Yutaka Taniyama. Japanese mathematician and teacher . Known for the Taniyama-Shimura conjecture, which was an important factor in proving Fermat’s Last Theorem .
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- 1 Biographical synthesis
- 1 Death
- 2 Publications
- 3 Sources
He was born on December from November of 1927 , he grew up in the small town of Kisai , about 50 km to the north of Tokyo . Her parents were Sahei, a doctor, and Kaku Taniyama. He had a large family with two older brothers and three older sisters, as well as a younger brother and a younger sister. Its Japanese name is: 谷 山 豊. It was meant to be Toyo Taniyama, but most people read it as Yutaka, a more common form, and he eventually came to use Yutaka himself.
He was a sickly boy and suffered from Tuberculosis , which caused him to miss high school for two years . After graduating from high school, he entered the University of Tokyo to study mathematics . During his undergraduate years, he read groups Theory of lies of Claude Chevalley and Foundations of algebraic geometry of André Weil and two other books of Weil curves and Abelian algebraic varieties. He attended conferences algebra of Masao Sugawaraand these encouraged him to become interested in the theory of numbers . He graduated in March of 1953 but, having lost years in school for illness , was considerably older than the other students who graduated that year.
He remained at the University of Tokyo as a ” special research student ” in the Department of Mathematics, although he did not have a thesis advisor, and later as an associate professor . In high school, he became interested in mathematics inspired by Teiji Takagi’s modern history of mathematics . There he developed a relationship of friendship with another student , Goro Shimura .
He became interested in algebraic number theory . He wrote Modern Theory of Numbers ( 1957 ) in Japanese , along with Goro Shimura. Although they thought about writing an English version , they lost enthusiasm and never had time to write it before Taniyama’s death . However, probably the reason in the 1957 preface :
It is difficult for us to say that the theory is presented in a completely satisfactory way. In any case, it can be said, we are allowed in the course of progress to climb to a certain height , in order to look back on our tracks, and then to have a vision of our destiny.
But above all, they were both fascinated by the study of modular forms, which are objects that exist in complex space and that are peculiar due to their level of symmetry .
Taniyama’s fame is mainly due to the two issues raised at the Symposium on Algebraic Number Theory held in Tokyo in 1955 (his meeting with Weil at this symposium would have a major influence on Taniyama’s work). There, he presented some problems that dealt with the relationship between modular shapes and elliptic curves. He had noticed some very peculiar similarities between the two types of entities. His observations led him to believe that each modular shape is related to some elliptic curve. Shimura later worked with Taniyama on this idea that modular shapes and elliptic curves were related, and this forms the basis of the Taniyama-Shimura conjecture:
Every elliptic curve defined on the rational field is a Jacobian factor of a field of modular functions. This conjecture proved to be an important part of Andrew Wiles’s proof of Fermat’s Last Theorem .
With an apparently bright future ahead, both in mathematics and in his private life (he was planning his marriage ), he committed suicide. In a note he left, he was very careful to describe exactly how far he had come in the calculus and linear algebra courses he had been teaching and to apologize to his colleagues for everything his death would entail. Regarding the reason that led him to kill himself, he explained:
Until yesterday, I had no definitive intention to commit suicide. … I don’t quite understand it myself, but it is not the result of a particular incident, or a specific issue.
A month later, the woman he was to marry also committed suicide.
He published the Jacobian paper varieties and number fields, and then “The L functions of the number fields” and “The zeta functions of the Abelian varieties . ” Apart from these two articles, his only other published article was “The distribution of 0 positive cycles in absolute classes of an algebraic variety with a field of finite constants”