ⓘ Fields Medal


Michael Atiyah

Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry. Atiyah grew up in Sudan and Egypt but spent most of his academic life in the United Kingdom at University of Oxford and University of Cambridge, and in the United States at the Institute for Advanced Study. He was the President of the Royal Society 1990–1995, founding director of the Isaac Newton Institute 1990–1996, master of Trinity College, Cambridge 1990–1997, chancellor of the University of Leicester 1995–2005, and the President of the Royal Society of Edinburgh 2005–2008. From 1997 until his dea ...


Enrico Bombieri

Enrico Bombieri is an Italian mathematician, known for his work in analytic number theory, Diophantine geometry, complex analysis, and group theory. He won a Fields Medal in 1974. Bombieri is currently Professor Emeritus in the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey.


Richard Borcherds

Richard Ewen Borcherds is a British mathematician currently working in quantum field theory. He is known for his work in lattices, number theory, group theory, and infinite-dimensional algebras, for which he was awarded the Fields Medal in 1998.


Jean Bourgain

Jean, Baron Bourgain February 28, 1954 – December 22, 2018) was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic theory and nonlinear partial differential equations from mathematical physics.


Akshay Venkatesh

Akshay Venkatesh is an Australian mathematician and a professor at the School of Mathematics at the 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. He is the only Australian to have won medals at both the International Physics Olympiad and International Mathematical Olympiad, which he did at the age of 12. In 2018, he was awarded the Fields Medal for his synthesis of analytic number theor ...


Cedric Villani

Cedric Patrice Thierry Villani is a French mathematician and politician working primarily on partial differential equations, Riemannian geometry and mathematical physics. He was awarded the Fields Medal in 2010 and he was the director of Sorbonne Universitys Institut Henri Poincare from 2009 to 2017. In one of two lectures given at the Royal Institution, Villani recalled that his initial inspiration regarding the field of mathematics came from the 1959 Walt Disney cartoon Donald in Mathmagic Land. This lecture is titled Birth of a Theorem. The English translation of his book Theoreme vivan ...

Fields Medal

ⓘ Fields 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, 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 mathematicians Nobel Prize, 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, 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.

The prize comes with a monetary award which, since 2006, has been CA$ 15.000. The name of the award is in honour of Canadian mathematician John Charles Fields. 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. 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. The medal belonging to one of the four joint winners, Caucher Birkar, was stolen shortly after the event. The ICM presented Birkar with a replacement medal a few days later.


1. 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 Fieldss 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." Moreover, an individual can only be awarded one Fields Medal; laureates are ineligible to be awarded future medals.

The monetary award is much lower than the 8 million Swedish kronor given with each Nobel prize as of 2014. Other major awards in mathematics, such as the Abel Prize and the Chern Medal, have larger monetary prizes compared to the Fields Medal.


2. Landmarks

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. Leon Motchane, founder and director of the Institut des Hautes Etudes Scientifiques, attended and accepted Grothendiecks Fields Medal on his behalf.

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."

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 Fermats 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. 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.

In 2006, Grigori Perelman, who proved the Poincare conjecture, refused his Fields Medal and did not attend the congress.

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. President Rouhani congratulated Mirzakhani for this notable success.


3. Medal

The medal was designed by Canadian sculptor R. Tait McKenzie.

  • 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". In capital Greek letters the word ΑΡXIMHΔΟΥΣ, or "of Archimedes".
  • On the reverse is the inscription in Latin

Translation: "Mathematicians gathered from the entire world have awarded 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.


4. Female recipients

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.

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