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Fields Medal | |
---|---|

The obverse of the Fields Medal | |

Awarded for | Outstanding contributions in mathematics attributed to young scientists |

Country | Varies |

Presented by | International Mathematical Union (IMU) |

Reward(s) | CA$15,000 |

First awarded | 1936 |

Last awarded | 2018 |

Website | mathunion |

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.

A **mathematician** is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

The **International Congress of Mathematicians** (**ICM**) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).

The **International Mathematical Union** (**IMU**) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Council for Science (ICSU) and supports the International Congress of Mathematicians. Its members are national mathematics organizations from more than 80 countries.

- Conditions of the award
- Fields medalists
- Landmarks
- Medal
- Female recipients
- See also
- References
- Further reading
- External links

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 ^{ [1] }^{ [2] }^{ [3] }, 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,^{ [4] } 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.^{ [5] }^{ [6] }

* Academic Ranking of World Universities* (

The **Abel Prize** is a Norwegian prize awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Prizes. It comes with a monetary award of 6 million Norwegian Kroner (NOK).

The prize comes with a monetary award which, since 2006, has been CA$ 15,000.^{ [7] }^{ [8] } The name of the award is in honour of Canadian mathematician John Charles Fields.^{ [9] } Fields was instrumental in establishing the award, designing the medal itself, and funding the monetary component.^{ [9] }

The **Canadian dollar** is the currency of Canada. It is abbreviated with the dollar sign **$**, or sometimes **Can$** or **C$** to distinguish it from other dollar-denominated currencies. It is divided into 100 cents (¢).

**Canadians** are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, several of these connections exist and are collectively the source of their being *Canadian*.

**John Charles Fields**, FRS, FRSC was a Canadian mathematician and the founder of the Fields Medal for outstanding achievement in mathematics.

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.^{ [10] }^{ [11] }^{ [12] } In all, sixty people have been awarded the Fields Medal.

**Lars Valerian Ahlfors** was a Finnish mathematician, remembered for his work in the field of Riemann surfaces and his text on complex analysis.

**Jesse Douglas** was an American mathematician and Fields Medalist known for his general solution of the Problem of Plateau.

**Maryam Mirzakhani** was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. In 2005, as a result of her research, she was honored in *Popular Science's* fourth annual "Brilliant 10" in which she was acknowledged as one of the top 10 young minds who have pushed their fields in innovative directions.

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.^{ [13] } The medal belonging to one of the four joint winners, Caucher Birkar, was stolen shortly after the event.^{ [14] } The ICM presented Birkar with a replacement medal a few days later.^{ [15] }

**Rio de Janeiro**, or simply **Rio**, is anchor to the Rio de Janeiro metropolitan area and the second-most populous municipality in Brazil and the sixth-most populous in the Americas. Rio de Janeiro is the capital of the state of Rio de Janeiro, Brazil's third-most populous state. Part of the city has been designated as a World Heritage Site, named "*Rio de Janeiro: Carioca Landscapes between the Mountain and the Sea*", by UNESCO on 1 July 2012 as a Cultural Landscape.

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.^{ [1] }^{ [2] }^{ [3] } 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."^{ [16] } Moreover, an individual can only be awarded one Fields Medal; laureates are ineligible to be awarded future medals.^{ [17] } 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 **Nobel Prize** is a set of annual international awards bestowed in several categories by Swedish and Norwegian institutions in recognition of academic, cultural, or scientific advances.

**John Bardeen** was an American physicist and electrical engineer. He is the only person to be awarded the Nobel Prize in Physics twice: first in 1956 with William Shockley and Walter Brattain for the invention of the transistor; and again in 1972 with Leon N Cooper and John Robert Schrieffer for a fundamental theory of conventional superconductivity known as the BCS theory.

