Fields Medal

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Fields Medal
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{{Use dmy dates|date=July 2017}}{{Use American English|date=July 2018}}

attributed to young scientists| presenter = International Mathematical Union (IMU)| country = Varies| reward = {{CA$}}15,}}}}{{distinguish|Field's metal}}The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years.The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as the mathematician's Nobel Prize,JOURNAL, Ball, Philip, Iranian is first woman to nab highest prize in maths,weblink Nature, en, 10.1038/nature.2014.15686, WEB,weblink Fields Medal,, 2018-03-29, WEB,weblink Fields Medal, The University of Chicago, en, 2018-03-29, although there are several key differences, including frequency of award, number of awards, and age limits. According to the annual Academic Excellence Survey by ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide,WEB,weblink Top Award, ShanghaiRanking Academic Excellence Survey 2017 {{!, Shanghai Ranking - 2017||access-date=2018-03-29}} and in another reputation survey conducted by IREG in 2013-14, the Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics.BOOK, IREG Observatory on Academic Ranking and Excellence, IREG List of International Academic Awards, IREG Observatory on Academic Ranking and Excellence, Brussels,weblink 3 March 2018, JOURNAL, Zheng, Juntao, Liu, Niancai, Mapping of important international academic awards, Scientometrics, 2015, 104, 763-791, 10.1007/s11192-015-1613-7, The prize comes with a monetary award which, since 2006, has been {{CA$|link=yes}}15,000.NEWS, Maths genius turns down top prize,weblink BBC, 22 August 2006, 22 August 2006, "Israeli wins 'Nobel' of Mathematics", The Jerusalem Post The name of the award is in honour of Canadian mathematician John Charles Fields.WEB,weblink About Us: The Fields Medal, The Fields Institute, University of Toronto, 21 August 2010, Fields was instrumental in establishing the award, designing the medal itself, and funding the monetary component.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. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions. In 2014, the Iranian mathematician Maryam Mirzakhani became the first female Fields Medalist.NEWS,weblink President Rouhani Congratulates Iranian Woman for Winning Math Nobel Prize, 14 August 2014, 14 August 2014, Fars News Agency, WEB,weblink International Mathematical Union, IMU Prizes 2014, 12 August 2014, NEWS,weblink Maryam Mirzakhani: Iranian newspapers break hijab taboo in tributes, correspondent, Saeed Kamali Dehghan Iran, 2017-07-16, The Guardian, 2017-07-18, en-GB, 0261-3077, In all, sixty people have been awarded the Fields Medal.The most recent group of Fields Medalists received their awards on 1 August 2018 at the opening ceremony of the IMU International Congress, held in Rio de Janeiro, Brazil.WEB,weblink Scientific Program: Program at a glance, ICM 2018 event website., The medal belonging to one of the four joint winners, Caucher Birkar, was stolen shortly after the event.NEWS,weblink World's most prestigious maths medal is stolen minutes after professor wins it, Philips, Don, 2018-08-01, The Guardian, 2018-08-01, en-GB, The ICM presented Birkar with a replacement medal a few days later.ICM announcement, August 4, 2018.

Conditions of the award

The Fields Medal has for a long time been regarded as the most prestigious award in the field of mathematics and is often described as the Nobel Prize of Mathematics. Unlike the Nobel Prize, the Fields Medal is only awarded every four years. The Fields Medal also has an age limit: a recipient must be under age 40 on 1 January of the year in which the medal is awarded. This is similar to restrictions applicable to the Clark Medal in economics. The under-40 rule is based on Fields's desire that "while it was in recognition of work already done, it was at the same time intended to be an encouragement for further achievement on the part of the recipients and a stimulus to renewed effort on the part of others."{{Harvnb|McKinnon Riehm|Hoffman|2011|p=183}} Moreover, an individual can only be awarded one Fields Medal; laureates are ineligible to be awarded future medals.WEB,weblink Rules for the Fields Medal,, This is in contrast with the Nobel Prize which has been awarded to an individual or an entity more than once, whether in the same category (John Bardeen and Frederick Sanger), or in different categories (Marie Curie and Linus Pauling).The monetary award is much lower than the 8 million Swedish kronor given with each Nobel prize as of 2014.WEB,weblink The Nobel Prize Amounts,, Nobel Foundation, 13 August 2014, Other major awards in mathematics, such as the Abel Prize and the Chern Medal, have larger monetary prizes compared to the Fields Medal.

