Goro Shimura

Gorō Shimura was born in Hamamatsu, Japan, on 23 February 1930.{{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}} Shimura graduated with a B.A. in mathematics and a D.Sc. in mathematics from the University of Tokyo in 1952 and 1958, respectively.{{MathGenealogy|id=18860}}

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. 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. Through André Weil he obtained a position at Princeton University.{{MacTutor Biography|id=Shimura}} 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.{{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}}

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.{{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}} 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.

Shimura had two children, Tomoko and Haru, with his wife Chikako. Shimura died on 3 May 2019 in Princeton, New Jersey at the age of 89.

Shimura was a colleague and a friend of Yutaka Taniyama, with whom he wrote the first book on the complex multiplication of abelian varieties and formulated the Taniyama–Shimura conjecture.{{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 }} Shimura then wrote a long series of major papers, extending the phenomena found in the theory of complex multiplication of elliptic curves and the theory of modular forms to higher dimensions (e.g. Shimura varieties). This work provided examples for which the equivalence between motivic and automorphic L-functions postulated in the Langlands program could be tested: automorphic forms realized in the cohomology of a Shimura variety have a construction that attaches Galois representations to them.{{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}}

In 1958, Shimura generalized the initial work of Martin Eichler on the Eichler–Shimura congruence relation between the local L-function of a modular curve and the eigenvalues of Hecke operators.{{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 }}{{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}} In 1959, Shimura extended the work of Eichler on the Eichler–Shimura isomorphism between Eichler cohomology groups and spaces of cusp forms which would be used in Pierre Deligne's proof of the Weil conjectures.{{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 }}{{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 }}

In 1971, Shimura's work on explicit class field theory in the spirit of Kronecker's Jugendtraum resulted in his proof of Shimura's reciprocity law.{{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 }} In 1973, Shimura established the Shimura correspondence between modular forms of half integral weight k+1/2, and modular forms of even weight 2k.{{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}}

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.{{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 }} Shimura dryly commented that his first reaction on hearing of Andrew Wiles's proof of the semistable case was 'I told you so'.{{cite web|url=https://www.pbs.org/wgbh/nova/proof/ |title=Nova Episode: The Proof|website=PBS}}

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.{{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}}

• {{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.{{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}}
• {{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}}{{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}} 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}}{{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}}
• {{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}}

• {{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}}

• {{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}}

{{reflist}}

• {{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]

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Category:1930 births

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Category:People from Hamamatsu

Category:Scientists from Hamamatsu

Category:University of Tokyo alumni

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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