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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 apologize 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.
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