Kiyosi Itô

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Template:Short description Template:Use dmy dates Template:Infobox scientist Template:Nihongo was a Japanese mathematician who made fundamental contributions to probability theory, in particular, the theory of stochastic processes. He invented the concept of stochastic integral and stochastic differential equation, and is known as the founder of so-called Itô calculus. He also pioneered the connections between stochastic calculus and differential geometry, known as stochastic differential geometry. He was invited for the International Congress of Mathematicians in Stockholm in 1962.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> So much were Itô's results useful to financial mathematics that he was sometimes called "the most famous Japanese in Wall Street".<ref name=jpntimes/>

Itô was a member of the faculty at University of Kyoto for most of his career and eventually became the director of their Research Institute for Mathematical Sciences. But he also spent multi-year stints at several foreign institutions, the longest of which took place at Cornell University.

Overview

Itô (right) with Issei Shiraishi in 1935. Shiraishi later became a mathematician.

Itô pioneered the theory of stochastic integration and stochastic differential equations, now known as Itô calculus. Its basic concept is the Itô integral, and among the most important results is a change of variable formula known as Itô's lemma (also known as the Itô formula). Itô also made contributions to the study of diffusion processes on manifolds, known as stochastic differential geometry.

Itô calculus is a method used in the mathematical study of random events and is applied in various fields, and is perhaps best known for its use in mathematical finance. In particular, the Itô's lemma's best known application is in the derivation of the Black–Scholes equation for option values.<ref name=jpntimes/>

Itô's methods are also used in other fields, including biology and physics.<ref name=jpntimes/> His results have been applied to population models, white noise, chemical reactions, and quantum physics, in addition to uses in various mathematical subjects such as differential geometry, partial differential equations, complex analysis, and harmonic analysis and potential theory.<ref name="protter">Template:Cite journal</ref>

Fellow mathematician Daniel W. Stroock noted that "People all over realized that what Ito had done explained things that were unexplainable before."<ref name=lohr/> Economist Robert C. Merton stated that Itô's work had provided him "a very useful tool" in his own prize-winning work.<ref name=lohr/>

Although the standard Hepburn romanization of his name is Kiyoshi Itō, he used the spelling Kiyosi Itô (Kunrei-shiki romanization). The alternative spellings Itoh and Ito are also sometimes seen in the Western world.

Itô was married with three daughters.<ref name=lohr/>

Biography

Kiyosi Itô (right) with his brother Seizō Itō in 1937. Seizō later became a mathematician.

Itô was born on 7 September 1915 in a farming area located west of Nagoya, Japan,<ref name=lohr/> that being the town of Hokusei-cho in Mie Prefecture.<ref name="times-obit">Template:Cite news</ref> He excelled in his studies as a youth.<ref name=lohr/> Admitted to the Imperial University of Tokyo, he studied mathematics and became interested in the underdeveloped field of probability theory, graduating from there in 1938,<ref name="times-obit"/> with his degree in mathematics being granted by the university's Faculty of Science.<ref name="pastdirs-bio"/>

Itô at the Cabinet Statistics Bureau in 1940

From 1939 to 1943 he worked as a Statistical Officer with the Statistics Bureau of the Cabinet Secretariat,<ref name="pastdirs-bio"/> There he was given rein by management to continue his research.<ref name="times-obit"/> His breakthrough paper, "On Stochastic Processes", appeared in 1942.<ref name="cornell-luminaries"/> In 1943, he was appointed an assistant professor at Nagoya Imperial University,<ref name="times-obit"/> where he benefited from discussions with the mathematicians Kōsaku Yosida and Shizuo Kakutani.<ref name="ito-fw"/> From investigations done during this period he published a series of articles in which he defined the stochastic integral and laid the foundations of the Itō calculus. Meanwhile, he received his Doctor of Science degree from the Imperial University of Tokyo in 1945.<ref name="pastdirs-bio"/>

These works were published despite the difficulties of life in Japan during World War II, including problems accessing libraries and especially the loss of contact with Western mathematicians and the lack of awareness of results from them.<ref name="protter"/><ref name="times-obit"/> For instance, the only other Japanese mathematician actively interested in Itô's work during the war, Gisiro Maruyama, read a mimeographed copy of a paper while in a military camp.<ref name="ito-fw"/> Scholarly activity during the Occupation of Japan had its difficulties; in one case, paper shortages were such that a lengthy Itô article could not be published in a Japanese journal and he had to arrange for an American journal to publish it instead.<ref name="ito-fw"/> Ito later referred to his time at Nagoya as having been during "the dark age of World War II and its aftermath."<ref name="ito-fw">Template:Cite book Subsequently reproduced in Template:Cite book </ref>

Itô, 1954

After this period he continued to develop his ideas on stochastic analysis with many important papers on the topic. In 1952, he became a professor at the University of Kyoto.<ref name=jpntimes/> His most well-known text, Probability Theory, appeared in 1953.<ref name="cornell-luminaries"/> Itô remained affiliated with Kyoto until his retirement in 1979. <ref name="times-obit"/> However, beginning in the 1950s, Itô spent long periods of time away from Japan.<ref name=lohr/> He was at the Institute for Advanced Study from 1954 to 1956 while on a Fulbright fellowship;<ref name="pastdirs-bio"/> while there he worked closely with William Feller and Henry McKean who were at nearby Princeton University.<ref name="ito-fw"/> He was a professor at Stanford University from 1961 to 1964 and a professor at Aarhus University from 1966 to 1969.<ref name="pastdirs-bio"/>

Then in 1969 Itô arrived at Cornell University, where he was a professor of mathematics for six years until 1975.<ref name="cornell-luminaries">Template:Cite news</ref> This was his longest stint outside Japan.<ref name="pastdirs-bio">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Among the courses he taught at Cornell was one in Higher Calculus.<ref>Template:Cite book</ref>

Itô wrote not only in Japanese but also in Chinese, German, French and English.<ref name=lohr/> However, his ability to converse in foreign languages was a different matter, and by his own admission his accent made him largely incomprehensible to Americans.<ref name=lohr>Template:Citation</ref>

When Itô left Cornell and returned to the University of Kyoto, he served as director of their Research Institute for Mathematical Sciences.<ref name=jpntimes/> After his retirement, he became professor emeritus at Kyoto University.<ref name=jpntimes/> He also had a post-retirement position as a professor at the private Gakushuin University for several years,<ref name="pastdirs-bio"/> a common practice among higher-ranking Japanese academics.<ref name="times-obit"/>

Itô c. 1991

Itô was recipient of the Wolf Prize and the Kyoto Prize.<ref name=lohr/> He was a member of the Japan Academy,<ref name="pastdirs-bio"/> and also a foreign member of the Académie des sciences in France and the National Academy of Sciences in the United States. <ref name=lohr/>

In his later years, Itô struggled with poor health.<ref name="times-obit"/> Itô was awarded the inaugural Gauss Prize in 2006 by the International Mathematical Union for his lifetime achievements.<ref name=jpntimes/> As he due to his health was unable to travel to Madrid, his youngest daughter, Junko Ito, received the Gauss Prize from King Juan Carlos I on his behalf.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }} See also {{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Later, IMU President Sir John Macleod Ball personally presented the medal to Itô at a special ceremony held in Kyoto.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> In October 2008, Itô was honored with Japan's Order of Culture, and an awards ceremony for the Order of Culture was held at the Imperial Palace.<ref>Template:Cite news</ref>

Itô died on November 10, 2008, in Kyoto, Japan, at age 93, of respiratory failure .<ref name=jpntimes>Template:Cite news</ref>

Selected publications

References

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See also

Further reading

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