Fields Medal

{{Short description|Mathematics award}} {{Distinguish|Field's metal}} {{Use American English|date=July 2018}} {{Use dmy dates|date=September 2021}} {{Infobox award | name = Fields Medal | image = FieldsMedalFront.jpg | caption = The obverse of the Fields Medal features Archimedes | awarded_for = Outstanding contributions in mathematics attributed to young scientists | presenter = International Mathematical Union | reward = {{CA$}}15,000 | year = {{Start date and age|1936}} | website = {{official URL}} |image2=FieldsMedalBack.jpg|caption2=The reverse of the medal}}

The '''Fields Medal''' is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a convention which takes place every four years. The name of the award honors the Canadian mathematician John Charles Fields.<ref name="Fields Institute About Us">{{cite web |url=http://www.fields.utoronto.ca/aboutus/jcfields/fields_medal.html |title=About Us: The Fields Medal |publisher=The Fields Institute, University of Toronto |access-date=21 August 2010 |archive-date=1 April 2022 |archive-url=https://web.archive.org/web/20220401044832/http://www.fields.utoronto.ca/aboutus/jcfields/fields_medal.html |url-status=live }}</ref> Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions to the field of mathematics.

The Fields Medal is regarded as one of the highest honors a mathematician can receive, according to the annual Academic Excellence Survey by ARWU,<ref>{{Cite web|url=http://www.shanghairanking.com/subject-survey/awards.html|title=Top Award, ShanghaiRanking Academic Excellence Survey 2017 {{!}} Shanghai Ranking – 2017|website=Shanghairanking.com|access-date=29 March 2018|archive-date=17 October 2020|archive-url=https://web.archive.org/web/20201017012526/http://www.shanghairanking.com/subject-survey/awards.html|url-status=dead}}</ref> and has been described as the Nobel Prize of Mathematics.<ref name=":0">{{Cite journal|last=Ball|first=Philip|title=Iranian is first woman to nab highest prize in maths|url=https://www.nature.com/news/iranian-is-first-woman-to-nab-highest-prize-in-maths-1.15686|journal=Nature|language=en|doi=10.1038/nature.2014.15686|year=2014|s2cid=180573813|doi-access=free|access-date=29 March 2018|archive-date=8 October 2019|archive-url=https://web.archive.org/web/20191008040735/https://www.nature.com/news/iranian-is-first-woman-to-nab-highest-prize-in-maths-1.15686|url-status=live}}</ref><ref name=":2">{{Cite web|url=https://mathshistory.st-andrews.ac.uk/Honours/FieldsMedal/|title=Fields Medal|website=mathshistory.st-andrews.ac.uk|access-date=29 March 2018|archive-date=26 May 2021|archive-url=https://web.archive.org/web/20210526200633/https://mathshistory.st-andrews.ac.uk/Honours/FieldsMedal/|url-status=live}}</ref><ref name=":3">{{Cite web|url=https://www.uchicago.edu/about/accolades/14/|title=Fields Medal|website=The University of Chicago|language=en|access-date=29 March 2018|archive-date=7 April 2019|archive-url=https://web.archive.org/web/20190407140029/https://www.uchicago.edu/about/accolades/14/|url-status=live}}</ref> In another reputation survey conducted by IREG in 2013–14, the Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics.<ref>{{cite book|author=IREG Observatory on Academic Ranking and Excellence|title=IREG List of International Academic Awards|publisher=IREG Observatory on Academic Ranking and Excellence|location=Brussels|url=http://ireg-observatory.org/en/pdfy/IREG-list-academic-awards-EN.pdf|access-date=3 March 2018|archive-date=12 March 2019|archive-url=https://web.archive.org/web/20190312125455/http://ireg-observatory.org/en/pdfy/IREG-list-academic-awards-EN.pdf|url-status=dead}}</ref><ref>{{cite journal|last1=Zheng|first1=Juntao|last2=Liu|first2=Niancai|title=Mapping of important international academic awards|journal=Scientometrics|date=2015|volume=104|issue=3|pages=763–791|doi=10.1007/s11192-015-1613-7|s2cid=25088286}}</ref>

The medal was first awarded in 1936 to Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas, and it has been awarded every four years since 1950. In 2014, the Iranian mathematician Maryam Mirzakhani became the first female Fields Medalist.<ref name="Farsnews">{{cite news|url=http://english.farsnews.ir/newstext.aspx?nn=13930523000321|title=President Rouhani Congratulates Iranian Woman for Winning Math Nobel Prize|date=14 August 2014|access-date=14 August 2014|publisher=Fars News Agency|archive-date=26 December 2018|archive-url=https://web.archive.org/web/20181226060915/http://en.farsnews.ir/newstext.aspx?nn=13930523000321%0A|url-status=dead}}</ref><ref>{{cite web|url=http://www.mathunion.org/general/prizes/2014|publisher=International Mathematical Union|title=IMU Prizes 2014|access-date=12 August 2014|archive-date=26 December 2018|archive-url=https://web.archive.org/web/20181226060901/https://www.mathunion.org/general/prizes/2014%0A|url-status=dead}}</ref><ref>{{Cite news|url=https://www.theguardian.com/world/2017/jul/16/maryam-mirzakhani-iranian-newspapers-break-hijab-taboo-in-tributes#img-2|title=Maryam Mirzakhani: Iranian newspapers break hijab taboo in tributes|last=Dehghan|first=Saeed Kamali Dehghan|date=16 July 2017|work=The Guardian|access-date=18 July 2017|language=en-GB|issn=0261-3077|archive-date=18 July 2017|archive-url=https://web.archive.org/web/20170718033745/https://www.theguardian.com/world/2017/jul/16/maryam-mirzakhani-iranian-newspapers-break-hijab-taboo-in-tributes#img-2|url-status=live}}</ref> With the exception of two PhD holders in physics (Edward Witten and Martin Hairer),<ref>{{cite web |title=Edward Witten |url=https://www.worldsciencefestival.com/participants/dr-edward-witten/ |publisher=World Science Festival |access-date=14 September 2020 |archive-date=8 April 2022 |archive-url=https://web.archive.org/web/20220408074621/https://www.worldsciencefestival.com/participants/dr-edward-witten/ |url-status=live }}</ref> only people with a PhD in mathematics have won the medal.<ref>{{cite web |last1=Kollár |first1=János |title=Is there a curse of the Fields medal? |url=https://web.math.princeton.edu/~kollar/FromMyHomePage/fm-essay.pdf |publisher=Princeton University |date=2014 |access-date=14 September 2020 |archive-date=9 March 2022 |archive-url=https://web.archive.org/web/20220309061236/http://web.math.princeton.edu/~kollar/FromMyHomePage/fm-essay.pdf |url-status=live }}</ref> In total, 64 people have been awarded the Fields Medal {{as of|2022|lc=y}}.<ref>{{cite web |title=Fields Medal |url=https://www.mathunion.org/imu-awards/fields-medal |publisher=International Mathematical Union |access-date=14 September 2020 |archive-date=26 December 2018 |archive-url=https://web.archive.org/web/20181226015744/https://www.mathunion.org/imu-awards/fields-medal |url-status=live }}</ref> The most recent group of Fields Medalists received their awards on 5 July 2022 in an online event which was live-streamed from Helsinki, Finland. It was originally meant to be held in Saint Petersburg, Russia, but was moved following the 2022 Russian invasion of Ukraine.

Fields was instrumental in establishing the award, designing the medal himself, and funding the monetary component, though he died before it was established and his plan was overseen by John Lighton Synge.<ref name="Fields Institute About Us" /> The prize includes a monetary award which, since 2006, has been {{CA$|link=yes}}15,000.<ref name="BBC">{{cite news |title= Maths genius turns down top prize |url= https://news.bbc.co.uk/2/hi/science/nature/5274040.stm |publisher= BBC |date= 22 August 2006 |access-date= 22 August 2006 |archive-date= 15 August 2010 |archive-url= https://web.archive.org/web/20100815015937/http://news.bbc.co.uk/2/hi/science/nature/5274040.stm |url-status= live }}</ref><ref>[https://www.jpost.com/Israel/Article.aspx?id=185366 "Israeli wins 'Nobel' of Mathematics"] {{Webarchive|url=https://web.archive.org/web/20130523181501/http://www.jpost.com/Israel/Article.aspx?id=185366 |date=23 May 2013 }}, ''The Jerusalem Post''</ref>

==Conditions of the award==

The Fields Medal is widely regarded as one of the most prestigious awards in the field of mathematics and is often described as the “Nobel Prize of Mathematics”. However, unlike the Nobel Prize, the Fields Medal is awarded once every four years and includes an age restriction: recipients must be under 40 years of age on 1 January of the year in which the medal is awarded.

The age limit reflects the intention of John Charles Fields that the award should not only recognize outstanding work already completed, but also encourage further achievement by the recipients and stimulate renewed effort among other mathematicians. In addition, an individual may receive the Fields Medal only once and is not eligible for future awards.<ref>{{cite web |url=http://darboux.mathunion.org/fileadmin/IMU/Prizes/Fields/Statutes%20Fields%20Medal.pdf |title=Rules for the Fields Medal |website=mathunion.org |access-date=1 May 2018 |archive-date=2 May 2018 |archive-url=https://web.archive.org/web/20180502070440/http://darboux.mathunion.org/fileadmin/IMU/Prizes/Fields/Statutes%20Fields%20Medal.pdf |url-status=live }}</ref>

==List of Fields medalists== In certain years, the Fields medalists have been officially cited for particular mathematical achievements, while in other years such specificities have not been given. However, in every year that the medal has been awarded, noted mathematicians have lectured at the International Congress of Mathematicians on each medalist's body of work. In the following table, official citations are quoted when possible (namely for the years 1958, 1998, and every year since 2006). For the other years through 1986, summaries of the ICM lectures, as written by Donald Albers, Gerald L. Alexanderson, and Constance Reid, are quoted.<ref>Albers, Donald J.; Alexanderson, G. L.; Reid, Constance. ''International mathematical congresses. An illustrated history 1893–1986''. Rev. ed. including ICM 1986. Springer-Verlag, New York, 1986</ref> In the remaining years (1990, 1994, and 2002), part of the text of the ICM lecture itself has been quoted. The upcoming awarding of the Fields Medal at the 2026 International Congress of the International Mathematical Union is planned to take place in Philadelphia.<ref>{{cite web |title=ICM 2026 |url=https://www.mathunion.org/icm/icm-2026 |website=International Mathematical Union |access-date=2 June 2024}}</ref>

