Heisuke Hironaka: Difference between revisions

{{Short description|Japanese mathematician (born 1931)}}

{{Use mdy dates|date=March 2014}}

| birth_date        = {{birth date and age|1931|04|09}}

| birth_place      = Yuu-chō, Kuga-Gun, [[Yamaguchi, Yamaguchi|Yamaguchi]], [[Japan]]<br />(modern-day [[Iwakuni, Yamaguchi]], [[Japan]])

| death_date        =  

| death_place      =  

| field            = [[Mathematics]]

| doctoral_students = José Manuel Aroca Hernández-Ros<br />Charles Barton, III<br />[[Dave Bayer]]<br />Bruce Bennett<br />Max Benson<br />[[Jacob E. Goodman]]<br />[[William Haboush]]<br />Jerome Hoffman<br />Audun Holme<br />Monique Lejeune-Jalabert<br />Takehiko Miyata<br />Loren Olson<br />[[Mary Schaps]]<br />Andrew Schwartz<br />{{interlanguage link|Mark Spivakovsky|de}}<br />[[Allen Tannenbaum]]<br />[[Bernard Teissier]]<br />Philip Wagreich<br />Boris Youssin

| spouse            = [[Wakako Hironaka]] (née Kimoto)

Hironaka was born on April 9, 1931 in [[Yamaguchi (city)|Yamaguchi]], Japan. He was inspired to study mathematics after a visiting [[Hiroshima University]] mathematics professor gave a lecture at his junior high school. Hironaka applied to the undergraduate program at Hiroshima University, but was unsuccessful. However, the following year, he was accepted into [[Kyoto University]] to study physics, entering in 1949 and receiving his Bachelor of Science and Master of Science from the university in 1954 and 1956. Hironaka initially studied physics, chemistry, and biology, but his third year as an undergraduate, he chose to move to taking courses in mathematics.<ref name=":1">{{Cite web |title=Heisuke Hironaka - Biography |url=https://mathshistory.st-andrews.ac.uk/Biographies/Hironaka/ |access-date=2023-12-01 |website=Maths History |language=en}}</ref>  

The same year, Hironaka was invited to a seminar group led by [[Yasuo Akizuki]], who would have a major influence on Hironaka's mathematical development. The group, informally known as the Akizuki School, discussed cutting-edge research developments including the [[resolution of singularities]] problem for which Hironaka later received the Fields Medal.<ref name=":2">{{Cite journal |last=Jackson |first=Allyn |date=October 2005 |title=Interview with Heisuke Hironaka |url=https://www.ams.org/notices/200509/fea-hironaka.pdf |journal=[[Notices of the American Mathematical Society]] |volume=52 |issue=9 |pages=1010–1019}}</ref> Hironaka has described his interest in this problem as having the logic and mystery of "a boy falling in love with a girl."<ref name=":3">{{Cite web |last=Harvard Magazine |first=Harvard Magazine |date=May 25, 2011 |title=Meet the 2011 Centennial Medalists |url=https://www.harvardmagazine.com/2011/05/centennial-medalists |url-status=live |archive-url=https://archive.today/20231201221551/https://www.harvardmagazine.com/2011/05/centennial-medalists |archive-date=December 1, 2023 |access-date=December 1, 2023 |website=Harvard Magazine}}</ref> In 1956, Akizuki invited then Harvard professor [[Oscar Zariski]] to Kyoto University. Hironaka took the opportunity to present his own research to Zariski, who suggested that Hironaka move to [[Harvard University]] to continue his studies.<ref name=":1" />

In 1957, Hironaka moved to the United States to attend Harvard University as a doctoral student under the direction of Zariski.<ref>{{cite web |title=GSAS ALUMNI |url=http://www.gsas.harvard.edu/alumni/centennial_medal_2011.php |url-status=dead |archive-url=https://web.archive.org/web/20120212092957/http://www.gsas.harvard.edu/alumni/centennial_medal_2011.php |archive-date=February 12, 2012 |access-date=March 10, 2014 |publisher=[[Harvard University]] |df=mdy-all}}</ref> Hironaka's [[abstract algebra|algebra]] background, developed under Akizuki, allowed him to bring fresh insights into mathematics discussions in Harvard, which placed a greater emphasis on geometric perspectives. In 1958–1959, [[Alexander Grothendieck]] visited Harvard University and was another important influence on Hironaka, inviting him to the [[Institut des Hautes Études Scientifiques|Institut des Hautes Études Scientifique]] (IHES) in Paris.<ref name=":2" />  

