Teiji Takagi (高木 貞治 ''Takagi Teiji'', April 21, 1875 – February 28, 1960) was a Japanese
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
, best known for proving the
Takagi existence theorem {{short description, Correspondence between finite abelian extensions and generalized ideal class groups
In class field theory, the Takagi existence theorem states that for any number field ''K'' there is a one-to-one inclusion reversing correspond ...
in
class field theory
In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field.
Hilbert is credit ...
. The
Blancmange curve
In mathematics, the blancmange curve is a self-affine curve constructible by midpoint subdivision. It is also known as the Takagi curve, after Teiji Takagi who described it in 1901, or as the Takagi–Landsberg curve, a generalization of the cur ...
, the graph of a nowhere-differentiable but
uniformly continuous
In mathematics, a real function f of real numbers is said to be uniformly continuous if there is a positive real number \delta such that function values over any function domain interval of the size \delta are as close to each other as we want. In ...
function, is also called the Takagi curve after his work on it.
Biography
He was born in the rural area of the
Gifu Prefecture
is a prefecture of Japan located in the Chūbu region of Honshu. Gifu Prefecture has a population of 1,991,390 () and has a geographic area of . Gifu Prefecture borders Toyama Prefecture to the north; Ishikawa Prefecture to the northwest, F ...
,
Japan
Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north ...
. 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
Imperial University (later
Tokyo Imperial University
, abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...
), at that time the only university in Japan before the
Imperial University System was established on June 18, 1897. There he learned mathematics from such European classic texts as
Salmon
Salmon () is the common name for several list of commercially important fish species, commercially important species of euryhaline ray-finned fish from the family (biology), family Salmonidae, which are native to tributary, tributaries of the ...
's ''Algebra'' and
Weber's ''Lehrbuch der Algebra''. Aided by
Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many ...
, he then studied at
Göttingen
Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...
. Aside from his work in
algebraic number theory
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...
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''
at the
International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the Nevanlinna Prize (to be rename ...
in
Strasbourg
Strasbourg (, , ; german: Straßburg ; gsw, label=Bas Rhin Alsatian, Strossburi , gsw, label=Haut Rhin Alsatian, Strossburig ) is the prefecture and largest city of the Grand Est region of eastern France and the official seat of the Eu ...
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
Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent.
Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory, contributing lar ...
in 1922, and was again pointed out by
Carl Ludwig Siegel
Carl Ludwig Siegel (31 December 1896 – 4 April 1981) was a German mathematician specialising in analytic number theory. He is known for, amongst other things, his contributions to the Thue–Siegel–Roth theorem in Diophantine approximation, ...
, and at the same time by
Helmut Hasse
Helmut Hasse (; 25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of ''p''-adic numbers to local class field theory and ...
, who lectured in Kiel in 1923 on class field theory and presented Takagi's work in a lecture at the meeting of the
DMV in 1925 in
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
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the Nevanlinna Prize (to be rename ...
in
Zurich and in 1936 was a member of the selection committee for the first
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...
.
He was also instrumental during
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
in the development of Japanese encryption systems; see
Purple
Purple is any of a variety of colors with hue between red and blue. In the RGB color model used in computer and television screens, purples are produced by mixing red and blue light. In the RYB color model historically used by painters, pu ...
.
The
Autonne-Takagi factorization of complex symmetric matrices is named in his honour.
Family
*
Sigekatu Kuroda
was a Japanese mathematician who worked in number theory and mathematical logic.
In 1942 he became a professor at the newly founded Nagoya Imperial University, where he stayed for over twenty years. He is responsible for much of the effort in ...
- son-in-law. Mathematician.
*
S.-Y. Kuroda - grandson (son of Sigekatu Kuroda). Mathematician and Chomskyan linguist.
Bibliography
*
References
External links
*
*
Takagi Lecturesby the
Mathematical Society of Japan
The Mathematical Society of Japan (MSJ, ja, 日本数学会) is a learned society for mathematics in Japan.
In 1877, the organization was established as the ''Tokyo Sugaku Kaisha'' and was the first academic society in Japan. It was re-organized ...
Teiji Takagi: collected papers(2nd edition), edited by S. Iyanaga, K. Iwasawa, K. Kodaita and K. Yosida. Pp 376. DM188. 1990. (Springer) / CAMBRIDGE UNIVERSITY PRESS / The Mathematical Association 1991
{{DEFAULTSORT:Takagi, Teiji
People from Gifu Prefecture
People of the Empire of Japan
1875 births
1960 deaths
19th-century Japanese mathematicians
20th-century Japanese mathematicians
Number theorists
University of Tokyo faculty
University of Göttingen alumni
University of Tokyo alumni
Recipients of the Order of Culture