Fields medalists{| class"wikitable sortable" style"margin: 1ex auto 1ex auto"

! Year! ICM location! MedalistsWEB,weblink The Fields Medalists, chronologically listed, International Mathematical Union (IMU), 8 May 2008, 25 March 2009, ! Nationality(when awarded)! Affiliation(when awarded)! Affiliation(current/last)! Reasons 1936 Oslo, Norway| Lars Ahlfors| Finland| University of Helsinki, FinlandHarvard University, USHTTP://WWW.AMS.ORG/NOTICES/199802/COMM-KRANTZ.PDF TITLE=LARS VALERIAN AHLFORS (1907-1996) ACCESSDATE=2017-03-31, HTTP://WWW.MATH.HARVARD.EDU/HISTORY/AHLFORS/>TITLE=LARS AHLFORS (1907-1996)PUBLISHER=HARVARD UNIVERSITY, DEPT. OF MATH., 19 August 2014, Riemann surfaces of inverse functions of entire and meromorphic functions. Opened up new fields of analysis."HTTPS://WWW.MATHUNION.ORG/FILEADMIN/IMU/PRIZES/FIELDS/1936/INDEX.HTML PUBLISHER=INTERNATIONAL MATHEMATICAL UNION,, | Jesse Douglas| United States| Massachusetts Institute of Technology, USCity College of New York, USHTTP://WWW.BRITANNICA.COM/EBCHECKED/TOPIC/170174/JESSE-DOUGLAS, Jesse Douglasencyclopedia=Encyclopædia BritannicaTITLE=THE WORK OF JESSE DOUGLAS ON MINIMAL SURFACES AUTHOR2=J. GRAY ACCESSDATE=2017-03-31 ARCHIVE-DATE=6 OCTOBER 2014 DF=DMY-ALL, | "Did important work on the Plateau problem which is concerned with finding minimal surfaces connecting and determined by some fixed boundary." 1950 Cambridge, US| Laurent Schwartz| France| University of Nancy, FranceUniversity of Paris VII, FranceHTTP://WWW-HISTORY.MCS.ST-AND.AC.UK/BIOGRAPHIES/SCHWARTZ.HTML, Laurent Moise Schwartzpublisher=School of Mathematics and Statistics University of St Andrews, ScotlandDATE=1 FEB 2001 TRANS-TITLE=A MATHEMATICIAN GRAPPLING WITH HIS CENTURY ARCHIVE-URL=HTTPS://ARCHIVE.IS/20140821114917/HTTP://WWW.SPRINGER.COM/BIRKHAUSER/HISTORY+OF+SCIENCE/BOOK/978-3-7643-6052-8 ARCHIVE-DATE=21 AUGUST 2014 PUBLISHER=BIRKHäUSER ACCESSDATE=21 AUGUST 2014, theory of distributions, a new notion of generalized function motivated by the Dirac delta-function of theoretical physics."HTTPS://WWW.MATHUNION.ORG/FILEADMIN/IMU/PRIZES/FIELDS/1950/INDEX.HTML PUBLISHER=INTERNATIONAL MATHEMATICAL UNION,, | Atle Selberg| Norway| Institute for Advanced Study, USInstitute for Advanced Study, USHTTP://WWW.AMS.ORG/NOTICES/200906/RTX090600692P-CORRECTED.PDF TITLE=REMEMBERING ATLE SELBERG, 1917-2007 ACCESSDATE=2017-03-31, Brun's sieve>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." 1954 Amsterdam, Netherlands| Kunihiko Kodaira| Japan University of Tokyo, Japan and Institute for Advanced Study, USHTTP://WWW.MATHUNION.ORG/ICM/ICM1954.1/ICM1954.1.OCR.PDF >FORMAT=PDF DATE=1954 ACCESSDATE=2017-03-31, University of Tokyo, JapanHTTP://WWW.AMS.ORG/NOTICES/199803/COMM-OBIT-SPENCER.PDF TITLE=KUNIHIKO KODAIRA (1915-1997) WEBSITE=AMS.ORG, 2017-03-31, algebraic varieties. He demonstrated, by sheaf cohomology, that such varieties are Hodge manifolds."HTTPS://WWW.MATHUNION.ORG/FILEADMIN/IMU/PRIZES/FIELDS/1954/INDEX.HTML PUBLISHER=INTERNATIONAL MATHEMATICAL UNION,, | Jean-Pierre Serre| France| University of Nancy, FranceCollège de France, FranceHTTP://WWW.MATH.RUG.NL/~TOP/LECTURES/DELFT.PDF TITLE=JEAN-PIERRE SERRE ACCESSDATE=2017-03-31, HTTP://WWW.BRITANNICA.COM/EBCHECKED/TOPIC/535878/JEAN-PIERRE-SERRE>TITLE=JEAN-PIERRE SERREENCYCLOPEDIA=ENCYCLOPæDIA BRITANNICA, 19 August 2014, 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 sheaf (mathematics)>sheaves." 