{| class="wikitable sortable" style="margin: 1ex auto 1ex auto" |- ! Year ! ICM location ! colspan=2|Medalists<ref name=IMU>{{cite web|url=http://www.mathunion.org/general/prizes/fields/prizewinners|title=The Fields Medalists, chronologically listed|publisher=International Mathematical Union (IMU)|date=8 May 2008|access-date=25 March 2009|archive-date=26 December 2018|archive-url=https://web.archive.org/web/20181226015744/https://www.mathunion.org/imu-awards/fields-medal|url-status=live}}</ref> ! Affiliation (when awarded) ! Affiliation (current/last) ! Reasons |- | rowspan=2| 1936 | rowspan=2| Oslo, Norway

| 60px | {{sortname|Lars|Ahlfors}} | University of Helsinki, Finland | Harvard University, US<ref>{{cite web |url=https://www.ams.org/notices/199802/comm-krantz.pdf |title=Lars Valerian Ahlfors (1907–1996) |website=Ams.org |access-date=31 March 2017 |archive-date=3 March 2022 |archive-url=https://web.archive.org/web/20220303211929/https://www.ams.org/notices/199802/comm-krantz.pdf |url-status=live }}</ref><ref>{{cite web|url=http://www.math.harvard.edu/history/ahlfors/|title=Lars Ahlfors (1907–1996)|date=7 November 2004|publisher=Harvard University, Dept. of Math.|access-date=19 August 2014|archive-date=23 November 2014|archive-url=https://web.archive.org/web/20141123144942/http://www.math.harvard.edu/history/ahlfors/|url-status=live}}</ref> | "Awarded medal for research on covering surfaces related to Riemann surfaces of inverse functions of entire and meromorphic functions. Opened up new fields of analysis."<ref name="36reasons">{{cite web |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1936/index.html |title=Fields Medals 1936 |publisher=International Mathematical Union |website=mathunion.org |access-date=7 April 2019 |archive-date=31 July 2020 |archive-url=https://web.archive.org/web/20200731102503/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1936/index.html |url-status=live }}</ref>

| 60px | {{sortname|Jesse|Douglas}} | Massachusetts Institute of Technology, US | City College of New York, US<ref>{{cite encyclopedia|url=https://www.britannica.com/EBchecked/topic/170174/Jesse-Douglas|title=Jesse Douglas|date=28 May 2010|encyclopedia=Encyclopædia Britannica|access-date=19 August 2014|archive-date=3 September 2014|archive-url=https://web.archive.org/web/20140903211356/http://www.britannica.com/EBchecked/topic/170174/Jesse-Douglas|url-status=live}}</ref><ref>{{cite web |url=http://wdb.ugr.es/~geometry/seminar/files/talks/MMicallef20130207.pdf |title=The work of Jesse Douglas on Minimal Surfaces |author1=Mario J. Micallef |author2=J. Gray |website=Wdb.ugr.es |access-date=31 March 2017 |archive-url=https://web.archive.org/web/20141006070205/http://wdb.ugr.es/~geometry/seminar/files/talks/MMicallef20130207.pdf |archive-date=6 October 2014 |url-status=dead }}</ref> | "Did important work on the Plateau problem which is concerned with finding minimal surfaces connecting and determined by some fixed boundary."<ref name="36reasons" />

| 60px | {{sortname|Laurent|Schwartz}} | University of Nancy, France | University of Paris VII, France<ref>{{cite web|url=http://www-history.mcs.st-and.ac.uk/Biographies/Schwartz.html|title=Laurent Moise Schwartz|date=24 June 2007|publisher=School of Mathematics and Statistics University of St Andrews, Scotland|access-date=19 August 2014|archive-date=6 October 2014|archive-url=https://web.archive.org/web/20141006092731/http://www-history.mcs.st-and.ac.uk/Biographies/Schwartz.html|url-status=live}}</ref><ref>{{cite book |last=Schwartz |first=Laurent |year=2001 |title=Un mathématicien aux prises avec le siècle |trans-title=A Mathematician Grappling with His Century |url=https://www.springer.com/birkhauser/history+of+science/book/978-3-7643-6052-8 |archive-url=https://archive.today/20140821114917/http://www.springer.com/birkhauser/history+of+science/book/978-3-7643-6052-8 |url-status=dead |archive-date=21 August 2014 |location=AMS |publisher=Birkhäuser |isbn=978-3-0348-7584-4 |access-date=21 August 2014 }}</ref> | "Developed the theory of distributions, a new notion of generalized function motivated by the Dirac delta-function of theoretical physics."<ref name="50reasons">{{cite web |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1950/index.html |title=Fields Medals 1950 |publisher=International Mathematical Union |website=mathunion.org |access-date=7 April 2019 |archive-date=8 April 2022 |archive-url=https://web.archive.org/web/20220408074621/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1950/index.html |url-status=live }}</ref>

| 60px | {{sortname|Atle|Selberg}} | Institute for Advanced Study, US | Institute for Advanced Study, US<ref>{{cite web |url=https://www.ams.org/notices/200906/rtx090600692p-corrected.pdf |title=Remembering Atle Selberg, 1917–2007 |website=Ams.org |access-date=31 March 2017 |archive-date=23 November 2021 |archive-url=https://web.archive.org/web/20211123172218/http://www.ams.org/notices/200906/rtx090600692p-corrected.pdf |url-status=live }}</ref> | "Developed generalizations of the sieve methods of Viggo Brun; achieved major results on zeros of the Riemann zeta function; gave an elementary proof of the prime number theorem (with P. Erdős), with a generalization to prime numbers in an arbitrary arithmetic progression."<ref name="50reasons" />

| 60px | {{sortname|Kunihiko|Kodaira}} | | Princeton University, US, University of Tokyo, Japan and Institute for Advanced Study, US<ref name="mathunion.org">{{cite web |url=http://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1954.1/ICM1954.1.ocr.pdf |title=Proceedings of the International Congress of Mathematicians |date=1954 |website=Mathunion.org |access-date=31 March 2017 |archive-date=29 March 2022 |archive-url=https://web.archive.org/web/20220329075759/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1954.1/ICM1954.1.ocr.pdf |url-status=live }}</ref> | University of Tokyo, Japan<ref>{{cite web |url=https://www.ams.org/notices/199803/comm-obit-spencer.pdf |title=Kunihiko Kodaira (1915–1997) |author=Donald C. Spencer |website=Ams.org |access-date=31 March 2017 |archive-date=23 February 2022 |archive-url=https://web.archive.org/web/20220223055632/https://www.ams.org/notices/199803/comm-obit-spencer.pdf |url-status=live }}</ref> | "Achieved major results in the theory of harmonic integrals and numerous applications to Kählerian and more specifically to algebraic varieties. He demonstrated, by sheaf cohomology, that such varieties are Hodge manifolds."<ref name="54reasons">{{cite web |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1954/index.html |title=Fields Medals 1954 |publisher=International Mathematical Union |website=mathunion.org |access-date=7 April 2019 |archive-date=8 April 2022 |archive-url=https://web.archive.org/web/20220408074624/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1954/index.html |url-status=live }}</ref>

| 60px | {{sortname|Jean-Pierre|Serre}} | University of Nancy, France | Collège de France, France<ref>{{cite web |url=http://www.math.rug.nl/~top/lectures/delft.pdf |title=Jean-Pierre Serre |website=Math.rug.nl |access-date=31 March 2017 |archive-date=16 June 2016 |archive-url=https://web.archive.org/web/20160616160010/http://www.math.rug.nl/~top/lectures/delft.pdf |url-status=live }}</ref><ref>{{cite encyclopedia|url=https://www.britannica.com/EBchecked/topic/535878/Jean-Pierre-Serre|title=Jean-Pierre Serre|date=5 February 1997|encyclopedia=Encyclopædia Britannica|access-date=19 August 2014|archive-date=6 October 2014|archive-url=https://web.archive.org/web/20141006104956/http://www.britannica.com/EBchecked/topic/535878/Jean-Pierre-Serre|url-status=live}}</ref> | "Achieved major results on the homotopy groups of spheres, especially in his use of the method of spectral sequences. Reformulated and extended some of the main results of complex variable theory in terms of sheaves."<ref name="54reasons" />

| | {{sortname|Klaus|Roth}} | University College London, UK | Imperial College London, UK<ref>{{Harvnb|McKinnon Riehm|Hoffman|2011|p=212}}</ref> | "for solving a famous problem of number theory, namely, the determination of the exact exponent in the Thue-Siegel inequality"<ref name="hopf">H. Hopf. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1958/ICM1958.ocr.pdf Proceedings of the International Congress of Mathematicians 1958.] {{Webarchive|url=https://web.archive.org/web/20220408074808/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1958/ICM1958.ocr.pdf |date=8 April 2022 }} Report of the Inaugural Session. p. liv</ref>

| 60px | {{sortname|René|Thom}} | University of Strasbourg, France | Institut des Hautes Études Scientifiques, France<ref>{{cite web |url=http://www.robertnowlan.com/pdfs/Thom,%20Rene.pdf |title=René Thom |website=Robertnowlan.com |access-date=31 March 2017 |archive-url=https://web.archive.org/web/20160527024340/http://www.robertnowlan.com/pdfs/Thom,%20Rene.pdf |archive-date=27 May 2016 |url-status=dead }}</ref> | "for creating the theory of 'Cobordisme' which has, within the few years of its existence, led to the most penetrating insight into the topology of differentiable manifolds."<ref name="hopf" />

| 60px | {{sortname|Lars|Hörmander}} | Stockholm University, Sweden | Lund University, Sweden<ref>{{cite web |url=http://smai.emath.fr/IMG/pdf/matapli100_Hormander.pdf |title=A tribute to Lars Hörmander |website=Smai.emath.fr |access-date=31 March 2017 |archive-date=4 June 2016 |archive-url=https://web.archive.org/web/20160604080024/http://smai.emath.fr/IMG/pdf/matapli100_Hormander.pdf |url-status=live }}</ref> | "Worked in partial differential equations. Specifically, contributed to the general theory of linear differential operators. The questions go back to one of Hilbert's problems at the 1900 congress."<ref name="62reasons">{{cite web |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1962/index.html |title=Fields Medals 1962 |publisher=International Mathematical Union |website=mathunion.org |access-date=7 April 2019 |archive-date=8 April 2022 |archive-url=https://web.archive.org/web/20220408074729/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1962/index.html |url-status=live }}</ref>

| 60px | {{sortname|John|Milnor}} | Princeton University, US | Stony Brook University, US<ref>{{cite web|url=http://www.math.sunysb.edu/~jack/|title=John W. Milnor|date=5 March 1997|publisher=Stony Brook University|access-date=17 August 2014|archive-date=30 August 2014|archive-url=https://web.archive.org/web/20140830025217/http://www.math.sunysb.edu/%7Ejack/|url-status=live}}</ref> | "Proved that a 7-dimensional sphere can have several differential structures; this led to the creation of the field of differential topology" (see exotic sphere).<ref name="62reasons" />

|rowspan=4| 1966 |rowspan=4| Moscow, USSR

| 60px | {{sortname|Michael|Atiyah}} | University of Oxford, UK | University of Edinburgh, UK<ref>{{cite web |language=es |url=http://upcommons.upc.edu/video/bitstream/2099.2/946/17/Poster05-AbelPrize-CV.pdf |title=Sir Michael F. Atiyah : The Abel Prize |website=Upcommons.upc.edu |access-date=31 March 2017 |archive-date=16 June 2013 |archive-url=https://web.archive.org/web/20130616140748/http://upcommons.upc.edu/video/bitstream/2099.2/946/17/Poster05-AbelPrize-CV.pdf |url-status=live }}</ref> | "Did joint work with Hirzebruch in K-theory; proved jointly with Singer the index theorem of elliptic operators on complex manifolds; worked in collaboration with Bott to prove a fixed point theorem related to the 'Lefschetz formula'."<ref name="66reasons">{{cite web |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1966/index.html |title=Fields Medals 1966 |publisher=International Mathematical Union |website=mathunion.org |access-date=7 April 2019 |archive-date=22 March 2019 |archive-url=https://web.archive.org/web/20190322225223/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1966/index.html |url-status=live }}</ref>

| | {{sortname|Paul|Cohen}} | Stanford University, US | Stanford University, US<ref>{{cite web |url=http://historicalsociety.stanford.edu/pdfmem/Cohen_P.pdf |title=Memorial Resolution – Paul Cohen (1934–2007) |date=2011 |publisher=Stanford Historical Society |access-date=24 August 2014 |url-status=dead |archive-url=https://web.archive.org/web/20150105133237/http://historicalsociety.stanford.edu/pdfmem/Cohen_P.pdf |archive-date=5 January 2015 }}</ref> | "Used technique called "forcing" to prove the independence in set theory of the axiom of choice and of the generalized continuum hypothesis. The latter problem was the first of Hilbert's problems of the 1900 Congress."<ref name="66reasons" />

| 60px | {{sortname|Alexander|Grothendieck}} | Institut des Hautes Études Scientifiques, France | Centre National de la Recherche Scientifique, France<ref>{{cite web |url=http://www.math.ucdenver.edu/~jloats/StudentCELEBS/Grothendieck_Trenkamp.pdf |title=Alexander Grothendieck |website=Math.ucdenver.edu |access-date=31 March 2017 |archive-date=20 October 2016 |archive-url=https://web.archive.org/web/20161020015323/http://www.math.ucdenver.edu/~jloats/StudentCELEBS/Grothendieck_Trenkamp.pdf |url-status=dead }}</ref> | "Built on work of Weil and Zariski and effected fundamental advances in algebraic geometry. He introduced the idea of K-theory (the Grothendieck groups and rings). Revolutionized homological algebra in his celebrated ‘''Tôhoku'' paper’."<ref name="66reasons" />

| 60px | {{sortname|Stephen|Smale}} | University of California, Berkeley, US | City University of Hong Kong, Hong Kong<ref>{{cite web|url=http://www6.cityu.edu.hk/ma/people/profile/smales.htm|title=Prof. Stephen SMALE (史梅爾)|date=5 April 2012|publisher=City University of Hong Kong|access-date=18 August 2014|archive-date=9 November 2014|archive-url=https://web.archive.org/web/20141109090333/http://www6.cityu.edu.hk/ma/people/profile/smales.htm|url-status=live}}</ref> | "Worked in differential topology where he proved the generalized Poincaré conjecture in dimension <math>n \geq 5</math>: Every closed, n-dimensional manifold homotopy-equivalent to the n-dimensional sphere is homeomorphic to it. Introduced the method of handle-bodies to solve this and related problems."<ref name="66reasons" />

|rowspan=4| 1970 |rowspan=4| Nice, France | 60px | {{sortname|Alan|Baker|Alan Baker (mathematician)}} | University of Cambridge, UK | Trinity College, Cambridge, UK<ref>{{cite web|url=http://www.heidelberg-laureate-forum.org/blog/laureate/alan-baker|title=The Laureates|date=25 September 2013|publisher=Heidelberg Laureate Forum Foundation (HLFF)|access-date=16 August 2014|archive-date=18 October 2014|archive-url=https://web.archive.org/web/20141018234635/http://www.heidelberg-laureate-forum.org/blog/laureate/alan-baker/|url-status=live}}</ref> | "Generalized the Gelfond-Schneider theorem (the solution to Hilbert's seventh problem). From this work he generated transcendental numbers not previously identified."<ref name="70reasons">{{cite web |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1970/index.html |title=Fields Medals 1970 |publisher=International Mathematical Union |website=mathunion.org |access-date=7 April 2019 |archive-date=8 April 2022 |archive-url=https://web.archive.org/web/20220408074621/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1970/index.html |url-status=live }}</ref>

| 60px | {{sortname|Heisuke|Hironaka}} | Harvard University, US | Kyoto University, Japan<ref>{{cite web |url=https://www.ams.org/notices/200509/fea-hironaka.pdf |title=Interview with Heisuke Hironaka |website=Ams.org |access-date=31 March 2017 |archive-date=8 April 2022 |archive-url=https://web.archive.org/web/20220408074623/https://www.ams.org/notices/200509/fea-hironaka.pdf |url-status=live }}</ref><ref>{{cite web|url=http://www.kurims.kyoto-u.ac.jp/en/emeritus.html|title=Professor Emeritus|date=26 May 2007|publisher=Research Institute for Mathematical Sciences, Kyoto, Japan|access-date=16 August 2014|archive-date=5 April 2022|archive-url=https://web.archive.org/web/20220405035547/https://www.kurims.kyoto-u.ac.jp/en/emeritus.html|url-status=dead}}</ref> | "Generalized work of Zariski who had proved for dimension ≤ 3 the theorem concerning the resolution of singularities on an algebraic variety. Hironaka proved the results in any dimension."<ref name="70reasons" />

| | {{sortname|Sergei|Novikov|Sergei Novikov (mathematician)}} | Moscow State University, USSR | Steklov Mathematical Institute, Russia Moscow State University, Russia University of Maryland-College Park, US<ref>{{cite web |url=http://www.mi.ras.ru/~snovikov/998.pdf |title=Interview with Sergey P. Novikov |website=Mi.ras.ru |access-date=31 March 2017 |archive-date=14 May 2016 |archive-url=https://web.archive.org/web/20160514032252/http://www.mi.ras.ru/~snovikov/998.pdf |url-status=live }}</ref><ref>{{cite web|url=http://www.mi.ras.ru/~snovikov/index.html|title=Novikov, Sergei Petrovich|date=1 January 2012|publisher=Russian Academy of Science|access-date=20 August 2014|archive-date=26 July 2014|archive-url=https://web.archive.org/web/20140726083130/http://www.mi.ras.ru/~snovikov/index.html|url-status=live}}</ref> | "Made important advances in topology, the most well-known being his proof of the topological invariance of the Pontryagin classes of the differentiable manifold. His work included a study of the cohomology and homotopy of Thom spaces."<ref name="70reasons" />

| 60px | {{sortname|John G.|Thompson}} | University of Cambridge, UK | University of Cambridge, UK University of Florida, US<ref>{{cite web |url=http://www.abelprize.no/c53860/binfil/download.php?tid=53792 |format=PDF |title=John Griggs Thompson |website=Abelprize.no |access-date=31 March 2017 |archive-date=11 June 2016 |archive-url=https://web.archive.org/web/20160611151241/http://www.abelprize.no/c53860/binfil/download.php?tid=53792 |url-status=dead }}</ref> | "Proved jointly with W. Feit that all non-cyclic finite simple groups have even order. The extension of this work by Thompson determined the minimal simple finite groups, that is, the simple finite groups whose proper subgroups are solvable."<ref name="70reasons" />

|rowspan=2| 1974 |rowspan=2| Vancouver, Canada

| 60px | {{sortname|Enrico|Bombieri}} | University of Pisa, Italy | Institute for Advanced Study, US<ref>{{cite book |editor1-last=Bartocci |editor1-first=Claudio |editor2-last=Betti |editor2-first=Renato |editor3-last=Guerraggio |editor3-first=Angelo |display-editors = 3 |editor4-last=Lucchetti |editor4-first=Roberto Lucchetti |title=Vite Mathematiche |trans-title=Mathematical Lives: Protagonists of the Twentieth Century From Hilbert to Wiles |edition=2011 |publisher=Springer |date=2011 |pages=2013–2014 |isbn=978-3642136054 }}</ref> | "Major contributions in the primes, in univalent functions and the local Bieberbach conjecture, in theory of functions of several complex variables, and in theory of partial differential equations and minimal surfaces – in particular, to the solution of Bernstein's problem in higher dimensions."<ref name="74reasons">{{cite web |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1974/index.html |title=Fields Medals 1974 |publisher=International Mathematical Union |website=mathunion.org |access-date=7 April 2019 |archive-date=8 April 2022 |archive-url=https://web.archive.org/web/20220408074703/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1974/index.html |url-status=live }}</ref>

| 60px | {{sortname|David|Mumford}} | Harvard University, US | Brown University, US<ref>{{cite web|url=https://www.dam.brown.edu/people/facultypage.mumford.html|title=David Mumford|publisher=The Division of Applied Mathematics, Brown University|access-date=18 August 2014|archive-date=6 October 2014|archive-url=https://web.archive.org/web/20141006072947/http://www.dam.brown.edu/people/facultypage.mumford.html|url-status=live}}</ref> | "Contributed to problems of the existence and structure of varieties of moduli, varieties whose points parametrize isomorphism classes of some type of geometric object. Also made several important contributions to the theory of algebraic surfaces."<ref name="74reasons" />

| 60px | {{sortname|Pierre|Deligne}} | Institut des Hautes Études Scientifiques, France | Institute for Advanced Study, US<ref>{{cite web |url=http://www.abelprize.no/c57681/binfil/download.php?tid=57756 |format=PDF |title=Pierre Deligne |website=Abelprize.no |access-date=31 March 2017 |archive-date=3 March 2016 |archive-url=https://web.archive.org/web/20160303181225/http://www.abelprize.no/c57681/binfil/download.php?tid=57756 |url-status=dead }}</ref> | "Gave solution of the three Weil conjectures concerning generalizations of the Riemann hypothesis to finite fields. His work did much to unify algebraic geometry and algebraic number theory."<ref name="78reasons">{{cite web |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1978/index.html |title=Fields Medals 1978 |publisher=International Mathematical Union |website=mathunion.org |access-date=7 April 2019 |archive-date=10 October 2020 |archive-url=https://web.archive.org/web/20201010144934/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1978/index.html |url-status=live }}</ref>

