Abstract.
This article is a brief historical report on Teiji Takagi which was prepared at the commencement of ‘Takagi Lectures’ of The Mathematical Society of Japan. The first of its two purposes is to give some informations on the circumstances of education and research of mathematics in Japan surrounding Takagi who could finally established himself as the founder of the Japanese school of modern mathematics. The other is a brief overview on Takagi’s works of mathematics some of which are still attractive to and influential on especially ambitious students of mathematics. The author hopes that careful readers may find some hints for the questions how and why Takagi was able to establish his class field theory. At the end of this article the readers will find an English translation of the preface of his book Algebraic theory of numbers (in Japanese) which is the only thing that he left for us to see his total view over class field theory after the establishment of Artin’s reciprocity law.
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References
T. Takagi, (Thesis) Über die im Bereich der rationalen complexen Zahlen Abel’schen Zahlkörper, J. College of Science, Imperial Univ. of Tokyo, 19 (1903), 1–42; Takagi Teiji Collected Papers, 13–39.
T. Takagi, Über eine Theorie des relative Abel’schen Zahlkörpers, J. College of Science, Imperial Univ. of Tokyo, 41 (1920), 1–133; Berichtigung zu meiner Arbeit: Ueber eine Theorie des relative Abel’schen Zahlkörpers, ibid.; Takagi Teiji Collected Papers, 73–166, (167).
T. Takagi, Teiji Takagi Collected Papers, Second Enlarged Edition, Springer-Verlag Tokyo, 1990.
T. Takagi, Topics from the history of mathematics of the 19th century (in Japanese), Kyoritsusha, 1933, originally published in the Collection of the courses on mathematics, Kyoritsushuppansha, 1931; Augmented edn., Kawade Shobou, 1942; new edn., Kyoritsu Shuppan, 1970; Iwanami-Softcover Books, 939-1 with a commentary by M. Sugiura, Iwanami Shoten, Tokyo, 1995.
T. Takagi, A course on analysis (in Japanese), Iwanami-Shoten, 1938, originally published in the Collection of courses on Mathematics, Iwanami-Shoten, 1933-35; enlarged edn., 1943; revised third edn., Iwanami-Shoten, Tokyo, 1961.
T. Takagi, Algebraic theory of numbers (in Japanese), Iwanami-Shoten, 1948, originally published in the Collection of courses on Mathematics, Iwanami-shoten, 1934–35; second edn., Iwanami-Shoten, Tokyo, 1971.
S. Iyanaga, Memories of Professor Teiji Takagi, In: Class Field Theory—Its Centenary and Prospect, (ed. K. Miyake), Adv. Stud. Pure Math., 30, Math. Soc. Japan, Tokyo, 2001, pp. 1–11.
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Communicated by: Toshiyuki Kobayashi
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Miyake, K. Teiji Takagi, Founder of the Japanese School of Modern Mathematics. Jpn. J. Math. 2, 151–164 (2007). https://doi.org/10.1007/s11537-007-0649-8
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DOI: https://doi.org/10.1007/s11537-007-0649-8