**Kenkichi Iwasawa** was a Japanese mathematician who worked in algebraic number theory.

- Takagi had retired in 1936, the year before Iwasawa began his studies, but his students Iyanaga and Suetuna were bringing to the university many ideas which they had developed during studies with the leading experts in Europe.
- Iwasawa graduated in 1940 and remained at Tokyo University to undertake graduate studies.
- Clearly Iwasawa found this a most difficult period in which to try to complete work for his doctorate.
- For a glimpse of the research that Iwasawa undertook at this time we look briefly at the paper On some types of topological groups which he published in the Annals of Mathematics in 1949.
- Iwasawa's results are related to Hilbert's fifth problem which asks whether any locally Euclidean topological groups is necessarily a Lie group.
- In his 1949 paper Iwasawa gives what is now known as the 'Iwasawa decomposition' of a real semisimple Lie group.
- In 1950 Iwasawa was invited to give an address at the International Congress of Mathematicians in Cambridge, Massachusetts.
- Artin was at the Institute during Iwasawa's two years there and he was one of the main factors in changing the direction of Iwasawa's research to algebraic number theory.
- In 1952 Iwasawa published Theory of algebraic functions in Japanese.
- Iwasawa then studies valuations, fields of algebraic functions giving definitions of prime divisors, ideles, valuation vectors and genus.
- It was Iwasawa's intention to return to Japan in 1952 after his visit to the Institute for Advanced Study but when he received the offer of a post of assistant professor at the Massachusetts Institute of Technology he decided to accept it.
- a general method in arithmetical algebraic geometry, known today as Iwasawa theory, whose central goal is to seek analogues for algebraic varieties defined over number field of the techniques which have been so successfully applied to varieties defined over finite fields by H Hasse, A Weil, B Dwork, A Grothendieck, P Deligne, and others.
- Iwasawa first lectured on his revolutionary ideas at the meeting of the American Mathematical Society in Seattle, Washington in 1956.
- The ideas were taken up immediately by Serre who saw their great potential and gave lectures to the Seminaire Bourbaki in Paris on Iwasawa theory.
- Iwasawa himself produced a series of deep papers throughout the 1960s which pushed his ideas much further.
- In 1967 Iwasawa left MIT when he was offered the Henry Burchard Fine Chair of Mathematics at Princeton and it was not long after he arrived there that he took on Greenberg as a research student.
- Professor Iwasawa usually came to the afternoon teas.
- In the late 1960s Iwasawa made a conjecture for algebraic number fields which, in some sense, was the analogue of the relationship which Weil had found between the zeta function and the divisor class group of an algebraic function field.
- Iwasawa remained as Henry Burchard Fine Professor of mathematics at Princeton until he retired in 1986.
- Iwasawa was much honoured for his achievements.
- today it is no exaggeration to say that Iwasawa's ideas have played a pivotal role in many of the finest achievements of modern arithmetical algebraic geometry on such questions as the conjecture of B Birch and H Swinnerton-Dyer on elliptic curve; the conjecture of B Birch, J Tate, and S Lichtenbaum on the orders of the K-groups of the rings of integers of number fields; and the work of A Wiles on the modularity of elliptic curves and Fermat's Last Theorem.

Born 11 September 1917, Shinshuku-mura (near Kiryu), Gumma Prefecture, Japan. Died 26 October 1998, Tokyo, Japan.

View full biography at MacTutor

Origin Japan

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive