Editing Goro Shimura

{{Short description|Japanese mathematician (1930–2019)}}
{{use dmy dates|date=May 2019}}
{{Family name hatnote|Shimura|lang=Japanese}}
{{Infobox scientist
| name              = Gorō Shimura
| image             = Goro_Shimura_in_1964.jpg 
| image_size        = 256px
| caption           = Goro Shimura in 1964, taken by [[Princeton University]] while he was a professor there
| birth_date        = {{birth date|1930|02|23|df=y}}
| birth_place       = [[Hamamatsu, Japan]]
| death_date        = {{death date and age|2019|05|03|1930|02|23|df=yes}}
| death_place       = [[Princeton, New Jersey|Princeton]], [[New Jersey]]
| nationality       = [[Japan]]ese
| fields            = [[Mathematics]]
| workplaces        = [[Princeton University]]
| alma_mater        = [[University of Tokyo]]
| doctoral_advisor  =
| doctoral_students = [[Don Blasius]]<br>[[Bill Casselman (mathematician)|Bill Casselman]]<br>[[Melvin Hochster]]<br>[[Robert Rumely]]<br>[[Alice Silverberg]]
| known_for         = [[abelian variety of CM-type|Complex multiplication of abelian varieties]]<br>[[Eichler-Shimura relation]]<br>[[Modularity theorem]]<br>[[Shimura correspondence]]<br>[[Shimura variety]]<br>[[Shimura subgroup]]<br>[[Shimura's reciprocity law]]
| awards            = [[Guggenheim Fellowship]] {{small|(1970)}}<br>[[Cole Prize]] {{small|(1977)}}<br>[[Asahi Prize]] {{small|(1991)}}<br>[[Steele Prize]] {{small|(1996)}}
}}
{{nihongo|'''Gorō Shimura'''|志村 五郎|Shimura Gorō|23 February 1930 – 3 May 2019}} was a Japanese [[mathematician]] and Michael Henry Strater [[Professor Emeritus]] of [[Mathematics]] at [[Princeton University]] who worked in [[number theory]], [[automorphic form]]s, and [[arithmetic geometry]].<ref name="death-announcement">{{cite web|url=https://www.math.princeton.edu/news/professor-emeritus-goro-shimura-1930-2019 |title=Professor Emeritus Goro Shimura 1930—2019 |publisher=Princeton University Department of Mathematics |date=3 May 2019 |access-date=3 May 2019}}</ref> He was known for developing the theory of [[abelian variety of CM-type|complex multiplication of abelian varieties]] and [[Shimura variety|Shimura varieties]], as well as posing the [[Taniyama–Shimura conjecture]] which ultimately led to the [[Wiles's proof of Fermat's Last Theorem|proof]] of [[Fermat's Last Theorem]].

==Biography==
Gorō Shimura was born in [[Hamamatsu]], [[Japan]], on 23 February 1930.<ref name="princeton-obit">{{cite web|url=https://www.princeton.edu/news/2019/05/08/goro-shimura-giant-number-theory-dies-89 |title=Goro Shimura, a 'giant' of number theory, dies at 89 |publisher=Princeton University Department of Mathematics |last=Fuller-Wright |first=Liz |date=8 May 2019 |access-date=9 May 2019}}</ref> Shimura graduated with a B.A. in mathematics and a D.Sc. in mathematics from the [[University of Tokyo]] in 1952 and 1958, respectively.<ref>{{MathGenealogy|id=18860}}</ref><ref name="princeton-obit"/>

After graduating, Shimura became a lecturer at the University of Tokyo, then worked abroad — including ten months in Paris and a seven-month stint at Princeton's [[Institute for Advanced Study]] — before returning to Tokyo, where he married Chikako Ishiguro.<ref name="mactutor"/><ref name="princeton-obit"/> He then moved from Tokyo to join the faculty of [[Osaka University]], but growing unhappy with his funding situation, he decided to seek employment in the United States.<ref name="mactutor"/><ref name="princeton-obit"/> Through [[André Weil]] he obtained a position at Princeton University.<ref name="mactutor">{{MacTutor Biography|id=Shimura}}</ref> Shimura joined the Princeton faculty in 1964 and retired in 1999, during which time he advised over 28 doctoral students and received the [[Guggenheim Fellowship]] in 1970, the [[Cole Prize]] for number theory in 1977, the [[Asahi Prize]] in 1991, and the [[Steele Prize]] for lifetime achievement in 1996.<ref name="death-announcement"/><ref>{{cite web|url=http://www.asahi.com/shimbun/award/asahi/english.html |title=The Asahi Prize |publisher=The Asahi Shimbun Company |access-date=4 May 2019}}</ref>

Shimura described his approach to mathematics as "phenomenological": his interest was in finding new types of interesting behavior in the theory of automorphic forms. He also argued for a "romantic" approach, something he found lacking in the younger generation of mathematicians.<ref>{{Cite book|first=Goro|last=Shimura|date=5 September 2008|title=The Map of My Life|edition=Hardcover|publisher=[[Springer-Verlag]]| location=Berlin|isbn=978-0-387-79714-4|mr=2442779|url=https://www.springer.com/mathematics/history+of+mathematics/book/978-0-387-79714-4}}</ref> Shimura used a two-part process for research, using one desk in his home dedicated to working on new research in the mornings and a second desk for perfecting papers in the afternoon.<ref name="princeton-obit"/>

Shimura had two children, Tomoko and Haru, with his wife Chikako.<ref name="princeton-obit"/> Shimura died on 3 May 2019 in [[Princeton, New Jersey|Princeton]], [[New Jersey]] at the age of 89.<ref name="death-announcement"/><ref name="princeton-obit"/>

==Research==
Shimura was a colleague and a friend of [[Yutaka Taniyama]], with whom he wrote the first book on the [[abelian variety of CM-type|complex multiplication of abelian varieties]] and formulated the Taniyama–Shimura conjecture.<ref>{{cite journal| last1=Shimura | first1=Goro | title=Yutaka Taniyama and his time. Very personal recollections | doi=10.1112/blms/21.2.186 | mr=976064 | year=1989 | journal=The Bulletin of the London Mathematical Society | issn=0024-6093 | volume=21 | issue=2 | pages=186–196| doi-access=free }}</ref> Shimura then wrote a long series of major papers, extending the phenomena found in the theory of [[complex multiplication|complex multiplication of elliptic curves]] and the theory of [[modular form]]s to higher dimensions (e.g. Shimura varieties). This work provided examples for which the equivalence between [[Motivic L-function|motivic]] and [[Automorphic L-function|automorphic ''L''-functions]] postulated in the [[Langlands program]] could be tested: [[automorphic form]]s realized in the [[cohomology]] of a Shimura variety have a construction that attaches [[Galois representation]]s to them.<ref name="langlands-shimura">{{cite book|title=Automorphic Forms, Representations, and L-Functions: Symposium in Pure Mathematics|publisher=Chelsea Publishing Company|editor-last1=Borel|editor-first1=Armand|editor-link1=Armand Borel|editor-last2=Casselman|editor-first2=William|editor-link2=Bill Casselman (mathematician)|last=Langlands|first=Robert|authorlink=Robert Langlands|year=1979|volume=XXXIII Part 1
|chapter-url=http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/pdf/autoreps-ps.pdf|chapter=Automorphic Representations, Shimura Varieties, and Motives. Ein Märchen|pages=205–246}}</ref>

In 1958, Shimura generalized the initial work of [[Martin Eichler]] on the [[Eichler–Shimura congruence relation]] between the [[local zeta function|local ''L''-function]] of a [[modular curve]] and the eigenvalues of [[Hecke operators]].<ref>{{cite journal| last1=Shimura | first1=Goro | title=Correspondances modulaires et les fonctions ζ de courbes algébriques | doi=10.2969/JMSJ/01010001 |mr=0095173 | year=1958 | journal=Journal of the Mathematical Society of Japan | issn=0025-5645 | volume=10 | pages=1–28| doi-access=free }}</ref><ref>{{cite book |first=Ilya |last=Piatetski-Shapiro |authorlink=Ilya Piatetski-Shapiro |chapter=Zeta functions of modular curves |title=Modular functions of one variable II |year=1972 |location=Antwerp |series=Lecture Notes in Mathematics |volume=349 |pages=317–360}}</ref> In 1959, Shimura extended the work of Eichler on the [[Eichler–Shimura isomorphism]] between Eichler cohomology groups and spaces of [[cusp form]]s which would be used in [[Pierre Deligne]]'s proof of the [[Weil conjectures]].<ref>{{cite journal| last1=Shimura | first1=Goro | title=Sur les intégrales attachées aux formes automorphes | doi=10.2969/jmsj/01140291 |mr=0120372 | year=1959 | journal=Journal of the Mathematical Society of Japan | issn=0025-5645 | volume=11 | issue=4 | pages=291–311| doi-access=free }}</ref><ref>{{cite book| last1=Deligne | first1=Pierre | author1-link=Pierre Deligne | title=Séminaire Bourbaki vol. 1968/69 Exposés 347-363 | url=http://www.numdam.org/item?id=SB_1968-1969__11__139_0 | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Lecture Notes in Mathematics | isbn=978-3-540-05356-9 | doi=10.1007/BFb0058801 | year=1971 | volume=179 | chapter=Formes modulaires et représentations l-adiques }}</ref>

In 1971, Shimura's work on explicit [[class field theory]] in the spirit of [[Hilbert's twelfth problem|Kronecker's Jugendtraum]] resulted in his proof of [[Shimura's reciprocity law]].<ref>{{cite book| last1=Shimura | first1=Goro | authorlink=Goro Shimura | title=Introduction to the arithmetic theory of automorphic functions | publisher=Iwanami Shoten | location=Tokyo | series=Publications of the Mathematical Society of Japan | year=1971 | volume=11 | zbl=0221.10029 }}</ref> In 1973, Shimura established the [[Shimura correspondence]] between modular forms of half integral weight ''k''+1/2, and modular forms of even weight 2''k''.<ref>{{cite journal| last1=Shimura | first1=Goro | title=On modular forms of half integral weight | jstor=1970831 | mr=0332663 | year=1973 | journal=[[Annals of Mathematics]] |series=Second Series | issn=0003-486X | volume=97 | issue=3 | pages=440–481 | doi=10.2307/1970831}}</ref>

Shimura's formulation of the Taniyama–Shimura conjecture (later known as the modularity theorem) in the 1950s played a key role in the proof of Fermat's Last Theorem by [[Andrew Wiles]] in 1995. In 1990, [[Kenneth Ribet]] proved [[Ribet's theorem]] which demonstrated that Fermat's Last Theorem followed from the semistable case of this conjecture.<ref>{{cite journal|first=Kenneth |last=Ribet |url=http://www.numdam.org/item?id=AFST_1990_5_11_1_116_0 |title=From the Taniyama-Shimura conjecture to Fermat's last theorem |journal=Annales de la Faculté des Sciences de Toulouse |series=Série 5 |volume=11 |issue=1 |year=1990 |pages=116–139 |doi=10.5802/afst.698|doi-access=free }}</ref> Shimura dryly commented that his first reaction on hearing of [[Andrew Wiles]]'s proof of the semistable case was 'I told you so'.<ref>{{cite web|url=https://www.pbs.org/wgbh/nova/proof/ |title=Nova Episode: The Proof|website=[[PBS]]}}</ref>

==Other interests==
His hobbies were [[shogi]] problems of extreme length and collecting [[Imari porcelain]]. ''The Story of Imari: The Symbols and Mysteries of Antique Japanese Porcelain'' is a non-fiction work about the Imari porcelain that he collected over 30 years that was published by [[Ten Speed Press]] in 2008.<ref name="princeton-obit"/><ref>{{Cite book|first=Goro|last=Shimura|date=1 June 2008|title=The Story of Imari: The Symbols and Mysteries of Antique Japanese Porcelain|edition=Hardcover|publisher=Ten Speed Press|isbn=978-1-58008-896-1|url=http://www.randomhouse.com/catalog/display.pperl?isbn=9781580088961}}</ref>