**Frederick Sanger** was a British biochemist who twice won the Nobel Prize in Chemistry, one of only two people to have done so in the same category, the fourth person overall with two Nobel Prizes, and the third person overall with two Nobel Prizes in the sciences. In 1958, he was awarded a Nobel Prize in Chemistry "for his work on the structure of proteins, especially that of insulin". In 1980, Walter Gilbert and Sanger shared half of the chemistry prize "for their contributions concerning the determination of base sequences in nucleic acids". The other half was awarded to Paul Berg "for his fundamental studies of the biochemistry of nucleic acids, with particular regard to recombinant DNA".

The monetary award is much lower than the 8,000,000 Swedish kronor (roughly 1,400,000 Canadian dollars)^{ [18] } given with each Nobel prize as of 2014.^{ [19] } Other major awards in mathematics, such as the Abel Prize and the Chern Medal, have larger monetary prizes compared to the Fields Medal.

Year | ICM location | Medalists^{ [20] } | Nationality (when awarded) | Affiliation (when awarded) | Affiliation (current/last) | Reasons |
---|---|---|---|---|---|---|

1936 | Oslo, Norway | Lars Ahlfors | Finland | University of Helsinki, Finland | Harvard University, US^{ [21] }^{ [22] } | "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."^{ [23] } |

Jesse Douglas | United States | Massachusetts Institute of Technology, US | City College of New York, US^{ [24] }^{ [25] } | "Did important work on the Plateau problem which is concerned with finding minimal surfaces connecting and determined by some fixed boundary."^{ [23] } | ||

1950 | Cambridge, US | Laurent Schwartz | France | University of Nancy, France | University of Paris VII, France^{ [26] }^{ [27] } | "Developed the theory of distributions, a new notion of generalized function motivated by the Dirac delta-function of theoretical physics."^{ [28] } |

Atle Selberg | Norway | Institute for Advanced Study, US | Institute for Advanced Study, US^{ [29] } | "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."^{ [28] } | ||

1954 | Amsterdam, Netherlands | Kunihiko Kodaira | Japan | University of Tokyo, Japan and Institute for Advanced Study, US^{ [30] } | University of Tokyo, Japan^{ [31] } | "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."^{ [32] } |

Jean-Pierre Serre | France | University of Nancy, France | Collège de France, France^{ [33] }^{ [34] } | "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."^{ [32] } | ||

1958 | Edinburgh, UK | Klaus Roth | United Kingdom | University College London, UK | Imperial College London, UK^{ [35] } | "Solved in 1955 the famous 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)."^{ [36] } |

René Thom | France | University of Strasbourg, France | Institut des Hautes Études Scientifiques, France^{ [37] } | "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."^{ [36] } | ||

1962 | Stockholm, Sweden | Lars Hörmander | Sweden | University of Stockholm, Sweden | Lund University, Sweden^{ [38] } | "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."^{ [39] } |

John Milnor | United States | Princeton University, US | Stony Brook University, US^{ [40] } | "Proved that a 7-dimensional sphere can have several differential structures; this led to the creation of the field of differential topology."^{ [39] } | ||

1966 | Moscow, USSR | Michael Atiyah | United Kingdom | University of Oxford, UK | University of Edinburgh, UK^{ [41] } | "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'."^{ [42] } |

Paul Joseph Cohen | United States | Stanford University, US | Stanford University, US^{ [43] } | "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."^{ [42] } | ||

Alexander Grothendieck | None | Institut des Hautes Études Scientifiques, France | Centre National de la Recherche Scientifique, France^{ [44] } | "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’."^{ [42] } | ||

Stephen Smale | United States | University of California, Berkeley, US | City University of Hong Kong, Hong Kong^{ [45] } | "Worked in differential topology where he proved the 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 handle-bodies to solve this and related problems."^{ [42] } | ||

1970 | Nice, France | Alan Baker | United Kingdom | University of Cambridge, UK | Trinity College, Cambridge, UK^{ [46] } | "Generalized the Gelfond-Schneider theorem (the solution to Hilbert's seventh problem). From this work he generated transcendental numbers not previously identified."^{ [47] } |

Heisuke Hironaka | Japan | Harvard University, US | Kyoto University, Japan^{ [48] }^{ [49] } | "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."^{ [47] } | ||