| 60px | {{sortname|Charles|Fefferman}} | Princeton University, US | Princeton University, US<ref>{{cite web |url=https://web.math.princeton.edu/WebCV/FeffermanCV.pdf |title=CV : Charles Fefferman |access-date=31 March 2017 |archive-date=8 April 2022 |archive-url=https://web.archive.org/web/20220408074624/https://web.math.princeton.edu/WebCV/FeffermanCV.pdf |url-status=live }}</ref> | "Contributed several innovations that revised the study of multidimensional complex analysis by finding correct generalizations of classical (low-dimensional) results."<ref name="78reasons" />

| 60px | {{sortname|Grigory|Margulis}} | Moscow State University, USSR | Yale University, US<ref>{{cite web|url=http://users.math.yale.edu/public_html/People/gam3.html|title=Yale Mathematics Department: Gregory A. Margulis|access-date=16 March 2015|archive-date=5 January 2015|archive-url=https://web.archive.org/web/20150105132947/http://users.math.yale.edu/public_html/People/gam3.html|url-status=live}}</ref> | "Provided innovative analysis of the structure of Lie groups. His work belongs to combinatorics, differential geometry, ergodic theory, dynamical systems, and Lie groups."<ref name="78reasons" />

|60x60px | {{sortname|Daniel|Quillen}} | Massachusetts Institute of Technology, US | University of Oxford, UK<ref>{{cite journal |url=https://www.ams.org/notices/201210/rtx121001392p.pdf |title=Daniel Quillen |first1=Eric |last1=Friedlander |author-link=Eric Friedlander |first2=Daniel |last2=Grayson |journal=Notices of the AMS |volume=59 |issue=10 |pages=1392–1406 |doi=10.1090/noti903 |doi-access=free |date=November 2012 |access-date=31 March 2017 |archive-date=8 April 2022 |archive-url=https://web.archive.org/web/20220408074623/https://www.ams.org/notices/201210/rtx121001392p.pdf |url-status=live }}</ref> | "The prime architect of the higher algebraic K-theory, a new tool that successfully employed geometric and topological methods and ideas to formulate and solve major problems in algebra, particularly ring theory and module theory."<ref name="78reasons" />

| 60px | {{sortname|Alain|Connes}} | Institut des Hautes Études Scientifiques, France | Institut des Hautes Études Scientifiques, France Collège de France, France Ohio State University, US<ref>{{cite web|url=http://www.alainconnes.org/en/|title=Alain Connes|date=25 May 2012|access-date=18 August 2014|archive-date=29 August 2014|archive-url=https://web.archive.org/web/20140829154109/http://www.alainconnes.org/en/|url-status=live}}</ref> | "Contributed to the theory of operator algebras, particularly the general classification and structure theorem of factors of type III, classification of automorphisms of the hyperfinite factor, classification of injective factors, and applications of the theory of C*-algebras to foliations and differential geometry in general."<ref name="82reasons">{{cite web |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1982/index.html |title=Fields Medals and Nevanlinna Prize 1982 |publisher=International Mathematical Union |website=mathunion.org |access-date=7 April 2019 |archive-date=3 December 2018 |archive-url=https://web.archive.org/web/20181203152158/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1982/index.html |url-status=live }}</ref>

| 60px | {{sortname|William|Thurston}} | Princeton University, US | Cornell University, US<ref>{{cite web|url=https://www.math.cornell.edu/spb/index.php|title=William P. Thurston, 1946–2012|date=30 August 2012|access-date=18 August 2014|archive-date=21 August 2016|archive-url=https://web.archive.org/web/20160821013938/http://www.math.cornell.edu/spb/index.php|url-status=live}}</ref> | "Revolutionized study of topology in 2 and 3 dimensions, showing interplay between analysis, topology, and geometry. Contributed idea that a very large class of closed 3-manifolds carry a hyperbolic structure."<ref name="82reasons" />

| 60px | {{sortname|Shing-Tung|Yau}} | Institute for Advanced Study, US | Tsinghua University, China<ref>{{cite web |url=http://www.doctoryau.com/yau_cv.pdf |title=CV : Shing-Tung Yau |website=Doctoryau.com |access-date=31 March 2017 |archive-url=https://web.archive.org/web/20171025135744/http://www.doctoryau.com/yau_cv.pdf |archive-date=25 October 2017 |url-status=usurped }}</ref> | "Made contributions in differential equations, also to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex Monge–Ampère equations."<ref name="82reasons" />

| 60px | {{sortname|Simon|Donaldson}} | University of Oxford, UK | Imperial College London, UK<ref>{{cite web|url=http://wwwf.imperial.ac.uk/~skdona/|title=Simon Donaldson (Royal Society Research Professor)|date=16 January 2008|publisher=Department of Mathematics, Imperial College, Queen's Gate, London|access-date=16 August 2014|archive-date=15 September 2014|archive-url=https://web.archive.org/web/20140915032606/http://wwwf.imperial.ac.uk/~skdona/|url-status=live}}</ref> Stony Brook University, US<ref>{{cite web|url=http://scgp.stonybrook.edu/people/faculty/bios/simon-donaldson|title=Simon Donaldson|access-date=16 March 2015|archive-date=20 March 2015|archive-url=https://web.archive.org/web/20150320072154/http://scgp.stonybrook.edu/people/faculty/bios/simon-donaldson|url-status=live}}</ref> | "Received medal primarily for his work on topology of four-manifolds, especially for showing that there is a differential structure on euclidian four-space which is different from the usual structure."<ref name="86reasons">{{cite web |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1986/index.html |title=Fields Medals and Nevanlinna Prize 1986 |publisher=International Mathematical Union |website=mathunion.org |access-date=7 April 2019 |archive-date=22 March 2019 |archive-url=https://web.archive.org/web/20190322225314/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1986/index.html |url-status=live }}</ref><ref name="IMU Fields Medal 1986">{{cite web | title=Fields Medals 1986 | website=International Mathematical Union (IMU) | date=1986 | url=https://www.mathunion.org/imu-awards/fields-medal/fields-medals-1986 | access-date=2024-01-24 | archive-date=24 January 2024 | archive-url=https://web.archive.org/web/20240124060355/https://www.mathunion.org/imu-awards/fields-medal/fields-medals-1986 | url-status=live }}</ref>

| 60px | {{sortname|Gerd|Faltings}} | Princeton University, US | Max Planck Institute for Mathematics, Germany<ref>{{cite web|url=http://www.heidelberg-laureate-forum.org/blog/laureate/gerd-faltings/|title=The Laureates|date=6 October 2013|publisher=Heidelberg Laureate Forum Foundation (HLFF)|access-date=16 August 2014|archive-url=https://web.archive.org/web/20141006065705/http://www.heidelberg-laureate-forum.org/blog/laureate/gerd-faltings/|archive-date=6 October 2014|url-status=dead}}</ref> | "Using methods of arithmetic algebraic geometry, he received medal primarily for his proof of the Mordell Conjecture."<ref name="86reasons" />

| 60px | {{sortname|Michael|Freedman}} | University of California, San Diego, US | Microsoft Station Q, US<ref>{{cite web|url=http://celebratio.org/cmmedia/essaypdf/19_main_3.pdf|title=Michael H. Freedman|author=Rob Kirby|date=2012|work=celebratio.org|url-status=dead|archive-url=https://web.archive.org/web/20141006102901/http://celebratio.org/cmmedia/essaypdf/19_main_3.pdf|archive-date=6 October 2014}}</ref> | "Developed new methods for topological analysis of four-manifolds. One of his results is a proof of the four-dimensional Poincaré Conjecture."<ref name="86reasons" />

| | {{sortname|Vladimir|Drinfeld}} | B Verkin Institute for Low Temperature Physics and Engineering, USSR<ref>{{cite encyclopedia|url=https://www.britannica.com/EBchecked/topic/171669/Vladimir-Gershonovich-Drinfeld|title=Vladimir Gershonovich Drinfeld|date=19 August 2009|encyclopedia=Encyclopædia Britannica|access-date=2 September 2014|archive-date=10 August 2014|archive-url=https://web.archive.org/web/20140810212856/http://www.britannica.com/EBchecked/topic/171669/Vladimir-Gershonovich-Drinfeld|url-status=live}}</ref> | University of Chicago, US<ref>{{cite web|url=http://www-history.mcs.st-and.ac.uk/Biographies/Drinfeld.html|title=Vladimir Gershonovich Drinfeld|date=18 August 2009|publisher=School of Mathematics and Statistics, University of St Andrews, Scotland|access-date=16 August 2014|archive-date=6 October 2014|archive-url=https://web.archive.org/web/20141006123607/http://www-history.mcs.st-and.ac.uk/Biographies/Drinfeld.html|url-status=live}}</ref> | "Drinfeld's main preoccupation in the last decade [are] Langlands' program and quantum groups. In both domains, Drinfeld's work constituted a decisive breakthrough and prompted a wealth of research."<ref>Yuri Ivanovich Manin. ''On the mathematical work of Vladimir Drinfeld''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1990.1/ICM1990.1.ocr.pdf Proceedings of the International Congress of Mathematicians 1990. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074657/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1990.1/ICM1990.1.ocr.pdf |date=8 April 2022 }} pp. 3–7</ref>

| 60px | {{sortname|Vaughan|Jones}} | University of California, Berkeley, US | University of California, Berkeley, US<ref>{{cite web|url=http://math.berkeley.edu/~vfr/vita/|title=Curriculum Vitae: Vaughan F. R. Jones|publisher=University of California, Berkeley|date=10 November 2001|access-date=16 August 2014|url-status=dead|archive-url=https://web.archive.org/web/20130806082228/http://math.berkeley.edu/~vfr/vita|archive-date=6 August 2013}}</ref> Vanderbilt University, US<ref>{{cite web|last=Salisbury|first=David|title=Fields Medalist joins Vanderbilt faculty|url=http://news.vanderbilt.edu/2011/04/vaughan-jones/|publisher=Vanderbilt University|access-date=17 May 2011|date=6 April 2011|archive-date=14 April 2011|archive-url=https://web.archive.org/web/20110414130456/http://news.vanderbilt.edu/2011/04/vaughan-jones/|url-status=live}}</ref> | "Jones discovered an astonishing relationship between von Neumann algebras and geometric topology. As a result, he found a new polynomial invariant for knots and links in 3-space."<ref>Joan S. Birman. ''The work of Vaughan F. R. Jones''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1990.1/ICM1990.1.ocr.pdf Proceedings of the International Congress of Mathematicians 1990. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074657/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1990.1/ICM1990.1.ocr.pdf |date=8 April 2022 }} pp. 9–18</ref>