== Works ==
=== Mathematical books ===
*{{citation|mr=0125113 |last1=Shimura|first1= Goro|last2= Taniyama|first2= Yutaka |title=Complex multiplication of abelian varieties and its applications to number theory|series= Publications of the Mathematical Society of Japan|volume= 6|publisher= The Mathematical Society of Japan|place= Tokyo|year= 1961}} Later expanded and published as {{harvtxt|Shimura|1997}}
*{{cite book|first=Goro|last=Shimura|year=1968|title=Automorphic Functions and Number Theory|series=Lecture Notes in Mathematics, Vol. 54|edition=Paperback|publisher=Springer|isbn=978-3-540-04224-2|url=https://www.springer.com/mathematics/book/978-3-540-04224-2}} 
*{{cite book|first=Goro|last=Shimura|date=1 August 1971|title=Introduction to the Arithmetic Theory of Automorphic Functions|edition=Paperback|publisher=Princeton University Press|isbn=978-0-691-08092-5|url=http://press.princeton.edu/titles/5530.html}} - It is published from [[Iwanami Shoten]] in Japan.<ref>{{cite journal|title=Review of ''Introduction to the Arithmetic Theory of Automorphic Functions'' by Goro Shimura|author=Goldstein, Larry Joel|journal=Bull. Amer. Math. Soc.|volume=79|year=1973|pages=514–516|doi=10.1090/S0002-9904-1973-13177-5|doi-access=free}}</ref>
*{{cite book|first=Goro|last=Shimura|date=1 July 1997|title=Euler Products and Eisenstein Series|series=CBMS Regional Conference Series in Mathematics|edition=Paperback|publisher=American Mathematical Society|isbn=978-0-8218-0574-9|url=https://archive.org/details/eulerproductseis0093shim|url-access=registration|ref=none}}
*{{cite book|first=Goro|last=Shimura|year=1997|title=Abelian Varieties with Complex Multiplication and Modular Functions|edition=Hardcover|publisher=Princeton University Press |isbn=978-0-691-01656-6|url=http://press.princeton.edu/titles/6242.html}}<ref>{{cite journal|title=Review of ''Abelian varieties with complex multiplication and modular functions'' by Goro Shimura|author=Ogg, A. P.|authorlink=Andrew Ogg|journal=Bull. Amer. Math. Soc. (N.S.)|volume=36|year=1999|pages=405–408|doi=10.1090/S0273-0979-99-00784-3|doi-access=free}}</ref> An expanded version of {{harvtxt|Shimura|Taniyama|1961}}.
*{{cite book|first=Goro|last=Shimura|date=22 August 2000|title=Arithmeticity in the Theory of Automorphic Forms|series=Mathematical Surveys and Monographs|edition=Paperback|publisher=American Mathematical Society|isbn=978-0-8218-2671-3}}<ref>{{cite journal|title=Review of ''Arithmeticity in the theory of automorphic forms'' by Goro Shimura|author=Yoshida, Hiroyuki|journal=Bull. Amer. Math. Soc. (N.S.)|volume=39|year=2002|pages=441–448|url=https://www.ams.org/journals/bull/2002-39-03/S0273-0979-02-00945-X|doi=10.1090/s0273-0979-02-00945-x|doi-access=free}}</ref>
*{{cite book|first=Goro|last=Shimura|date=1 March 2004|title=Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups|series=Mathematical Surveys and Monographs|edition=Hardcover|publisher=American Mathematical Society |isbn=978-0-8218-3573-9|url=https://www.ams.org/bookstore-getitem/item=SURV-109}}
*{{cite book|first=Goro|last=Shimura|year=2007|title=Elementary Dirichlet Series and Modular Forms|series=Springer Monographs in Mathematics|edition=Hardcover|publisher=Springer|isbn=978-0-387-72473-7|url=https://www.springer.com/mathematics/numbers/book/978-0-387-72473-7}}
**{{cite book|first=Goro|last=Shimura|date=28 December 2009|title=Elementary Dirichlet Series and Modular Forms|series=Springer Monographs in Mathematics|edition=Paperback|publisher=Springer New York|isbn=978-1-4419-2478-0}}
*{{cite book|first=Goro|last=Shimura|date=15 July 2010|title=Arithmetic of Quadratic Forms|series=Springer Monographs in Mathematics|edition=Hardcover|publisher=Springer|isbn=978-1-4419-1731-7|url=https://www.springer.com/mathematics/algebra/book/978-1-4419-1731-7}}