Sergei Novikov | Soviet Union | Moscow State University, USSR | Steklov Mathematical Institute, Russia Moscow State University, Russia University of Maryland-College Park, US | "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."^{ [47] } | ||

John G. Thompson | United States | University of Cambridge, UK | University of Cambridge, UK University of Florida, US | "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."^{ [47] } | ||

1974 | Vancouver, Canada | Enrico Bombieri | Italy | University of Pisa, Italy | Institute for Advanced Study, US^{ [53] } | "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."^{ [54] } |

David Mumford | United States | Harvard University, US | Brown University, US^{ [55] } | "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."^{ [54] } | ||

1978 | Helsinki, Finland | Pierre Deligne | Belgium | Institut des Hautes Études Scientifiques, France | Institute for Advanced Study, US^{ [56] } | "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."^{ [57] } |

Charles Fefferman | United States | Princeton University, US | Princeton University, US^{ [58] } | "Contributed several innovations that revised the study of multidimensional complex analysis by finding correct generalizations of classical (low-dimensional) results."^{ [57] } | ||

Grigori Margulis | Soviet Union | Moscow State University, USSR | Yale University, US^{ [59] } | "Provided innovative analysis of the structure of Lie groups. His work belongs to combinatorics, differential geometry, ergodic theory, dynamical systems, and Lie groups."^{ [57] } | ||

Daniel Quillen | United States | Massachusetts Institute of Technology, US | University of Oxford, UK^{ [60] } | "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."^{ [57] } | ||

1982 | Warsaw, Poland | Alain Connes | France | Institut des Hautes Études Scientifiques, France | Institut des Hautes Études Scientifiques, France Collège de France, France Ohio State University, US | "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."^{ [62] } |

William Thurston | United States | Princeton University, US | Cornell University, US^{ [63] } | "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."^{ [62] } | ||

Shing-Tung Yau | None | Institute for Advanced Study, US | Harvard University, US^{ [64] } | "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."^{ [62] } | ||

1986 | Berkeley, US | Simon Donaldson | United Kingdom | University of Oxford, UK | Imperial College London, UK^{ [65] } Stony Brook University, US^{ [66] } | "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."^{ [67] } |

Gerd Faltings | West Germany | Princeton University, US | Max Planck Institute for Mathematics, Germany^{ [68] } | "Using methods of arithmetic algebraic geometry, he received medal primarily for his proof of the Mordell Conjecture."^{ [67] } | ||

Michael Freedman | United States | University of California, San Diego, US | Microsoft Station Q, US^{ [69] } | "Developed new methods for topological analysis of four-manifolds. One of his results is a proof of the four-dimensional Poincaré Conjecture."^{ [67] } | ||

1990 | Kyoto, Japan | Vladimir Drinfeld | Soviet Union | B Verkin Institute for Low Temperature Physics and Engineering, USSR^{ [70] } | University of Chicago, US^{ [71] } | "For his work on quantum groups and for his work in number theory." |

Vaughan F. R. Jones | New Zealand | University of California, Berkeley, US | University of California, Berkeley, US,^{ [72] } Vanderbilt University, US | "For his discovery of an unexpected link between the mathematical study of knots – a field that dates back to the 19th century – and statistical mechanics, a form of mathematics used to study complex systems with large numbers of components." | ||

Shigefumi Mori | Japan | Kyoto University, Japan | Kyoto University, Japan^{ [74] } | "For the proof of Hartshorne’s conjecture and his work on the classification of three-dimensional algebraic varieties." | ||

Edward Witten | United States | Institute for Advanced Study, US | Institute for Advanced Study, US^{ [75] } | " Time and again he has surprised the mathematical community by a brilliant application of physical insight leading to new and deep mathematical theorems."^{ [76] } | ||

1994 | Zurich, Switzerland | Jean Bourgain | Belgium | Institut des Hautes Études Scientifiques, France | Institute for Advanced Study, US^{ [77] } | "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." |

