since none were available in Japanese. After attending a high school for gifted students, he went on to the [[University of Tokyo|Imperial University]] (University of Tokyo), at that time the only university in Japan before the [[National Seven Universities|Imperial University System]] was established on June 18, 1897. There he learned mathematics from such European classic texts as [[George Salmon|Salmon]]'s ''Algebra'' and [[Heinrich M. Weber|Weber]]'s ''Lehrbuch der Algebra''. Aided by [[David Hilbert|Hilbert]], he then studied at [[Göttingen]]. Aside from his work in [[algebraic number theory]] he wrote a great number of Japanese textbooks on mathematics and geometry.

During World War I, he was isolated from European mathematicians and developed his existence theorem in class field theory, building on the work of Heinrich Weber. As an Invited Speaker, he presented a synopsis of this research in a talk ''Sur quelques théoremes généraux de la théorie des nombres algébriques''<ref>{{cite book|chapter-url=http://www.mathunion.org/ICM/ICM1920/Main/icm1920.0185.0188.ocr.pdf|pages=185–188|year=1921|title=Compte rendu du Congrès international des mathématiciens tenu à Strasbourg du 22 au 30 Septembre 1920|chapter=''Sur quelques théoremes généraux de la théorie des nombres algébriques'' par T. Takagi|url-status=dead|archive-url=https://web.archive.org/web/20171028200936/http://www.mathunion.org/ICM/ICM1920/Main/icm1920.0185.0188.ocr.pdf|archive-date=2017-10-28}}</ref> at the [[International Congress of Mathematicians]] in [[Strasbourg]] in 1920. There he found little recognition of the value of his research, since algebraic number theory was then studied mainly in Germany and German mathematicians were excluded from the Congress. Takagi published his theory in the same year in the journal of the University of Tokyo. However, the significance of Takagi's work was first recognized by [[Emil Artin]] in 1922, and was again pointed out by [[Carl Ludwig Siegel]], and at the same time by [[Helmut Hasse]], who lectured in Kiel in 1923 on class field theory and presented Takagi's work in a lecture at the meeting of the [[German Mathematical Society|DMV]] in 1925 in [[Gdańsk|Danzig]] and in his ''Klassenkörperbericht'' (class field report) in the 1926 annual report of the DMV. Takagi was then internationally recognized as one of the world's leading number theorists. In 1932 he was vice-president of the [[International Congress of Mathematicians]] in [[Zürich]] and in 1936 was a member of the selection committee for the first [[Fields Medal]].

He was also instrumental during [[World War II]] in the development of Japanese  encryption systems; see [[Purple (cipher machine)|Purple]].

The [[Symmetric matrices#Complex symmetric matrices|Autonne-Takagi factorization of complex symmetric matrices]] is named in his honour.

==Family==
* [[Sigekatu Kuroda]], son-in-law, a mathematician.
* [[S.-Y. Kuroda]], grandson (son of Sigekatu Kuroda), mathematician and Chomskyan linguist.

==Bibliography==

*{{citation|mr=1129240
|last=Takagi|first= Teiji
|title=Collected papers
|edition=2 |editor-first= Shokichi|editor-last= Iyanaga |publisher= Springer-Verlag|series=Springer Collected Works in Mathematics|orig-year= 1990|isbn=978-4431549949|year=2014|doi=10.1007/978-4-431-54995-6}}

==References==
{{reflist}}

==External links==
* {{Commons category-inline|Teiji Takagi}}
* {{MacTutor Biography|id=Takagi}}
* [http://www.kurims.kyoto-u.ac.jp/~toshi/jjm/JJM_HP/contents/jjm-takagi.htm Takagi Lectures] by the [[Mathematical Society of Japan]]
*[https://www.cambridge.org/core/journals/mathematical-gazette/article/teiji-takagi-collected-papers-2nd-edition-edited-by-s-iyanaga-k-iwasawa-k-kodaita-and-k-yosida-pp-376-dm188-1990-isbn-3540700579-springer/2C3C7B5F7CBFC529D2109C95D035EDB8 Teiji Takagi: collected papers] (2nd edition), edited by S. Iyanaga, K. Iwasawa, K. Kodaita and K. Yosida. Pp 376. DM188. 1990. {{ISBN|3-540-70057-9}} (Springer) / CAMBRIDGE UNIVERSITY PRESS / The Mathematical Association 1991

{{Authority control}}

{{DEFAULTSORT:Takagi, Teiji}}
[[Category:People from Gifu Prefecture]]
[[Category:People from the Empire of Japan]]
[[Category:1875 births]]
[[Category:1960 deaths]]
[[Category:19th-century Japanese mathematicians]]
[[Category:20th-century Japanese mathematicians]]
[[Category:Number theorists]]
[[Category:Academic staff of the University of Tokyo]]
[[Category:University of Göttingen alumni]]
[[Category:University of Tokyo alumni]]
[[Category:Recipients of the Order of Culture]]
[[Category:Scientists from Gifu Prefecture]]