Returning to Harvard in 1960, Hironaka received his [[Doctor of Philosophy|PhD]] for his thesis ''On the Theory of Birational Blowing-up.''<ref name=":4">{{Cite web |date=1960 |title=On the theory of birational blowing-up |url=https://id.lib.harvard.edu/alma/990038590670203941/catalog |access-date=2023-12-01 |website=hollis.harvard.edu |language=en}}</ref>

Hironaka was an Associate Professor of Mathematics at [[Brandeis University]] from 1960–1963. He taught at [[Columbia University]] from 1964–1968 and became a professor of mathematics at [[Harvard University]] from 1968 until becoming ''[[emeritus]]'' in 1992.

Hironaka returned to Japan for a joint professorship at the [[Research Institute for Mathematical Sciences]] and [[Kyoto University]] from 1975–1983 and was the Institute Director from 1983–1985.<ref>{{cite web|url=http://www.kurims.kyoto-u.ac.jp/en/emeritus.html|title=Professor Emeritus|publisher=[[Research Institute for Mathematical Sciences]], [[Kyoto University]]|access-date=March 10, 2014|archive-date=April 4, 2014|archive-url=https://web.archive.org/web/20140404225904/http://www.kurims.kyoto-u.ac.jp/en/emeritus.html|url-status=dead}}</ref>   

Hironaka was the president of [[Yamaguchi University]] from 1996–2002.<ref>{{cite web |title=Former President of Yamaguchi University |url=http://www.yamaguchi-u.ac.jp/english/17/66.html |url-status=dead |archive-url=https://web.archive.org/web/20140310070409/http://www.yamaguchi-u.ac.jp/english/17/66.html |archive-date=March 10, 2014 |access-date=March 10, 2014 |publisher=[[Yamaguchi University]] |df=mdy-all}}</ref>

In 2017 he posted to his personal webpage a manuscript that claims to prove the existence of a resolution of singularities in positive characteristic.<ref>{{cite web|url=http://www.math.harvard.edu/~hironaka/pRes.pdf|title=Resolution of singularities in positive characteristics|publisher=[[Harvard University]]|access-date=May 17, 2017}}</ref>

==Awards==

Hironaka received a Fields Medal, the highest honor in mathematics, at the [[International Congress of Mathematicians]] at Nice in 1970 at 39, just under the 40 year age limit.  

List of Awards:  

* [[Asahi Prize]] (1967)

* [[Fields Medal]] in 1970.<ref name=":0" />

* [[Japan Academy Prize (academics)|Japan Academy Prize]] (1970)

* [[Guggenheim Fellowship]] (1971)<ref>{{Cite web |title=Mathematics Archives - Page 13 of 20 |url=https://www.gf.org/field-of-study/mathematics/ |url-status=live |archive-url=https://archive.today/20231202214217/https://www.gf.org/field-of-study/mathematics/page/13/ |archive-date=2023-12-02 |access-date=2023-12-02 |website=John Simon Guggenheim Memorial Foundation... |language=en}}</ref>

* [[Order of Culture]] (1975)<ref>{{Cite web |title=文化勲章 |url=https://www.kyoto-u.ac.jp/ja/about/history/honor/award-b/culture |url-status=live |archive-url=https://archive.today/20231202221342/https://www.kyoto-u.ac.jp/ja/about/history/honor/award-b/culture |archive-date=2023-12-02 |access-date=2023-12-02 |website=京都大学 |language=ja}}</ref>