| 60px | {{sortname|Shigefumi|Mori}} | Kyoto University, Japan | Kyoto University, Japan<ref>{{cite web|url=http://www.heidelberg-laureate-forum.org/blog/laureate/shigefumi-mori/|title=The Laureates|publisher=Heidelberg Laureate Forum Foundation (HLFF)|date=10 April 2014|access-date=16 August 2014|archive-url=https://web.archive.org/web/20140815120453/http://www.heidelberg-laureate-forum.org/blog/laureate/shigefumi-mori/|archive-date=15 August 2014|url-status=dead}}</ref> | "The most profound and exciting development in algebraic geometry during the last decade or so was [...] ''Mori's Program'' in connection with the classification problems of algebraic varieties of dimension three." "Early in 1979, Mori brought to algebraic geometry a completely new excitement, that was his proof of Hartshorne's conjecture."<ref>Heisuke Hironaka. ''On the work of Shigefumi Mori''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1990.1/ICM1990.1.ocr.pdf Proceedings of the International Congress of Mathematicians 1990. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074657/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1990.1/ICM1990.1.ocr.pdf |date=8 April 2022 }} pp. 19–25</ref>

| 60px | {{sortname|Edward|Witten}} | Institute for Advanced Study, US | Institute for Advanced Study, US<ref>{{cite web |url=http://www.sns.ias.edu/~witten/CurrentCV.pdf |title=Edward Witten – Vita |date=2011 |access-date=26 October 2011 |url-status=dead |archive-url=https://web.archive.org/web/20120204111241/http://www.sns.ias.edu/~witten/CurrentCV.pdf |archive-date=4 February 2012 }}</ref> | "Time and again he has surprised the mathematical community by a brilliant application of physical insight leading to new and deep mathematical theorems."<ref>{{cite web |url=http://www.mathunion.org/ICM/ICM1990.1/Main/icm1990.1.0031.0036.ocr.pdf |title=On the Work of Edward Witten |author=Michael Atiyah |website=Mathunion.org |access-date=31 March 2017 |url-status=dead |archive-url=https://web.archive.org/web/20170301004342/http://www.mathunion.org/ICM/ICM1990.1/Main/icm1990.1.0031.0036.ocr.pdf |archive-date=1 March 2017 }}</ref>

| 60px | {{sortname|Jean|Bourgain}} | Institut des Hautes Études Scientifiques, France | Institute for Advanced Study, US<ref>{{cite web |url=https://www.math.ias.edu/files/bourgain/CVBourgain.pdf |title=CV : Jean Bourgain |website=Math.ias.edu |access-date=31 March 2017 |archive-date=30 May 2017 |archive-url=https://web.archive.org/web/20170530041057/https://www.math.ias.edu/files/bourgain/CVBourgain.pdf |url-status=live }}</ref> | "Bourgain's work touches on several central topics of mathematical analysis: the geometry of Banach spaces, convexity in high dimensions, harmonic analysis, ergodic theory, and finally, nonlinear partial differential equations from mathematical physics."<ref>Luis Caffarelli. ''The work of Jean Bourgain''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1994.1/ICM1994.1.ocr.pdf Proceedings of the International Congress of Mathematicians 1994. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074735/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1994.1/ICM1994.1.ocr.pdf |date=8 April 2022 }} pp. 3–5</ref> |-

| 60px | {{sortname|Pierre-Louis|Lions}} | University of Paris 9, France | Collège de France, France École polytechnique, France<ref>{{cite web|url=http://www.college-de-france.fr/site/pierre-louis-lions/biographie.htm|title=Collège de France|website=College-de-france.fr|date=16 December 2013|access-date=18 August 2014|archive-date=15 September 2013|archive-url=https://web.archive.org/web/20130915103327/http://www.college-de-france.fr/site/pierre-louis-lions/biographie.htm|url-status=live}}</ref> | "His contributions cover a variety of areas, from probability theory to partial differential equations (PDEs). Within the PDE area he has done several beautiful things in nonlinear equations. The choice of his problems have always been motivated by applications."<ref>S. R. S. Varadhan. ''The work of Pierre-Louis Lions''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1994.1/ICM1994.1.ocr.pdf Proceedings of the International Congress of Mathematicians 1994. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074735/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1994.1/ICM1994.1.ocr.pdf |date=8 April 2022 }} pp. 6–10</ref>

| 60px | {{sortname|Jean-Christophe|Yoccoz}} | Paris-Sud 11 University, France | Collège de France, France<ref>{{cite web|url=http://www.college-de-france.fr/site/jean-christophe-yoccoz/biographie.htm|title=Collège de France|website=College-de-france.fr|date=16 December 2013|access-date=18 August 2014|archive-date=5 January 2015|archive-url=https://web.archive.org/web/20150105141948/http://www.college-de-france.fr/site/jean-christophe-yoccoz/biographie.htm|url-status=live}}</ref> | "Yoccoz obtained a very enlightening proof of Bruno's theorem, and he was able to prove the converse [...] Palis and Yoccoz obtained a complete system of C∞ conjugation invariants for Morse-Smale diffeomorphisms."<ref>Adrien Douady. ''Presentation de Jean-Christophe Yoccoz''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1994.1/ICM1994.1.ocr.pdf Proceedings of the International Congress of Mathematicians 1994. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074735/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1994.1/ICM1994.1.ocr.pdf |date=8 April 2022 }} pp. 11–16</ref>

| 60px | {{sortname|Efim|Zelmanov}} | University of Wisconsin-Madison University of Chicago, US | Steklov Mathematical Institute, Russia, University of California, San Diego, US<ref>{{cite web |url=http://www.ime.usp.br/~grishkov/papers/CV.Zelm..pdf |title=CV : Efim Zelmanov |website=Ime.usp.br |access-date=31 March 2017 |archive-date=2 July 2017 |archive-url=https://web.archive.org/web/20170702045759/https://www.ime.usp.br/~grishkov/papers/CV.Zelm..pdf |url-status=live }}</ref> | "For the solution of the restricted Burnside problem."<ref>Walter Feit. ''On the Work of Efim Zelmanov''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1994.1/ICM1994.1.ocr.pdf Proceedings of the International Congress of Mathematicians 1994. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074735/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1994.1/ICM1994.1.ocr.pdf |date=8 April 2022 }} pp. 17–24</ref>

| 60px | {{sortname|Richard|Borcherds}} | University of California, Berkeley, US University of Cambridge, UK | University of California, Berkeley, US<ref>{{cite web|url=http://www.heidelberg-laureate-forum.org/blog/laureate/richard-borcherds/|title=The Laureates|publisher=Heidelberg Laureate Forum Foundation (HLFF)|date=10 April 2014|access-date=16 August 2014|archive-url=https://web.archive.org/web/20141006103635/http://www.heidelberg-laureate-forum.org/blog/laureate/richard-borcherds/|archive-date=6 October 2014|url-status=dead}}</ref> | "For his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex algebras and Borcherds' Lie algebras, the proof of the Conway–Norton moonshine conjecture and the discovery of a new class of automorphic infinite products."<ref name="1998cer">''Opening ceremony''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1998.1/ICM1998.1.ocr.pdf Proceedings of the International Congress of Mathematicians 1998. Volume I] {{Webarchive|url=https://web.archive.org/web/20220422051649/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1998.1/ICM1998.1.ocr.pdf |date=22 April 2022 }} pp. 46–48</ref>

| 60px | {{sortname|Timothy|Gowers}} | University of Cambridge, UK | University of Cambridge, UK<ref>{{cite encyclopedia|url=https://www.britannica.com/EBchecked/topic/240293/William-Timothy-Gowers|title=William Timothy Gowers|encyclopedia=Encyclopædia Britannica|date=28 March 2009|access-date=16 August 2014|archive-date=6 October 2014|archive-url=https://web.archive.org/web/20141006080937/http://www.britannica.com/EBchecked/topic/240293/William-Timothy-Gowers|url-status=live}}</ref> | "For his contributions to functional analysis and combinatorics, developing a new vision of infinite-dimensional geometry, including the solution of two of Banach's problems and the discovery of the so called Gowers' dichotomy: every infinite dimensional Banach space contains either a subspace with many symmetries (technically, with an unconditional basis) or a subspace every operator on which is Fredholm of index zero."<ref name="1998cer" />

| 60px | {{sortname|Maxim|Kontsevich}} | Institut des Hautes Études Scientifiques, France Rutgers University, US | Institut des Hautes Études Scientifiques, France Rutgers University, US<ref>{{cite web|url=https://www.ihes.fr/~maxim/CVAnglais.html|title=CV Maxim Kontsevich|publisher=Institut des Hautes Études Scientifiques|date=22 November 2009|access-date=16 August 2014|url-status=dead|archive-url=https://web.archive.org/web/20141010040126/http://www.ihes.fr/~maxim/CVAnglais.html|archive-date=10 October 2014}}</ref> | "For his contributions to algebraic geometry, topology, and mathematical physics, including the proof of Witten's conjecture of intersection numbers in moduli spaces of stable curves, construction of the universal Vassiliev invariant of knots, and formal quantization of Poisson manifolds."<ref name="1998cer" />

| 60px | {{sortname|Curtis T.|McMullen}} | Harvard University, US | Harvard University, US<ref>{{cite web |url=http://abel.math.harvard.edu/~ctm/vita/resume.pdf |title=CV : Curtis T McMullen |website=Abel.math.harvard.edu |access-date=31 March 2017 |archive-date=10 February 2017 |archive-url=https://web.archive.org/web/20170210173438/http://abel.math.harvard.edu/~ctm/vita/resume.pdf |url-status=live }}</ref> | "For his contributions to the theory of holomorphic dynamics and geometrization of three-manifolds, including proofs of Bers' conjecture on the density of cusp points in the boundary of the Teichmüller space, and Kra's theta-function conjecture."<ref name="1998cer" />