Pierre-Louis Lions | France | University of Paris 9, France | Collège de France, France École polytechnique, France | "... Such nonlinear partial differential equation simply do not have smooth or even C1 solutions existing after short times. ... The only option is therefore to search for some kind of "weak" solution. This undertaking is in effect to figure out how to allow for certain kinds of "physically correct" singularities and how to forbid others. ... Lions and Crandall at last broke open the problem by focusing attention on viscosity solutions, which are defined in terms of certain inequalities holding wherever the graph of the solution is touched on one side or the other by a smooth test function." | ||

Jean-Christophe Yoccoz | France | Paris-Sud 11 University, France | Collège de France, France^{ [79] } | "Proving stability properties - dynamic stability, such as that sought for the solar system, or structural stability, meaning persistence under parameter changes of the global properties of the system." | ||

Efim Zelmanov | Russia | University of California, San Diego, US | Steklov Mathematical Institute, Russia, University of California, San Diego, US | "For his solution to the restricted Burnside problem." | ||

1998 | Berlin, Germany | Richard Borcherds | United Kingdom | University of California, Berkeley, US | University of California, Berkeley, US^{ [81] } | "For his work on the introduction of vertex algebras, the proof of the Moonshine conjecture and for his discovery of a new class of automorphic infinite products." |

Timothy Gowers | United Kingdom | University of Cambridge, UK | University of Cambridge, UK^{ [82] } | "William Timothy Gowers has provided important contributions to functional analysis, making extensive use of methods from combination theory. These two fields apparently have little to do with each other, and a significant achievement of Gowers has been to combine these fruitfully." | ||

Maxim Kontsevich | Russia | Institut des Hautes Études Scientifiques, France | Institut des Hautes Études Scientifiques, France Rutgers University, US | "Contributions to four problems of geometry." | ||

Curtis T. McMullen | United States | Harvard University, US | Harvard University, US^{ [84] } | "He has made important contributions to various branches of the theory of dynamical systems, such as the algorithmic study of polynomial equations, the study of the distribution of the points of a lattice of a Lie group, hyperbolic geometry, holomorphic dynamics and the renormalization of maps of the interval." | ||

2002 | Beijing, China | Laurent Lafforgue | France | Institut des Hautes Études Scientifiques, France | Institut des Hautes Études Scientifiques, France^{ [85] } | "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." |

Vladimir Voevodsky | Russia | Institute for Advanced Study, US | Institute for Advanced Study, US^{ [86] } | "He defined and developed motivic cohomology and the A1-homotopy theory of algebraic varieties; he proved the Milnor conjectures on the K-theory of fields." | ||

2006 | Madrid, Spain | Andrei Okounkov | Russia | Princeton University, US | Columbia University, US^{ [87] } | "For his contributions bridging probability, representation theory and algebraic geometry." |

Grigori Perelman (declined) | Russia | None | St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences, Russia^{ [88] } | "For his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow." | ||

Terence Tao | Australia | University of California, Los Angeles, US | University of California, Los Angeles, US^{ [89] } | "For his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory." | ||

Wendelin Werner | France | Paris-Sud 11 University, France | ETH Zurich, Switzerland^{ [90] } | "For his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory." | ||

2010 | Hyderabad, India | Elon Lindenstrauss | Israel | Hebrew University of Jerusalem, Israel | Hebrew University of Jerusalem, Israel^{ [91] } | "For his results on measure rigidity in ergodic theory, and their applications to number theory." |

Ngô Bảo Châu | Vietnam, France | Paris-Sud 11 University, France | University of Chicago, US Vietnam Institute for Advanced Study, Vietnam | "For his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods." | ||

Stanislav Smirnov | Russia | University of Geneva, Switzerland | University of Geneva, Switzerland St. Petersburg State University, Russia | "For the proof of conformal invariance of percolation and the planar Ising model in statistical physics." | ||

Cédric Villani | France | École Normale Supérieure de Lyon, France Institut Henri Poincaré, France | Lyon University, France Institut Henri Poincaré, France | "For his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation." | ||

