Kenkichi Iwasawa ( ''Iwasawa Kenkichi'', September 11, 1917 – October 26, 1998) 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, structure, space, models, and change. History On ...

who is known for his influence on algebraic number theory.

Biography

Iwasawa was born in Shinshuku-mura, a town near Kiryū, in

Gunma Prefecture is a Prefectures of Japan, prefecture of Japan located in the Kantō region of Honshu. Gunma Prefecture has a population of 1,937,626 (1 October 2019) and has a geographic area of 6,362 Square kilometre, km2 (2,456 Square mile, sq mi). Gunma P ...

. He attended

elementary school A primary school (in Ireland, the United Kingdom, Australia, Trinidad and Tobago, Jamaica, and South Africa), junior school (in Australia), elementary school or grade school (in North America and the Philippines) is a school for primary ed ...

there, but later moved to

Tokyo Tokyo (; ja, 東京, , ), officially the Tokyo Metropolis ( ja, 東京都, label=none, ), is the capital and largest city of Japan. Formerly known as Edo, its metropolitan area () is the most populous in the world, with an estimated 37.468 ...

to attend Musashi High School. From 1937 to 1940 Iwasawa studied as an

undergraduate Undergraduate education is education conducted after secondary education and before postgraduate education. It typically includes all postsecondary programs up to the level of a bachelor's degree. For example, in the United States, an entry-lev ...

Tokyo Imperial University , abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...

, after which he entered

graduate school Postgraduate or graduate education refers to Academic degree, academic or professional degrees, certificates, diplomas, or other qualifications pursued by higher education, post-secondary students who have earned an Undergraduate education, un ...

at University of Tokyo and became an assistant in the Department of Mathematics. In 1945 he was awarded a

Doctor of Science degree Doctor of Science ( la, links=no, Scientiae Doctor), usually abbreviated Sc.D., D.Sc., S.D., or D.S., is an academic research degree awarded in a number of countries throughout the world. In some countries, "Doctor of Science" is the degree used f ...

. However, this same year Iwasawa became sick with

pleurisy Pleurisy, also known as pleuritis, is inflammation of the membranes that surround the lungs and line the chest cavity ( pleurae). This can result in a sharp chest pain while breathing. Occasionally the pain may be a constant dull ache. Other sy ...

, and was unable to return to his position at the university until April 1947. From 1949 to 1955 he worked as assistant professor at Tokyo University. In 1950, Iwasawa was invited to

Cambridge, Massachusetts Cambridge ( ) is a city in Middlesex County, Massachusetts, United States. As part of the Boston metropolitan area, the cities population of the 2020 U.S. census was 118,403, making it the fourth most populous city in the state, behind Boston, ...

to give a lecture at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

on his method to study

Dedekind zeta functions In mathematics, the Dedekind zeta function of an algebraic number field ''K'', generally denoted ζ''K''(''s''), is a generalization of the Riemann zeta function (which is obtained in the case where ''K'' is the field of rational numbers Q). It ca ...

using integration over ideles and duality of adeles; this method was also independently obtained by

John Tate John Tate may refer to: * John Tate (mathematician) (1925–2019), American mathematician * John Torrence Tate Sr. (1889–1950), American physicist * John Tate (Australian politician) (1895–1977) * John Tate (actor) (1915–1979), Australian act ...

and is sometimes called Iwasawa–Tate theory. Iwasawa spent the next two years at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...

, and in Spring of 1952 was offered a job at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

, where he worked until 1967. From 1967 until his retirement in 1986, Iwasawa served as Professor of Mathematics at

. He returned to Tokyo with his wife in 1987. Among Iwasawa's most famous students are Robert F. Coleman, Bruce Ferrero, Ralph Greenberg,

Gustave Solomon Gustave Solomon (October 27, 1930 – January 31, 1996) was an American mathematician and electrical engineer who was one of the founders of the algebraic theory of error detection and correction. Career Solomon completed his Ph.D. in mathema ...

, Larry Washington, and Eugene M. Luks.

Research

Iwasawa is known for introducing what is now called

Iwasawa theory In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by (), as part of the theory of cyclotomic fields. In th ...

, which developed from researches on

cyclotomic field In number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to , the field of rational numbers. Cyclotomic fields played a crucial role in the development of modern algebra and number theory because of ...

s from the later 1950s. Before that he worked on

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...

s and

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...

s, introducing the general

Iwasawa decomposition In mathematics, the Iwasawa decomposition (aka KAN from its expression) of a semisimple Lie group generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix (QR decomposition, a cons ...

List of books available in English

*''Lectures on p-adic L-functions'' / by Kenkichi Iwasawa (1972) *''Local class field theory'' / Kenkichi Iwasawa (1986) *''Algebraic functions'' / Kenkichi Iwasawa ; translated by Goro Kato (1993) *

References

Sources

* *

External links