1958 Edinburgh, UK| Klaus Roth| United Kingdom| University College London, UKImperial College London, UK{{Harvnb>McKinnon Riehm2011|p=212}}Thue-Siegel-Roth theorem>Thue-Siegel problem concerning the approximation to algebraic numbers by rational numbers and proved in 1952 that a sequence with no three numbers in arithmetic progression has zero density (a conjecture of Erdős and Turán of 1935)."HTTPS://WWW.MATHUNION.ORG/FILEADMIN/IMU/PRIZES/FIELDS/1958/INDEX.HTML >TITLE=FIELDS MEDALS 1958 WEBSITE=MATHUNION.ORG, | René Thom| France| University of Strasbourg, FranceInstitut des Hautes Études Scientifiques, FranceHTTP://WWW.ROBERTNOWLAN.COM/PDFS/THOM,%20RENE.PDF TITLE=RENé THOM ACCESSDATE=2017-03-31, | "In 1954 invented and developed the theory of cobordism in algebraic topology. This classification of manifolds used homotopy theory in a fundamental way and became a prime example of a general cohomology theory." 1962 Stockholm, Sweden| Lars Hörmander| Sweden| University of Stockholm, SwedenLund University, SwedenHTTP://SMAI.EMATH.FR/IMG/PDF/MATAPLI100_HORMANDER.PDF TITLE=A TRIBUTE TO LARS HöRMANDER ACCESSDATE=2017-03-31, 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."HTTPS://WWW.MATHUNION.ORG/FILEADMIN/IMU/PRIZES/FIELDS/1962/INDEX.HTML PUBLISHER=INTERNATIONAL MATHEMATICAL UNION,, | John Milnor| United States| Princeton University, USStony Brook University, USHTTP://WWW.MATH.SUNYSB.EDU/~JACK/DATE=5 MARCH 1997ACCESSDATE=17 AUGUST 2014, | "Proved that a 7-dimensional sphere can have several differential structures; this led to the creation of the field of differential topology." 1966 Moscow, USSR| Michael Atiyah| United Kingdom| University of Oxford, UKUniversity of Edinburgh, UKESFORMAT=PDF WEBSITE=UPCOMMONS.UPC.EDU, 2017-03-31, K-theory; proved jointly with Singer the Atiyah–Singer index theorem>index theorem of elliptic operators on complex manifolds; worked in collaboration with Bott to prove a fixed point theorem related to the 'Lefschetz fixed-point theorem'."HTTPS://WWW.MATHUNION.ORG/FILEADMIN/IMU/PRIZES/FIELDS/1966/INDEX.HTML PUBLISHER=INTERNATIONAL MATHEMATICAL UNION,, Paul Cohen (mathematician)>Paul Joseph Cohen| United States| Stanford University, USStanford University, USHTTP://HISTORICALSOCIETY.STANFORD.EDU/PDFMEM/COHEN_P.PDF ACCESSDATE=2014-08-24 ARCHIVEURL=HTTPS://WEB.ARCHIVE.ORG/WEB/20150105133237/HTTP://HISTORICALSOCIETY.STANFORD.EDU/PDFMEM/COHEN_P.PDF DF=DMY-ALL, Forcing (mathematics)>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."| Alexander Grothendieck| None| Institut des Hautes Études Scientifiques, FranceCentre National de la Recherche Scientifique, FranceHTTP://WWW.MATH.UCDENVER.EDU/~JLOATS/STUDENTCELEBS/GROTHENDIECK_TRENKAMP.PDF TITLE=ALEXANDER GROTHENDIECK ACCESSDATE=2017-03-31, algebraic geometry. He introduced the idea of K-theory (the Grothendieck groups and rings). Revolutionized homological algebra in his celebrated ‘Grothendieck's Tôhoku paper>Tôhoku paper’."