2014 | Seoul, South Korea | Artur Avila | Brazil, France | University of Paris VII, France CNRS, France Instituto Nacional de Matemática Pura e Aplicada, Brazil | University of Paris VII, France CNRS, France 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."^{ [95] } |

Manjul Bhargava | Canada, United States | Princeton University, US | Princeton University, US^{ [96] }^{ [97] }^{ [98] } | "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."^{ [95] } | ||

Martin Hairer | Austria | University of Warwick, UK | 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."^{ [95] } | ||

Maryam Mirzakhani | Iran | Stanford University, US | Stanford University, US^{ [99] }^{ [100] } | "For her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces."^{ [95] } | ||

2018 | Rio de Janeiro, Brazil | Caucher Birkar | Iran, United Kingdom | University of Cambridge, UK | University of Cambridge, UK | "For the proof of the boundedness of Fano varieties and for contributions to the minimal model program."^{ [101] } |

Alessio Figalli | Italy | 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."^{ [101] } | ||

Peter Scholze | Germany | University of Bonn, Germany | University of Bonn, Germany | "For transforming arithmetic algebraic geometry over p-adic fields through his introduction of perfectoid spaces, with application to Galois representations, and for the development of new cohomology theories."^{ [101] } | ||

Akshay Venkatesh | Australia | Stanford University, US | Stanford University, US Institute for Advanced Study, US | "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."^{ [101] } | ||

The medal was first awarded in 1936 to the Finnish mathematician Lars Ahlfors and the 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 1954, Jean-Pierre Serre became the youngest winner of the Fields Medal, at 27. He retains this distinction.

In 1966, Alexander Grothendieck boycotted the ICM, held in Moscow, to protest Soviet military actions taking place in Eastern Europe.^{ [103] } Léon Motchane, founder and director of the Institut des Hautes Études Scientifiques, attended and accepted Grothendieck's Fields Medal on his behalf.^{ [104] }

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.

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."^{ [105] }

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.

In 1990, Edward Witten became the first physicist to win the award.

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.^{ [106] } 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.^{ [107] }^{ [108] }

In 2006, Grigori Perelman, who proved the Poincaré conjecture, refused his Fields Medal^{ [7] } and did not attend the congress.^{ [109] }

In 2014, Maryam Mirzakhani became the first woman as well as the first Iranian 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.^{ [110] }^{ [111] }^{ [112] }^{ [113] } President Rouhani congratulated her for this notable success.^{ [10] }

The medal was designed by Canadian sculptor R. Tait McKenzie.^{ [114] }

- On the obverse is Archimedes and a quote attributed to him which reads in Latin: "Transire suum pectus mundoque potiri" ("Rise above oneself and grasp the world"). The date is written in Roman numerals and contains an error ("MCNXXXIII" rather than "MCMXXXIII").
^{ [115] }In capital Greek letters the word ΑΡXIMHΔΟΥΣ, or "of Archimedes". - On the reverse is the inscription (in Latin):

*CONGREGATI**EX TOTO ORBE**MATHEMATICI**OB SCRIPTA INSIGNIA**TRIBUERE*

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 ⅔.)

The rim bears the name of the prizewinner.

In terms of the most prestigious awards in STEM fields, only a small proportion have been awarded to women. The Fields Medal has been obtained only one time by a woman, Maryam Mirzakhani, in 2014, out of a total of (currently) 60 medalists.^{ [116] }^{ [117] }

The **Rolf Nevanlinna Prize** is awarded once every 4 years at the International Congress of Mathematicians, for outstanding contributions in Mathematical Aspects of Information Sciences including:

- All mathematical aspects of computer science, including computational complexity theory, logic of programming languages, analysis of algorithms, cryptography, computer vision, pattern recognition, information processing and modelling of intelligence.
- Scientific computing and numerical analysis. Computational aspects of optimization and control theory. Computer algebra.

**Manjul Bhargava** is a Canadian-American mathematician. He is the R. Brandon Fradd Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory at Leiden University, and also holds Adjunct Professorships at the Tata Institute of Fundamental Research, the Indian Institute of Technology Bombay, and the University of Hyderabad. He is known primarily for his contributions to number theory.