| 60px | {{sortname|Laurent|Lafforgue}} | Institut des Hautes Études Scientifiques, France | Institut des Hautes Études Scientifiques, France<ref>{{cite web|url=https://www.ihes.fr/~lafforgue/cv.html|title=Curriculum Vitae|publisher=ihes|date=6 December 2005|access-date=19 August 2014|archive-date=10 March 2022|archive-url=https://web.archive.org/web/20220310232627/http://laurentlafforgue.org/cv.html|url-status=live}}</ref> | "Laurent Lafforgue has been awarded the Fields Medal for his proof of the Langlands correspondence for the full linear groups GLr (r≥1) over function fields of positive characteristic."<ref>Gérard Laumon. ''The work of Laurent Lafforgue''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2002.1/ICM2002.1.ocr.pdf Proceedings of the International Congress of Mathematicians 2002. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074623/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2002.1/ICM2002.1.ocr.pdf |date=8 April 2022 }} pp. 91–97</ref>

| 60px | {{sortname|Vladimir|Voevodsky}} | Institute for Advanced Study, US | Institute for Advanced Study, US<ref>{{cite web |url=http://www.math.ias.edu/~vladimir/Site3/home_files/mitcv12.pdf |title=CV : Vladimir Voevodsky |website=Math.ias.edu |access-date=31 March 2017 |archive-date=2 April 2016 |archive-url=https://web.archive.org/web/20160402041701/http://www.math.ias.edu/~vladimir/Site3/home_files/mitcv12.pdf |url-status=live }}</ref> | "He defined and developed motivic cohomology and the A1-homotopy theory, provided a framework for describing many new cohomology theories for algebraic varieties; he proved the Milnor conjectures on the K-theory of fields."<ref>Christophe Soulé. ''The work of Vladimir Voevodsky''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2002.1/ICM2002.1.ocr.pdf Proceedings of the International Congress of Mathematicians 2002. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074623/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2002.1/ICM2002.1.ocr.pdf |date=8 April 2022 }} pp. 99–103</ref>

|rowspan=4| 2006 |rowspan=4| Madrid, Spain

| 60px | {{sortname|Andrei|Okounkov}} | Princeton University, US | Columbia University, US<ref>{{cite web|url=http://www.math.columbia.edu/people/directory/?dname=Okounkov&did=69|title=Department of Mathematics|date=20 December 2012|publisher=Columbia University, Department of Mathematics|access-date=19 August 2014|archive-date=6 October 2014|archive-url=https://web.archive.org/web/20141006102403/http://www.math.columbia.edu/people/directory/?dname=Okounkov&did=69|url-status=live}}</ref> University of California, Berkeley, US<ref>{{cite web|url=https://math.berkeley.edu/people/faculty/andrei-okounkov|access-date=August 22, 2022|title=Andrei Okounkov|publisher=Berkeley Mathematics|website=math.berkeley.edu|archive-date=22 February 2023|archive-url=https://web.archive.org/web/20230222214335/https://math.berkeley.edu/people/faculty/andrei-okounkov|url-status=live}}</ref> | "For his contributions bridging probability, representation theory and algebraic geometry."<ref name="2006cer">''Opening ceremony''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2006.1/ICM2006.1.ocr.pdf Proceedings of the International Congress of Mathematicians 2006. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074623/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2006.1/ICM2006.1.ocr.pdf |date=8 April 2022 }} p. 36</ref>

| 60px | {{sortname|Grigori|Perelman}} ''(declined)'' | None | St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences, Russia<ref>{{cite encyclopedia|url=https://www.britannica.com/EBchecked/topic/1272681/Grigori-Perelman|date=28 May 2008|encyclopedia=Encyclopædia Britannica|access-date=19 August 2014|title=Grigori Perelman | Biography & Facts|archive-date=16 September 2014|archive-url=https://web.archive.org/web/20140916012923/http://www.britannica.com/EBchecked/topic/1272681/Grigori-Perelman|url-status=live}}</ref> | "For his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow."<ref name="2006cer" />

| 60px | {{sortname|Terence|Tao}} | University of California, Los Angeles, US | University of California, Los Angeles, US<ref>{{cite web|url=https://www.math.ucla.edu/~tao/preprints/cv.html|title=Vitae and Bibliography for Terence Tao|date=16 March 2010|publisher=UCLA Dept. of Math.|access-date=19 August 2014|archive-date=8 April 2000|archive-url=https://web.archive.org/web/20000408183915/https://www.math.ucla.edu/~tao/preprints/cv.html|url-status=live}}</ref> | "For his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory."<ref name="2006cer" />

| 60px | {{sortname|Wendelin|Werner}} | Paris-Sud 11 University, France | ETH Zurich, Switzerland<ref>{{cite web|url=http://www.math.ethz.ch/~wewerner/|title=Wendelin WERNER|date=18 September 2013|publisher=ETH Zurich|access-date=19 August 2014|archive-date=6 October 2014|archive-url=https://web.archive.org/web/20141006131413/http://www.math.ethz.ch/~wewerner/|url-status=live}}</ref> | "For his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory."<ref name="2006cer" />

| 60px | {{sortname|Elon|Lindenstrauss}} | Hebrew University of Jerusalem, Israel Princeton University, US | Hebrew University of Jerusalem, Israel<ref>{{cite web|url=http://www.huji.ac.il/huji/nobel/lindE.htm|title=Nobel at HU|date=5 July 2011|publisher=The Hebrew University of Jerusalem|access-date=16 August 2014|archive-date=14 August 2014|archive-url=https://web.archive.org/web/20140814071745/http://www.huji.ac.il/huji/nobel/lindE.htm|url-status=live}}</ref> | "For his results on measure rigidity in ergodic theory, and their applications to number theory."<ref name="2010cer">''Opening ceremony''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2010.1/ICM2010.1.pdf Proceedings of the International Congress of Mathematicians 2010. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074655/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2010.1/ICM2010.1.pdf |date=8 April 2022 }} p. 23</ref>

| 60px | Ngô Bảo Châu | Paris-Sud 11 University, France Institute for Advanced Study, US | University of Chicago, US Institute for Advanced Study, US<ref>{{cite web|url=http://www.heidelberg-laureate-forum.org/blog/laureate/bao-chau-ngo/|title=Ngô Bảo Châu › Heidelberg Laureate Forum|access-date=16 March 2015|archive-url=https://web.archive.org/web/20150207021714/http://www.heidelberg-laureate-forum.org/blog/laureate/bao-chau-ngo/|archive-date=7 February 2015|url-status=dead}}</ref> | "For his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods."<ref name="2010cer" />

| 60px | {{sortname|Stanislav|Smirnov}} | University of Geneva, Switzerland | University of Geneva, Switzerland St. Petersburg State University, Russia<ref>{{cite web|url=http://www.unige.ch/~smirnov/|title=Home Page of Stanislav Smirnov|access-date=16 March 2015|archive-date=19 June 2013|archive-url=https://web.archive.org/web/20130619221150/http://www.unige.ch/~smirnov/|url-status=live}}</ref> | "For the proof of conformal invariance of percolation and the planar Ising model in statistical physics."<ref name="2010cer" />

| 60px | {{sortname|Cédric|Villani}} | École Normale Supérieure de Lyon, France Institut Henri Poincaré, France | Lyon University, France Institut Henri Poincaré, France<ref>{{cite web |url=http://cedricvillani.org/wp-content/uploads/2012/10/cv-2012.pdf |title=CV : Cedric Villani |website=Cedricvillani.org |access-date=31 March 2017 |archive-url=https://web.archive.org/web/20160623224603/http://cedricvillani.org/wp-content/uploads/2012/10/cv-2012.pdf |archive-date=23 June 2016 |url-status=dead }}</ref> | "For his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation."<ref name="2010cer" />

| 60px | {{sortname|Artur|Avila}} | University of Paris VII, France CNRS, France Instituto Nacional de Matemática Pura e Aplicada, Brazil | University of Zurich, Switzerland Instituto Nacional de Matemática Pura e Aplicada, Brazil | "For his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalization as a unifying principle."<ref name="2014cer">''Opening ceremony''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2014.1/ICM2014.1.pdf Proceedings of the International Congress of Mathematicians 2014. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074729/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2014.1/ICM2014.1.pdf |date=8 April 2022 }} p. 23</ref>

| 60px | {{sortname|Manjul|Bhargava}} | Princeton University, US | Princeton University, US<ref>{{cite web |url=http://www2.maths.ox.ac.uk/cmi/library/research_award/Bhargava/CV.pdf |title=CV : Manjul Bhargava |website=2.maths.ox.ac.uk |access-date=31 March 2017 |archive-date=22 December 2014 |archive-url=https://web.archive.org/web/20141222225037/http://www2.maths.ox.ac.uk/cmi/library/research_award/Bhargava/CV.pdf |url-status=live }}</ref><ref>{{cite web |url=http://www.mathunion.org/fileadmin/IMU/Prizes/2014/news_release_bhargava.pdf |title=The Work of Manjul Bhargava |website=Mathunion.org |access-date=31 March 2017 |url-status=dead |archive-url=https://web.archive.org/web/20170713133635/http://www.mathunion.org/fileadmin/IMU/Prizes/2014/news_release_bhargava.pdf |archive-date=13 July 2017 }}</ref><ref>{{cite web|url=https://www.math.princeton.edu/directory/faculty|title=Faculty|date=8 May 2012|publisher=The Princeton University, Department of Mathematics|access-date=19 December 2014|url-status=dead|archive-url=https://web.archive.org/web/20141225194217/http://www.math.princeton.edu/directory/faculty|archive-date=25 December 2014}}</ref> | "For developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves."<ref name="2014cer" />

| 60px | {{sortname|Martin|Hairer}} | University of Warwick, UK | École Polytechnique Fédérale de Lausanne, Switzerland Imperial College London, UK | "For his outstanding contributions to the theory of stochastic partial differential equations, and in particular for the creation of a theory of regularity structures for such equations."<ref name="2014cer" />

| 60px | {{sortname|Maryam|Mirzakhani}} | Stanford University, US | Stanford University, US<ref>{{cite web|url=http://www2.maths.ox.ac.uk/cmi/library/annual_report/ar2008/08Interview.pdf|title=Interview with Research Fellow Maryam Mirzakhani|access-date=24 August 2014|archive-date=27 August 2014|archive-url=https://web.archive.org/web/20140827222953/http://www2.maths.ox.ac.uk/cmi/library/annual_report/ar2008/08Interview.pdf|url-status=live}}</ref><ref>{{cite web|url=http://mathematics.stanford.edu/people/faculty-lecturers/|title=Department of Mathematics|date=22 January 2009|publisher=Stanford University|access-date=19 December 2014|archive-date=21 December 2014|archive-url=https://web.archive.org/web/20141221152037/http://mathematics.stanford.edu/people/faculty-lecturers/|url-status=live}}</ref> | "For her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces."<ref name="2014cer" />

