Yutaka Taniyama (谷山 豊, November 12, 1927 - November 17, 1958) was a Japanese mathematician. He is known for his Taniyama-Shimura conjecture.
Taniyama was born in Kisai, Saitama (north of Tokyo), Japan. His first name was actually Toyo, but many people misinterpreted his name as Yutaka, and he came to accept that name.
In high school, he became interested in mathematics inspired by Teiji Takagi's modern history of mathematics.
Taniyama studied mathematics at the University of Tokyo after the end of World War II, and here he developed a friendship with another student named Goro Shimura. He graduated in 1953. He remained there as a 'special research student', then as an associate professor.
His interests were in algebraic number theory. He wrote Modern number theory (1957) in Japanese, jointly with Goro Shimura. Although they planned an English language version, they lost enthusiasm and never found the time to write it before Taniyama's death.
But before all, they were fascinated with the study of modular forms, which are objects that exist in complex space that are peculiar because of their inordinate level of symmetry.
Taniyama's fame is mainly due to two problems posed by him at the symposium on Algebraic Number Theory held in Tokyo in 1955 (His meeting with Weil at this symposium was to have a major influence on Taniyama's work). There he presented some problems that dealt with the relationship between modular forms and elliptic curves. He had noticed some extremely peculiar similarities between the two types of entities. Taniyama's observations led him to believe that every modular form is somehow matched up with some elliptic curve. Shimura later worked with Taniyama on this idea that modular forms and elliptic curves are linked and this form the basis of the Taniyama-Shimura conjecture:
Every elliptic curve defined over the rational field is a factor of the jacobian of a modular function field.
This conjecture proved to be a major factor in the proof of Fermat's Last Theorem by Wiles.
With seemingly a great future in front of him, both in mathematics and his life (he was planning marriage) he took his own life. In a note he left he took great care to describe exactly where he had reached in the calculus and linear algebra courses he was teaching and to apologise to his colleagues for the trouble his death would cause them. As to the reason for taking his life he says:
Until yesterday I had no definite intention of killing myself. ... I don't quite understand it myself, but it is not the result of a particular incident, nor of a specific matter.
About a month later the girl who he was planning to marry also committed suicide.