The **Carl Friedrich Gauss Prize for Applications of Mathematics** is a mathematics award, granted jointly by the International Mathematical Union and the German Mathematical Society for "outstanding mathematical contributions that have found significant applications outside of mathematics". The award receives its name from the German mathematician Carl Friedrich Gauss. With its premiere in 2006, it is to be awarded every fourth year, at the International Congress of Mathematicians.

**Akshay Venkatesh** is an Australian mathematician and was a professor at Stanford University. He is a professor at Institute for Advanced Study. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces, ergodic theory, and algebraic topology.

The **ICTP Ramanujan Prize for Young Mathematicians from Developing Countries** is a mathematics prize awarded annually by the International Centre for Theoretical Physics and named after the mathematician Srinivasa Ramanujan. It was founded in 2004, and was first awarded in 2005.

**Robert "Bob" Osserman** was an American mathematician who worked in geometry. He is specially remembered for his work on the theory of minimal surfaces.

**Artur Avila Cordeiro de Melo** is a Brazilian and French mathematician working primarily on dynamical systems and spectral theory. He is one of the winners of the 2014 Fields Medal, being the first Latin American to win such an award. He is a researcher at both the IMPA and the CNRS.

The **Chern Medal** is an international award recognizing outstanding lifelong achievement of the highest level in the field of mathematics. The prize is given at the International Congress of Mathematicians (ICM), which is held every four years.

The **Leelavati Award** is an award for outstanding contribution to public outreach in mathematics. It is named after the 12th-century mathematical treatise "Lilavati" devoted to arithmetic and algebra written by the Indian mathematician Bhāskara II, also known as Bhaskara Achārya. In the book the author posed, in verse form, a series of problems in (elementary) arithmetic to one Leelavati and followed them up with hints to solutions. This work appears to have been the main source of learning arithmetic and algebra in medieval India. The work was also translated into Persian and was influential in West Asia.

**Caucher Birkar** is a UK-based Iranian Kurdish mathematician and a professor at the University of Cambridge.

The **Ruth Lyttle Satter Prize in Mathematics**, also called the **Satter Prize**, is one of twenty-one prizes given out by the American Mathematical Society (AMS). It is presented biennially in recognition of an outstanding contribution to mathematics research by a woman in the previous six years. The award was established in 1990 using a donation from Joan Birman, in memory of her sister, Ruth Lyttle Satter, who worked primarily in biological sciences, and was a proponent for equal opportunities for women in science. First awarded in 1991, the award is intended to "honor [Satter's] commitment to research and to encourage women in science". The winner is selected by the council of the AMS, based on the recommendation of a selection committee. The prize is awarded at the Joint Mathematics Meetings during odd numbered years, and has always carried a modest cash reward. Since 2003, the prize has been $5,000, while from 1997 to 2001, the prize came with $1,200, and prior to that it was $4,000. If a joint award is made, the prize money is split between the recipients.

This is a timeline of **women in mathematics**.

**Marcelo Miranda Viana da Silva** is a Brazilian mathematician working in dynamical systems theory.

**Philibert Nang** is a Gabonese mathematician known for his work in algebra.

**Carlos Gustavo Tamm de Araújo Moreira** is a Brazilian mathematician working on dynamical systems, ergodic theory, number theory and combinatorics. Moreira is currently a researcher at the Instituto Nacional de Matemática Pura e Aplicada (IMPA).

**Jillian Beryl Adler** née **Smidt** is a South African Professor of Mathematics education at the University of the Witwatersrand and the President of the International Commission on Mathematical Instruction (2017–2020). Adler's work has focused on the teaching and learning of mathematics particularly in multilingual classrooms.

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*Turbulent Times in Mathematics: The Life of J.C. Fields and the History of the Fields Medal*. Providence, RI: American Mathematical Society. ISBN 0-8218-6914-0. - Monastyrsky, Michael (1998).
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