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 corresponde ...

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 cre ...

. 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, ...

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 n ...

. 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 commercially important species of euryhaline ray-finned fish from the family Salmonidae, which are native to tributaries of the North Atlantic (genus '' Salmo'') and North Pacific (genus '' Onco ...

's ''Algebra'' and

Weber Weber (, or ; German: ) is a surname of German origin, derived from the noun meaning " weaver". In some cases, following migration to English-speaking countries, it has been anglicised to the English surname 'Webber' or even 'Weaver'. Notable pe ...

's ''Lehrbuch der Algebra''. Aided by Hilbert, he then studied at

Göttingen Göttingen (, , ; nds, Chöttingen) is a university city in Lower Saxony, central Germany, the capital of the eponymous district. The River Leine runs through it. At the end of 2019, the population was 118,911. General information The ori ...

. 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 o ...

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 rena ...

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 ...

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 l ...

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

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 h ...

. 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 World War II by country, vast majority of the world's countries—including all of the great power ...

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 ...

. 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 , aka S.-Y. Kuroda, was Professor Emeritus and Research Professor of Linguistics at the University of California, San Diego. Although a pioneer in the application of Chomskyan generative syntax to the Japanese language, he is known for the br ...

- grandson (son of Sigekatu Kuroda). Mathematician and Chomskyan linguist.

Bibliography

References

External links

* *
Takagi Lectures
by 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