| Stephen Smale| United States| University of California, Berkeley, USCity University of Hong Kong, Hong KongHTTP://WWW6.CITYU.EDU.HK/MA/PEOPLE/PROFILE/SMALES.HTM, Prof. Stephen SMALE (史梅爾)publisher=City University of Hong Kong, 18 August 2014, generalized Poincaré conjecture in dimension n≥5: Every closed, n-dimensional manifold homotopy-equivalent to the n-dimensional sphere is homeomorphic to it. Introduced the method of Handlebody>handle-bodies to solve this and related problems." 1970 Nice, FranceAlan Baker (mathematician)>Alan Baker| United Kingdom| University of Cambridge, UKTrinity College, Cambridge, UKHTTP://WWW.HEIDELBERG-LAUREATE-FORUM.ORG/BLOG/LAUREATE/ALAN-BAKERDATE=25 SEPTEMBER 2013ACCESSDATE=16 AUGUST 2014, Baker's theorem>Generalized the Gelfond-Schneider theorem (the solution to Hilbert's seventh problem). From this work he generated transcendental numbers not previously identified."HTTPS://WWW.MATHUNION.ORG/FILEADMIN/IMU/PRIZES/FIELDS/1970/INDEX.HTML >TITLE=FIELDS MEDALS 1970 WEBSITE=MATHUNION.ORG, | Heisuke Hironaka| Japan| Harvard University, USKyoto University, JapanHTTP://WWW.AMS.ORG/NOTICES/200509/FEA-HIRONAKA.PDF TITLE=INTERVIEW WITH HEISUKE HIRONAKA ACCESSDATE=2017-03-31, HTTP://WWW.KURIMS.KYOTO-U.AC.JP/EN/EMERITUS.HTML>TITLE=NO TITLEPUBLISHER=RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, KYOTO, JAPAN, 16 August 2014, | "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."Sergei Novikov (mathematician)>Sergei Novikov| Soviet Union| Moscow State University, USSR| Steklov Mathematical Institute, RussiaMoscow State University, RussiaUniversity of Maryland-College Park, USWEB,weblink PDF, Interview with Sergey P. Novikov,, 2017-03-31, WEB,weblink Novikov, Sergei Petrovich, 1 January 2012, Russian Academy of Science, 20 August 2014, | "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."| John G. Thompson| United States| University of Cambridge, UK| University of Cambridge, UKUniversity of Florida, USWEB,weblink PDF, John Griggs Thompson,, 2017-03-31, Walter Feit>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." 1974 Vancouver, Canada| Enrico Bombieri| Italy| University of Pisa, ItalyInstitute for Advanced Study, USBARTOCCI EDITOR2-LAST=BETTI EDITOR3-LAST=GUERRAGGIO DISPLAY-EDITORS = 3 EDITOR4-FIRST=ROBERTO LUCCHETTI TRANS-TITLE=MATHEMATICAL LIVES: PROTAGONISTS OF THE TWENTIETH CENTURY FROM HILBERT TO WILES EDITION=2011 PUBLICATION-DATE=2011 ISBN=978-3642136054, 18 August 2014, 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."HTTPS://WWW.MATHUNION.ORG/FILEADMIN/IMU/PRIZES/FIELDS/1974/INDEX.HTML PUBLISHER=INTERNATIONAL MATHEMATICAL UNION,, | David Mumford| United States| Harvard University, USBrown University, USHTTP://WWW.DAM.BROWN.EDU/PEOPLE/FACULTYPAGE.MUMFORD.HTMLTITLE=DAVID MUMFORD=12 MAY 2006ACCESSDATE=18 AUGUST 2014, Moduli space>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." 1978 Helsinki, Finland| Pierre Deligne| Belgium| Institut des Hautes Études Scientifiques, FranceInstitute for Advanced Study, USHTTP://WWW.ABELPRIZE.NO/C57681/BINFIL/DOWNLOAD.PHP?TID=57756 TITLE=PIERRE DELIGNE ACCESSDATE=2017-03-31,

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