|rowspan=4| 2018 |rowspan=4| Rio de Janeiro, Brazil | 60px | {{sortname|Caucher|Birkar}} | University of Cambridge, UK | Tsinghua University, China | "For the proof of the boundedness of Fano varieties and for contributions to the minimal model program."<ref name="2018cer">''Opening ceremonies''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2018/ICM-2018-vol1-ver1-eb.pdf Proceedings of the International Congress of Mathematicians 2018. Volume I] {{Webarchive|url=https://web.archive.org/web/20220408074623/https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2018/ICM-2018-vol1-ver1-eb.pdf |date=8 April 2022 }} pp. 13–16</ref>

| 60px | {{sortname|Alessio|Figalli}} | Swiss Federal Institute of Technology Zurich, Switzerland | Swiss Federal Institute of Technology Zurich, Switzerland | "For contributions to the theory of optimal transport and its applications in partial differential equations, metric geometry and probability."<ref name="2018cer" />

| 60px | {{sortname|Peter|Scholze}} | University of Bonn, Germany | University of Bonn, Germany | "For having transformed arithmetic algebraic geometry over p-adic fields."<ref name="2018cer" />

| 60px | {{sortname|Akshay|Venkatesh}} | Stanford University, US | Institute for Advanced Study, US<ref>{{cite web|url=https://www.ias.edu/press-releases/faculty-appointee-akshay-venkatesh-awarded-2018-fields-medal|title=Faculty Appointee Akshay Venkatesh Awarded 2018 Fields Medal|date=August 2018|access-date=2 August 2018|archive-date=24 January 2022|archive-url=https://web.archive.org/web/20220124080025/https://www.ias.edu/news/press-releases/venkatesh-fields|url-status=live}}</ref> |"For his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects."<ref name="2018cer" /> |- |rowspan=4| 2022 |rowspan=4| Helsinki, Finland{{efn|ICM 2022 was originally planned to be held in Saint Petersburg, Russia, but was moved online following the 2022 Russian invasion of Ukraine. The award ceremony for the Fields Medals and prize winner lectures took place in Helsinki, Finland and were live-streamed.<ref>{{Cite web |title=Decision of the Executive Committee of the IMU on the upcoming ICM 2022 and IMU General Assembly |url=https://www.mathunion.org/fileadmin/IMU/ICM2022/ICM_2022_statement.pdf |access-date=5 July 2022 |archive-date=2 April 2022 |archive-url=https://web.archive.org/web/20220402092339/https://www.mathunion.org/fileadmin/IMU/ICM2022/ICM_2022_statement.pdf |url-status=live }}</ref><ref>{{cite web|url=https://www.mathunion.org/icm/virtual-icm-2022|title=Virtual ICM 2022|website=International Mathematical Union|access-date=5 July 2022|archive-date=1 June 2023|archive-url=https://web.archive.org/web/20230601054456/https://www.mathunion.org/icm/virtual-icm-2022|url-status=live}}</ref>}} | 60px | {{sortname|Hugo|Duminil-Copin}} | Institut des Hautes Études Scientifiques, France University of Geneva, Switzerland<ref name="unige.ch">{{cite web | url=https://www.unige.ch/sciences/math/fields2022/en | title=Hugo Duminil-Copin – Fields Medal 2022 – UNIGE | date=28 June 2022 | access-date=5 July 2022 | archive-date=6 July 2022 | archive-url=https://web.archive.org/web/20220706023552/https://www.unige.ch/sciences/math/fields2022/en | url-status=live }}</ref> | Institut des Hautes Études Scientifiques, France University of Geneva, Switzerland<ref name="unige.ch"/> | "For solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four."<ref name="2022fields">{{cite web|url=https://www.mathunion.org/imu-awards/fields-medal/fields-medals-2022|title=Fields Medals 2022|website=International Mathematical Union|access-date=5 July 2022|archive-date=5 July 2022|archive-url=https://web.archive.org/web/20220705072608/https://www.mathunion.org/imu-awards/fields-medal/fields-medals-2022|url-status=live}}</ref>

|- | 60px | {{sortname|June|Huh}} | Princeton University, US | Princeton University, US | "For bringing the ideas of Hodge theory to combinatorics, the proof of the Dowling–Wilson conjecture for geometric lattices, the proof of the Heron–Rota–Welsh conjecture for matroids, the development of the theory of Lorentzian polynomials, and the proof of the strong Mason conjecture."<ref name="2022fields" />

|- | 60px | {{sortname|James|Maynard|James Maynard (mathematician)}} | University of Oxford, UK | University of Oxford, UK | "For contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation."<ref name="2022fields" />

|- | 60px | {{sortname|Maryna|Viazovska}} | École Polytechnique Fédérale de Lausanne, Switzerland | École Polytechnique Fédérale de Lausanne, Switzerland | "For the proof that the <math>E_8</math> lattice provides the densest packing of identical spheres in 8 dimensions, and further contributions to related extremal problems and interpolation problems in Fourier analysis."<ref name="2022fields" /><ref>{{cite web |date=July 5, 2022 |first1=Thomas |last1=Lin |first2=Erica |last2=Klarreich |title=Ukrainian Mathematician Maryna Viazovska Wins Fields Medal |url=https://www.quantamagazine.org/ukrainian-mathematician-maryna-viazovska-wins-fields-medal-20220705/ |access-date=18 July 2022 |archive-date=5 July 2022 |archive-url=https://web.archive.org/web/20220705072102/https://www.quantamagazine.org/ukrainian-mathematician-maryna-viazovska-wins-fields-medal-20220705/ |url-status=live }}</ref> |}

==Landmarks== The medal was first awarded in 1936 to the Finnish mathematician Lars Ahlfors and the American mathematician Jesse Douglas.

In 1954, Jean-Pierre Serre became the youngest winner of the Fields Medal, at 27.<ref>{{cite journal | last1 = Nawlakhe | first1 = Anil | last2 = Nawlakhe | first2 = Ujwala | last3 = Wilson | first3 = Robin | author3-link = Robin Wilson (mathematician) | date = July 2011 | department = Stamp Corner | doi = 10.1007/s00283-011-9244-1 | issue = 4 | journal = The Mathematical Intelligencer | pages = 70 | title = Fields Medallists | volume = 33| s2cid = 189866710 | doi-access = free }}</ref> He retains this distinction.<ref>{{Cite web |last=Raikar |first=Sanat Pai |date=2023-05-08 |title=Fields Medal |url=https://www.britannica.com/science/Fields-Medal |access-date=2023-06-22 |website=Encyclopædia Britannica |language=en |archive-date=7 February 2022 |archive-url=https://web.archive.org/web/20220207104118/https://www.britannica.com/science/Fields-Medal |url-status=live }}</ref>

In 1966, Alexander Grothendieck boycotted the ICM, held in Moscow, to protest against Soviet military actions taking place in Eastern Europe.<ref>{{cite journal|last=Jackson|first=Allyn|date=October 2004|title=As If Summoned from the Void: The Life of Alexandre Grothendieck|url=https://www.ams.org/notices/200410/fea-grothendieck-part2.pdf|journal=Notices of the American Mathematical Society|volume=51|issue=9|page=1198|access-date=26 August 2006|archive-date=25 August 2006|archive-url=https://web.archive.org/web/20060825030446/http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf|url-status=live}}</ref> Léon Motchane, founder and director of the Institut des Hautes Études Scientifiques, attended and accepted Grothendieck's Fields Medal on his behalf.<ref>{{cite web|url=https://www.ams.org/samplings/this-math-month/thismathmonth-aug|title=This Mathematical Month – August|publisher=American Mathematical Society|archive-url=https://web.archive.org/web/20100811071525/http://www.ams.org/samplings/this-math-month/thismathmonth-aug|archive-date=11 August 2010|url-status=dead}}</ref>

In 1970, Sergei Novikov, because of restrictions placed on him by the Soviet government, was unable to travel to the congress in Nice to receive his medal.<ref>{{cite web |last1=Raikar |first1=Sanat Pai |title=Fields Medal |date=15 December 2023 |url=https://www.britannica.com/science/Fields-Medal |access-date=7 February 2022 |archive-date=7 February 2022 |archive-url=https://web.archive.org/web/20220207104118/https://www.britannica.com/science/Fields-Medal |url-status=live }}</ref>

In 1978, Grigory Margulis, because of restrictions placed on him by the Soviet government, was unable to travel to the congress in Helsinki to receive his medal. The award was accepted on his behalf by Jacques Tits, who said in his address: "I cannot but express my deep disappointment—no doubt shared by many people here—in the absence of Margulis from this ceremony. In view of the symbolic meaning of this city of Helsinki, I had indeed grounds to hope that I would have a chance at last to meet a mathematician whom I know only through his work and for whom I have the greatest respect and admiration."<ref>[http://www-history.mcs.st-andrews.ac.uk/Biographies/Margulis.html Margulis biography] {{Webarchive|url=https://web.archive.org/web/20191019123826/http://www-history.mcs.st-andrews.ac.uk/Biographies/Margulis.html |date=19 October 2019 }}, School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved 27 August 2006.</ref>

In 1982, the congress was due to be held in Warsaw but had to be rescheduled to the next year, because of martial law introduced in Poland on 13 December 1981. The awards were announced at the ninth General Assembly of the IMU earlier in the year and awarded at the 1983 Warsaw congress.<ref>{{Cite web |title=1982 ICM - Warsaw |url=https://mathshistory.st-andrews.ac.uk/ICM/ICM_Warsaw_1983/ |access-date=2024-06-05 |website=Maths History |language=en}}</ref>

In 1990, Edward Witten became the first physicist to win the award.<ref name="National Science Foundation">{{cite web | title=The National Medal of Science 50th Anniversary | website=National Science Foundation | url=https://www.nsf.gov/news/special_reports/medalofscience50/witten.jsp | access-date=2022-08-30 | archive-date=22 June 2022 | archive-url=https://web.archive.org/web/20220622125848/https://www.nsf.gov/news/special_reports/medalofscience50/witten.jsp | url-status=live }}</ref>