* [[Person of Cultural Merit]] (1975)<ref>{{Cite web |title=文化功労者 |url=https://www.kyoto-u.ac.jp/ja/about/history/honor/award-b/cultural-merit |archive-url=https://archive.today/20231202221617/https://www.kyoto-u.ac.jp/ja/about/history/honor/award-b/cultural-merit |archive-date=2023-12-02 |access-date=2023-12-02 |website=京都大学 |language=ja}}</ref>

* [[Harvard Centennial Medal]] (2011)<ref name=":3" />

== Influence on Asian Mathematics ==

Hironaka has been active in promoting mathematical education, particularly in Japan and South Korea. Hironaka wrote or co-authored 26 books on mathematics and other topics.<ref name=":3" />

In 1980, he started a summer seminar for Japanese high school students, and later created a program for Japanese and American college students. In 1984 he established the Japanese Association for Mathematical Sciences (JAMS) to fund these seminars, serving as executive director.<ref name=":2" /> Additional funding was received from corporations and the Japanese government. Harvard emeritus math professor [[Shing-Tung Yau]] noted that "In the 1980s there were few domestic grant opportunities for foreign travel or exchange [...] today, one can see the fruits of Hironaka’s efforts in the number of former JAMS fellows who have become professors of mathematics across the United States and Japan."<ref name=":3" />  

As visiting professor at [[Seoul National University]] in 2008–2009, Hironaka mentored undergraduate student [[June Huh]], a former high school drop-out and aspiring poet, encouraging his interest in pursuing math for graduate school. Huh won a Fields medal in 2022 for the linkages he found between [[algebraic geometry]] and [[combinatorics]].<ref>{{Cite web |last=Cepelewicz |first=Jordana |date=July 5, 2022 |title=He Dropped Out to Become a Poet. Now He's Won a Fields Medal. |url=https://www.quantamagazine.org/june-huh-high-school-dropout-wins-the-fields-medal-20220705/ |url-status=live |archive-url=https://archive.today/20220705140842/https://www.quantamagazine.org/june-huh-high-school-dropout-wins-the-fields-medal-20220705/ |archive-date=July 5, 2022 |access-date=November 30, 2022 |website=Quanta Magazine}}</ref>

== Personal life ==

Hironaka married [[Wakako Hironaka|Wakako Kimoto]] in 1960, a Brandeis Wien International Scholar who entered Japanese politics through her election to the House of Councillors in 1986. They have a son Jo, and daughter Eriko, who is also a mathematician.<ref name=":1" /><ref>{{Cite web |title=Eriko Hironaka |url=https://www.math.fsu.edu/~hironaka/ |access-date=2023-11-30 |website=www.math.fsu.edu}}</ref>

On his love for mathematics, Hironaka said "I accumulate anything to do with numbers. For instance, I have more than 10,000 photos of flowers and leaves. I like to just count the numbers and compare them. I am so pleased to be a mathematician, because I can see the mathematical interest in things."<ref name=":2" />

== Selected Publications ==

* Hironaka, H. (1957). [https://projecteuclid.org/journals/memoirs-of-the-college-of-science-university-of-kyoto-series-a-mathematics/volume-30/issue-2/On-the-arithmetic-genera-and-the-effective-genera-of-algebraic/10.1215/kjm/1250777055.full "On the arithmetic genera and the effective genera of algebraic curves,"] ''Mem. College Sci. Univ. Kyoto Ser. A Math.'', '''30'''(2): 177-195. DOI: 10.1215/kjm/1250777055  

* Hironaka, H. (1964), [https://www.jstor.org/stable/1970486 "The Resolution of Singularities of an Algebraic Variety over a Field of Characteristic Zero."] ''Annals of Mathematics''., '''79'''(1):109-203. https://doi.org/10.2307/1970486

* Hironaka, H. (1991), [https://link.springer.com/chapter/10.1007/978-3-642-76709-8_10 "Fame, sweet and bitter."] In P. Hilton, F. Hirzebruch, and R. Remmert (Eds.), [https://link.springer.com/book/10.1007/978-3-642-76709-8 Miscellanea mathematica](pp. 155-176)

*[[Hironaka decomposition]]

*[[Hironaka's criterion]]

*[[René Thom]]

== References ==

== External links ==