=== Non-fiction ===
*{{cite book|first=Goro|last=Shimura|date=1 June 2008|title=The Story of Imari: The Symbols and Mysteries of Antique Japanese Porcelain|edition=Hardcover|publisher=Ten Speed Press|isbn=978-1-58008-896-1|url=http://www.randomhouse.com/catalog/display.pperl?isbn=9781580088961}}
*{{cite book|first=Goro|last=Shimura|date=5 September 2008|title=The Map of My Life|edition=Hardcover|publisher=[[Springer-Verlag]]| location=Berlin|isbn=978-0-387-79714-4|mr=2442779|url=https://www.springer.com/mathematics/history+of+mathematics/book/978-0-387-79714-4}}
**{{cite book|first=Goro|last=Shimura|date=28 December 2009|title=The Map of My Life|edition=Paperback|publisher=Springer New York|isbn=978-1-4419-2724-8}}

=== Collected papers ===
*{{cite book|first=Goro|last=Shimura|year=2002|title=Collected Papers|edition=Hardcover|volume=I: 1954–1965|publisher=Springer|isbn=978-0-387-95406-6|url=https://www.springer.com/mathematics/algebra/book/978-0-387-95406-6}}
*{{cite book|first=Goro|last=Shimura|year=2002|title=Collected Papers|edition=Hardcover|volume=II: 1967–1977|publisher=Springer|isbn=978-0-387-95416-5|url=https://www.springer.com/mathematics/algebra/book/978-0-387-95416-5}}
*{{cite book|first=Goro|last=Shimura|year=2003|title=Collected Papers|edition=Hardcover|volume=III: 1978–1988|publisher=Springer|isbn=978-0-387-95417-2|url=https://www.springer.com/mathematics/algebra/book/978-0-387-95417-2}}
*{{cite book|first=Goro|last=Shimura|year=2003|title=Collected Papers|edition=Hardcover|volume=IV: 1989–2001|publisher=Springer|isbn=978-0-387-95418-9|url=https://www.springer.com/mathematics/algebra/book/978-0-387-95418-9}}

==References==
{{reflist}}

==External links==
*{{wikiquote-inline}}
*{{MathGenealogy|id=18860}}
* [https://www.princeton.edu/news/2019/05/08/goro-shimura-giant-number-theory-dies-89  Goro Shimura, a ‘giant’ of number theory, dies at 89 / Princeton University]
* [https://www.ias.edu/scholars/goro-shimura The New York Times, Goro Shimura, 89, Mathematician with Broad Impact, Is Dead Princeton University, Professor Emeritus Goro Shimura 1930–2019]

{{authority control}}

{{DEFAULTSORT:Shimura, Goro}}
[[Category:1930 births]]
[[Category:2019 deaths]]
[[Category:People from Hamamatsu]]
[[Category:Scientists from Hamamatsu]]
[[Category:University of Tokyo alumni]]
[[Category:20th-century Japanese mathematicians]]
[[Category:21st-century Japanese mathematicians]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Number theorists]]
[[Category:Academic staff of Osaka University]]
[[Category:Princeton University faculty]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Japanese emigrants to the United States]]
[[Category:Academic staff of the University of Tokyo]]