Kiyoshi Ito
Encyclopedia
was a Japanese
mathematician
whose work is now called Itō calculus
. The basic concept of this calculus is the Itō integral, and among the most important results is Itō's lemma
. The Itō calculus facilitates mathematical understanding of random events
. His theory is widely applied in various fields, and is perhaps best known for its use in financial mathematics.
Although the standard Hepburn romanization
of his name is Itō, the spellings Itô (as in Kunrei-shiki romanization) or Ito are often seen in the West
as well.
(Inabe
) in Mie Prefecture
on the main island of Honshū
. After high school he studied mathematics
at the Imperial University Tokyo, from which he graduated at the age of 23. After that he started to work for the national statistical office, where he published two of his seminal works on probability
and stochastic processes.
In 1945, he was awarded a Ph.D.
for his work. Seven years later he became a professor at the University of Kyoto, where he remained until his retirement in 1979. In addition, he held professorships at University of Aarhus
from 1966 to 1969, and Cornell University
from 1969 to 1975. Itō was awarded the inaugural Carl Friedrich Gauss Prize
in 2006 for his lifetime achievements. As he was unable to travel to Madrid
, his youngest daughter, Junko Itō
(a professor of Linguistics
at the University of California, Santa Cruz
, specializing in phonology
), received the Gauss Prize from the King of Spain on his behalf.
In October 2008, Itō was honored with Japan's Order of Culture
; and an awards ceremony for the Order of Culture was held at the Imperial Palace.
Itō wrote in Chinese
, German
, French
and English
.
Itō's formula was celebrated at a financial conference many years after he developed it. As a pure mathematician, Itō was bemused at all the fuss and claimed not to remember deriving the formula in the first place.
Itō died on November 10, 2008 in Kyoto, Japan. He was 93.
Japanese people
The are an ethnic group originating in the Japanese archipelago and are the predominant ethnic group of Japan. Worldwide, approximately 130 million people are of Japanese descent; of these, approximately 127 million are residents of Japan. People of Japanese ancestry who live in other countries...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
whose work is now called Itō calculus
Ito calculus
Itō calculus, named after Kiyoshi Itō, extends the methods of calculus to stochastic processes such as Brownian motion . It has important applications in mathematical finance and stochastic differential equations....
. The basic concept of this calculus is the Itō integral, and among the most important results is Itō's lemma
Ito's lemma
In mathematics, Itō's lemma is used in Itō stochastic calculus to find the differential of a function of a particular type of stochastic process. It is named after its discoverer, Kiyoshi Itō...
. The Itō calculus facilitates mathematical understanding of random events
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
. His theory is widely applied in various fields, and is perhaps best known for its use in financial mathematics.
Although the standard Hepburn romanization
Hepburn romanization
The is named after James Curtis Hepburn, who used it to transcribe the sounds of the Japanese language into the Latin alphabet in the third edition of his Japanese–English dictionary, published in 1887. The system was originally proposed by the in 1885...
of his name is Itō, the spellings Itô (as in Kunrei-shiki romanization) or Ito are often seen in the West
Western world
The Western world, also known as the West and the Occident , is a term referring to the countries of Western Europe , the countries of the Americas, as well all countries of Northern and Central Europe, Australia and New Zealand...
as well.
Biography
Itō was born in HokuseiHokusei, Mie
was a town located in Inabe District, Mie, Japan.On December 1, 2003 Hokusei was merged with the towns of Inabe, Daian and Fujiwara, all from Inabe District, to form the new city of Inabe....
(Inabe
Inabe, Mie
, is a city located in the northernmost tip of Mie Prefecture in Japan along the border with Gifu and Shiga prefectures. The city was formed on December 1, 2003 from the merger of the towns of Inabe, Hokusei, Daian and Fujiwara, all from Inabe District....
) in Mie Prefecture
Mie Prefecture
is a prefecture of Japan which is part of the Kansai regions on Honshū island. The capital is the city of Tsu.- History :Until the Meiji Restoration, Mie prefecture was known as Ise Province and Iga Province....
on the main island of Honshū
Honshu
is the largest island of Japan. The nation's main island, it is south of Hokkaido across the Tsugaru Strait, north of Shikoku across the Inland Sea, and northeast of Kyushu across the Kanmon Strait...
. After high school he studied mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at the Imperial University Tokyo, from which he graduated at the age of 23. After that he started to work for the national statistical office, where he published two of his seminal works on probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
and stochastic processes.
In 1945, he was awarded a Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
for his work. Seven years later he became a professor at the University of Kyoto, where he remained until his retirement in 1979. In addition, he held professorships at University of Aarhus
University of Aarhus
Aarhus University , located in the city of Aarhus, Denmark, is Denmark's second oldest and second largest university...
from 1966 to 1969, and Cornell University
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
from 1969 to 1975. Itō was awarded the inaugural Carl Friedrich Gauss Prize
Carl Friedrich Gauss Prize
The Carl Friedrich Gauss Prize for Applications of Mathematics is a mathematics award, granted jointly by the International Mathematical Union and the German Mathematical Society for "outstanding mathematical contributions that have found significant applications outside of mathematics". The award...
in 2006 for his lifetime achievements. As he was unable to travel to Madrid
Madrid
Madrid is the capital and largest city of Spain. The population of the city is roughly 3.3 million and the entire population of the Madrid metropolitan area is calculated to be 6.271 million. It is the third largest city in the European Union, after London and Berlin, and its metropolitan...
, his youngest daughter, Junko Itō
Junko Itō
Junko Itō is a professor of linguistics at the University of California, Santa Cruz. She is the daughter of mathematician Kiyoshi Itō.Itō focuses on phonology and morphology. She is primarily known for her research into syllable structure within an optimality theoretic framework. Her work has...
(a professor of Linguistics
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
at the University of California, Santa Cruz
University of California, Santa Cruz
The University of California, Santa Cruz, also known as UC Santa Cruz or UCSC, is a public, collegiate university; one of ten campuses in the University of California...
, specializing in phonology
Phonology
Phonology is, broadly speaking, the subdiscipline of linguistics concerned with the sounds of language. That is, it is the systematic use of sound to encode meaning in any spoken human language, or the field of linguistics studying this use...
), received the Gauss Prize from the King of Spain on his behalf.
In October 2008, Itō was honored with Japan's Order of Culture
Order of Culture
The is a Japanese order, established on February 11, 1937. The order has one class only, and may be awarded to men and women for contributions to Japan's art, literature or culture; recipients of the order also receive an annuity for life...
; and an awards ceremony for the Order of Culture was held at the Imperial Palace.
Itō wrote in Chinese
Chinese language
The Chinese language is a language or language family consisting of varieties which are mutually intelligible to varying degrees. Originally the indigenous languages spoken by the Han Chinese in China, it forms one of the branches of Sino-Tibetan family of languages...
, German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
, French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...
and English
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...
.
Itō's formula was celebrated at a financial conference many years after he developed it. As a pure mathematician, Itō was bemused at all the fuss and claimed not to remember deriving the formula in the first place.
Itō died on November 10, 2008 in Kyoto, Japan. He was 93.
External links
- Bibliography of Kiyoshi Itō
- Kiyoshi Itō at Research Institute for Mathematical SciencesResearch Institute for Mathematical SciencesThe is a research institute attached to Kyoto University, hosting researchers in the mathematical sciences from all over Japan. The institute is often abbreviated as RIMS...