Takagi Teiji

Takagi Teiji

Takagi Teiji ( Japanese 高木 貞 治 ; born April 21, 1875 in the village of Kazuya near Gifu ; † February 19, 1960 in Tokyo ) was a Japanese number theorist .

Life

Takagi grew up in the country and showed signs of mathematical talent at an early age. In 1894 he began his studies at the Imperial University (at that time the only university in Japan), using primarily foreign textbooks, in particular Heinrich Weber's algebra . After graduating in 1897, he was selected as one of twelve students to study abroad. He studied in Berlin with Frobenius , Fuchs and Schwarz . After reading the recently published "number report" by David Hilbert , which summarized and promoted the knowledge of algebraic number theory at the time, he decided to continue studying with Hilbert in Göttingen (from 1900). Hilbert, however, turned to completely different areas after writing the number report (basics of geometry, integral equations).

In 1901 Takagi returned to Japan and became an assistant professor at his alma mater, which was now called Tokyo University . He received his doctorate in 1903 with the number theoretical investigations undertaken in Göttingen (his doctoral supervisor was Hilbert), in which he proved, among other things, a conjecture by Leopold Kronecker ("Kronecker's youthful dream") about Abelian extensions of imaginary quadratic number fields. In 1904 he was given a full professorship in Tokyo, which he held until his retirement in 1936. From 1904 he began to write a number of textbooks that were still missing in Japan at that time.

During the First World War he worked largely in isolation and developed his existential theorem of class field theory , building on the work of Heinrich Weber. He lectured on this at the International Congress of Mathematicians in Strasbourg in 1920, although he found hardly any response, since algebraic number theory was mainly practiced in Germany at that time and German mathematicians were excluded from the congress. Takagi published his theory in the Tokyo University magazine that same year. Its importance was only recognized by Emil Artin in 1922, who in turn was referred to Takagi's work by Carl Ludwig Siegel (Takagi had sent Siegel his work and he recognized its importance), and at the same time by Helmut Hasse , who lectured in Kiel in 1923 held on class field theory and presented Takagi's work in a lecture at the meeting of the German Mathematicians Association (DMV) in Gdansk in 1925 and in his class field report in the annual report of the DMV 1926. Takagi was then internationally recognized. In 1932 he was Vice President of the International Congress of Mathematicians in Zurich and in 1936 in the selection committee for the first Fields Medal . During the Second World War he worked on Japanese encryption systems ("Purple").

Takagi had been married since 1902 and had three sons and five daughters.

He is credited with connecting Japan to modern mathematics at the beginning of the 20th century through his research and teaching. He wrote a calculus textbook that was widely and widely used in Japan, and he wrote a book on the history of mathematics in the 19th century. He was awarded the Order of Culture in 1940 .

Shōkichi Iyanaga and Kenjiro Shoda are among his students .

Fonts

• "Collected Papers", Springer 1990 (With the biography of Iyanaga), ISBN 3-540-70057-9
• "About a theory of the Relative-Abelian number field", Journal College of Science Imperial University of Tokyo, Vol. 41, 1920, pp. 1-133
• "About the reciprocity law in any algebraic number field", J. College Science Imp.Univ.Tokio, Vol. 44, 1922, pp. 1-50
• "Algebraic Number Theory" 1948

literature

• Benjamin H. Yandell: The honors class. Hilbert's problems and their solvers. AK Peters, Natick MA 2001

Web links

Commons : Teiji Takagi  - collection of images, videos and audio files

• John J. O'Connor, Edmund F. Robertson :  Takagi Teiji. In: MacTutor History of Mathematics archive .
• Takagi theory of the circular body , Crelles Journal Vol. 157, 1927

Japanese name: As is common in Japan, the family name comes before the first name in this article . Thus Takagi is the family name, Teiji the first name.