In 1998, at the ICM, Andrew Wiles was presented by the chair of the Fields Medal Committee, Yuri I. Manin, with the first-ever IMU silver plaque in recognition of his proof of Fermat's Last Theorem. Don Zagier referred to the plaque as a "quantized Fields Medal". Accounts of this award frequently make reference that at the time of the award Wiles was over the age limit for the Fields medal.<ref>[http://wwwa.britannica.com/eb/article-9090319 Wiles, Andrew John] {{webarchive|url=https://web.archive.org/web/20080827194548/http://wwwa.britannica.com/eb/article-9090319|date=27 August 2008}}, Encyclopædia Britannica. Retrieved 27 August 2006.</ref> Although Wiles was slightly over the age limit in 1994, he was thought to be a favorite to win the medal; however, a gap (later resolved by Taylor and Wiles) in the proof was found in 1993.<ref>[https://web.archive.org/web/20010430062600/http://www.icm2002.org.cn/general/prize/medal/1998.htm Fields Medal Prize Winners (1998)], 2002 International Congress of Mathematicians. Retrieved 27 August 2006. {{webarchive|url=https://web.archive.org/web/20070927193530/http://www.icm2002.org.cn/general/prize/medal/1998.htm|date=27 September 2007}}</ref><ref>{{cite journal |url=https://www.ams.org/notices/199810/comm-fields.pdf |journal=Notices of the AMS |date=November 1998 |volume=45 |issue=10 |pages=1359 |title=Borcherds, Gowers, Kontsevich, and McMullen Receive Fields Medals |access-date=28 April 2021 |archive-date=23 April 2021 |archive-url=https://web.archive.org/web/20210423161336/http://www.ams.org/notices/199810/comm-fields.pdf |url-status=live }}</ref>

In 2006, Grigori Perelman, who proved the Poincaré conjecture, refused his Fields Medal, stated "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo."<ref name="BBC" /><ref>{{Cite news |date=24 March 2010|title=Russian maths genius Perelman urged to take $1m prize|url=https://news.bbc.co.uk/2/hi/8585407.stm|publisher=BBC News}}</ref> and did not attend the congress.<ref>{{cite magazine|url=http://www.newyorker.com/fact/content/articles/060828fa_fact2|title=Manifold Destiny: A legendary problem and the battle over who solved it.|last1=Nasar|first1=Sylvia|date=21 August 2006|magazine=The New Yorker|access-date=24 August 2006|archive-url=https://web.archive.org/web/20060831020716/http://www.newyorker.com/fact/content/articles/060828fa_fact2|archive-date=31 August 2006|url-status=live|last2=Gruber|first2=David}}</ref>

In 2014, Maryam Mirzakhani became the first Iranian as well as the first woman to win the Fields Medal, and Artur Avila became the first South American and Manjul Bhargava became the first person of Indian origin to do so.<ref name="CF">{{Cite book|url=http://unesdoc.unesco.org/images/0023/002315/231519e.pdf|title=A Complex Formula: Girls and Women in Science, Technology, Engineering and Mathematics in Asia|last=UNESCO|publisher=Paris, UNESCO|year=2015|isbn=978-92-9223-492-8|pages=23|access-date=3 May 2017|archive-date=15 November 2017|archive-url=https://web.archive.org/web/20171115233123/http://unesdoc.unesco.org/images/0023/002315/231519e.pdf|url-status=live}}</ref><ref>{{Cite news|url=https://www.theguardian.com/world/2017/jul/16/maryam-mirzakhani-iranian-newspapers-break-hijab-taboo-in-tributes#img-2|title=Maryam Mirzakhani: Iranian newspapers break hijab taboo in tributes|author=Saeed Kamali Dehghan|date=16 July 2017|work=The Guardian|access-date=18 July 2017|language=en-GB|issn=0261-3077|archive-date=18 July 2017|archive-url=https://web.archive.org/web/20170718033745/https://www.theguardian.com/world/2017/jul/16/maryam-mirzakhani-iranian-newspapers-break-hijab-taboo-in-tributes#img-2|url-status=live}}</ref>

==Medal== thumb|right|The reverse of the Fields Medal The medal was designed by Canadian sculptor R. Tait McKenzie.<ref>{{cite web |url=http://www.fields.utoronto.ca/aboutus/jcfields/fields_medal.html |title=Fields Institute – The Fields Medal |publisher=Fields.utoronto.ca |date=9 August 1932 |access-date=21 August 2010 |archive-date=1 April 2022 |archive-url=https://web.archive.org/web/20220401044832/http://www.fields.utoronto.ca/aboutus/jcfields/fields_medal.html |url-status=live }}</ref> It is made of 14KT gold, has a diameter of 63.5mm, and weighs 169g.<ref>{{cite web |url=https://www.mathunion.org/imu-awards/fields-medal |title=Fields Medal |publisher=International Mathematical Union |date=2022 |access-date=July 7, 2022 |archive-date=26 December 2018 |archive-url=https://web.archive.org/web/20181226015744/https://www.mathunion.org/imu-awards/fields-medal |url-status=live }}</ref>

* On the obverse is Archimedes and a quote attributed to 1st century AD poet Manilius, which reads in Latin: {{lang|la|Transire suum pectus mundoque potiri|italic=no}} ("To surpass one's understanding and master the world").<ref>{{Cite journal|last=Riehm|first=C.|date=2002|title=The early history of the Fields Medal|url=https://www.ams.org/notices/200207/comm-riehm.pdf|journal=Notices of the AMS|volume=49|issue=7|pages=778–782|quote=The Latin inscription from the Roman poet Manilius surrounding the image may be translated 'To pass beyond your understanding and make yourself master of the universe.' The phrase comes from Manilius's Astronomica 4.392 from the first century A.D. (p. 782).|access-date=28 April 2021|archive-date=26 October 2006|archive-url=https://web.archive.org/web/20061026000014/http://www.ams.org/notices/200207/comm-riehm.pdf|url-status=live}}</ref><ref>{{Cite web|date=5 February 2015|title=The Fields Medal|url=http://www.fields.utoronto.ca/about/fields-medal|access-date=23 April 2021|website=Fields Institute for Research in Mathematical Sciences|language=en|archive-date=23 April 2021|archive-url=https://web.archive.org/web/20210423094533/http://www.fields.utoronto.ca/about/fields-medal|url-status=live}}</ref> The year number 1933 is written in Roman numerals and contains an error (MC'''N'''XXXIII rather than MC'''M'''XXXIII).<ref>{{cite book|first=Eberhard|last=Knobloch|author-link=Eberhard Knobloch|chapter=Generality and Infinitely Small Quantities in Leibniz's Mathematics: The Case of his Arithmetical Quadrature of Conic Sections and Related Curves|title=Infinitesimal Differences: Controversies between Leibniz and his Contemporaries|editor-first1=Ursula|editor-last1=Goldenbaum|editor-first2=Douglas|editor-last2=Jesseph|publisher=Walter de Gruyter|date=2008}}</ref> In capital Greek letters the word Ἀρχιμηδους, or "of Archimedes," is inscribed. * On the reverse is the inscription:

:: {{lang|la|Congregati ex toto orbe mathematici ob scripta insignia tribuere|italic=no}}

Translation: "Mathematicians gathered from the entire world have awarded [understood but not written: 'this prize'] for outstanding writings."

In the background, there is the representation of Archimedes' tomb, with the carving illustrating his theorem On the Sphere and Cylinder, behind an olive branch. (This is the mathematical result of which Archimedes was reportedly most proud: Given a sphere and a circumscribed cylinder of the same height and diameter, the ratio between their volumes is equal to {{frac|2|3}}.)

The rim bears the name of the prizewinner.<ref name="Fields Institute for Research in Mathematical Sciences 2015">{{cite web | title=The Fields Medal | website=Fields Institute for Research in Mathematical Sciences | date=2015-02-05 | url=http://www.fields.utoronto.ca/about/fields-medal | access-date=2022-08-30 | archive-date=23 April 2021 | archive-url=https://web.archive.org/web/20210423094533/http://www.fields.utoronto.ca/about/fields-medal | url-status=live }}</ref>

==Female recipients==

The Fields Medal has had two female recipients, Maryam Mirzakhani from Iran in 2014, and Maryna Viazovska from Ukraine in 2022.<ref name="CF" /><ref name="DZH">{{Cite web |title=Друга жінка в історії: українка Марина В'язовська отримала престижну математичну нагороду |url=https://life.pravda.com.ua/society/2022/07/5/249420/ |url-status=live |archive-url=https://web.archive.org/web/20220713211953/https://life.pravda.com.ua/society/2022/07/5/249420/ |archive-date=13 July 2022 |access-date=2022-07-11 |website=Українська правда _Життя}}</ref>

==In popular culture==

The Fields Medal gained some recognition in popular culture due to references in the 1997 film, ''Good Will Hunting''. In the movie, Gerald Lambeau (Stellan Skarsgård) is an MIT professor who won the award prior to the events of the story. Throughout the film, references made to the award are meant to convey its prestige in the field.<ref>{{Cite news|date=2018-08-01|title=Maths gives its 'Nobel Prize' to an Australian — here's why it matters|language=en-AU|work=ABC News|url=https://www.abc.net.au/news/2018-08-01/fields-medals-to-be-awarded-to-best-mathematical-minds/10049510|access-date=2021-12-20|archive-date=8 April 2022|archive-url=https://web.archive.org/web/20220408074618/https://www.abc.net.au/news/2018-08-01/fields-medals-to-be-awarded-to-best-mathematical-minds/10049510|url-status=live}}</ref> In the 2005-2010 TV series NUMB3RS (TV series) the leading character, mathematics professor Charlie Eppes, is portrayed as a Fields nominee.

==See also== {{Portal|Mathematics}} {{div col|colwidth=20em}} * Abel Prize * Kyoto Prize * List of prizes known as the Nobel or the highest honors of a field * List of mathematics awards * Nevanlinna Prize * Rolf Schock Prizes * Turing Award * Wolf Prize in Mathematics {{div col end}}

==Notes== {{notelist}}

==References== {{Reflist|30em}}

==Further reading== {{Refbegin}} * {{Cite book |last1= McKinnon Riehm |first1= Elaine |last2= Hoffman |first2= Frances |year= 2011 |title= Turbulent Times in Mathematics: The Life of J.C. Fields and the History of the Fields Medal |location= Providence, RI |publisher= American Mathematical Society |isbn= 978-0-8218-6914-7 }} * {{Cite book |last= Monastyrsky |first= Michael |year= 1998 |title= Modern Mathematics in the Light of the Fields Medal |location= Wellesley, MA |publisher= A. K. Peters |isbn= 1-56881-083-0 }} * {{Cite journal |last=Tropp |first= Henry S. |year= 1976 |title= The Origins and History of the Fields Medal |journal= Historia Mathematica |volume= 3 |issue= 2 |pages= 167–181 |doi= 10.1016/0315-0860(76)90033-1 |doi-access= }}. {{Refend}}

==External links== {{Commons category|Fields medal}} * {{Official website}} * [https://www.britannica.com/science/Fields-Medal Overview] at britannica.com

Category:Fields Medalists Category:Awards established in 1936 Category:Awards with age limits Category:Mathematics awards