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was a Japanese
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
who worked in
algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...
.


Biography

Tannaka was born in
Matsuyama 270px, Matsuyama City Hall 270px, Ehime Prefectural Capital Building is the capital city of Ehime Prefecture, on the island of Shikoku, in Japan and is also Shikoku's largest city. , the city had an estimated population of 505,948 in 243,541 h ...
,
Ehime Prefecture is a Prefectures of Japan, prefecture of Japan located on the island of Shikoku. Ehime Prefecture has a population of 1,334,841 and a geographic area of 5,676 km2 (2,191 sq mi). Ehime Prefecture borders Kagawa Prefecture to the northeast, Toku ...
on December 27, 1908. After receiving a Bachelor of Science in mathematics from Tohoku Imperial University in 1932, he was appointed a lecturer in the university in 1934 and received a
Doctor of Science A Doctor of Science (; most commonly abbreviated DSc or ScD) is a science doctorate awarded in a number of countries throughout the world. Africa Algeria and Morocco In Algeria, Morocco, Libya and Tunisia, all universities accredited by the s ...
degree from the university in 1941. He was promoted to assistant professor in 1942 and full professor in 1945. Tannaka was a member at the
Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...
from September 1955 to April 1957. Tannaka retired from Tohoku University in 1972, after which he served as a full professor at
Tohoku Gakuin University is a private university in Sendai, Miyagi, Sendai, Miyagi Prefecture, Japan. It was founded in 1886 under the influence of the Reformed Church in the United States, German Reformed Church missionaries. Miyagi Gakuin Women's University is its sist ...
until 1981. Tannaka was an editor of the Tohoku Mathematical Journal and a member of the board of directors of the
Mathematical Society of Japan The Mathematical Society of Japan (MSJ, ) is a learned society for mathematics in Japan. In 1877, the organization was established as the ''Tokyo Sugaku Kaisha'' and was the first academic society in Japan. It was re-organized and re-established i ...
. Tannaka was also in charge of the "Mathematics Chat" article series in the monthly ' magazine from 1960 onwards. Tannaka died in Tokyo on October 25, 1986.


Research

Tannaka is known for developing the theory of
Tannaka–Krein duality In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. It is a natural extension of Pontryagin duality, between compact and discrete commutative topologi ...
, which generalizes
Pontryagin duality In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative group of complex numbers of modulus one), ...
to
noncommutative In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a p ...
compact group In mathematics, a compact (topological) group is a topological group whose topology realizes it as a compact topological space (when an element of the group is operated on, the result is also within the group). Compact groups are a natural gen ...
s and led to the development of Tannakian formalism.


Awards

Tannaka was a recipient of the Order of the Rising Sun (3rd Class) in 1980.


See also

* Tannaka–Artin problem


References

{{DEFAULTSORT:Tannaka, Tadao 20th-century Japanese mathematicians 1908 births 1986 deaths Academic staff of Tohoku University Tohoku University alumni Institute for Advanced Study visiting scholars Academic staff of Tohoku Gakuin University People from Matsuyama, Ehime Scientists from Ehime Prefecture Recipients of the Order of the Rising Sun, 3rd class