# Fields Medal: Award Winners & the History of the Biggest Prize in Mathematics

The Fields Medal, officially known as the International Medal for Outstanding Discoveries in Mathematics, is an award granted to two, three, or four mathematicians under 40 years of age every four years at the International Congress of the International Mathematical Union (IMU) to recognize outstanding mathematical achievement for existing work and the promise of future achievement.

The award’s name honors the renowned Canadian mathematician John Charles Fields (1863–1932).

The Executive Committee of the International Mathematical Union chooses the Fields Medal Committee, which the IMU President typically chairs. It then needs to select at least two, with a strong preference for four, Fields Medalists and have regard for representing a diversity of mathematical fields. A candidate’s 40th birthday must not fall before the 1st of January of the year of the Congress at which they are awarded the Fields Medal.

Although the Fields Medal is often referred to as the mathematical equivalent of the Nobel Prize, there are several significant differences between the two, including the award criteria, frequency of the award, number of awards, age limits, and monetary value.

## History of Fields Medal

The Fields Medal originated from surplus funds that John Charles Fields, a professor of mathematics at the University of Toronto, raised as the organizer and president of the 1924 International Congress of Mathematicians in Toronto. After printing the conference proceedings, the Committee of the International Congress had US Dollars 2,700 left and voted to put aside 2,500 US Dollars for establishing two medals that would be awarded later.

In contrast to Fields’s explicit request, the proposed awards came to be known as the Fields Medals after an endowment from his estate. The first two Fields Medals were awarded in 1936, and an anonymous donation increased the number of prize medals starting in 1966. Medalists currently also receive a small cash award of USD 1,500. Since 1982, a related award, the Rolf Nevanlinna Prize, has also been presented at every International Congress of Mathematicians. It is awarded to a young mathematician for notable work related to the mathematical aspects of information science.

The International Mathematical Union’s executive committee appoints Fields Medal and Nevanlinna Prize committees, which can suggest candidates to the secretary of the International Mathematical Union in writing. Since 1936, the medals have been presented at every International Congress of Mathematicians. Except for two Ph.D. holders in physics (Edward Witten and Martin Hairer), only individuals with a Ph.D. in mathematics have won the medal.

Also see: Abel Prize Winners

## Fields Medal Award Winners in 2022

• Hugo Duminil-Copin: For solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four.
• June Huh: 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.
• James Maynard: 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.
• Maryna Viazovska: For the proof that the $E_8$ lattice provides the densest packing of identical spheres in 8 dimensions and further contributions to related extremal problems and interpolation problems in Fourier analysis.

## Landmarks

1. 1936 – The Fields Medal was first awarded to the American mathematician Jesse Douglas and the Finnish mathematician Lars Ahlfors. Since 1950, it has been awarded every four years to honor younger mathematical researchers.
2. 1954 – The 27-year-old Jean-Pierre Serre became the youngest winner of the Fields Medal. He retains that distinction to this day.
3. 1966 – Alexander Grothendieck boycotted the International Congress of Mathematicians (held in Moscow) to protest Soviet military actions in Eastern Europe. Therefore, Léon Motchane, the founder and director of the Institut des Hautes Études Scientifiques, attended and accepted Grothendieck’s Fields Medal on his behalf.
4. 1970 – Sergei Novikov could not travel to the Congress in Nice to receive his Fields Medal because of restrictions the Soviet government put on him.
5. 1978 – Grigory Margulis could not travel to the Congress in Helsinki and receive his Fields Medal due to similar restrictions the Soviet government placed on him. Jacques Tits accepted the award was accepted on his behalf.
6. 1982 – The Congress was planned to be held in Warsaw but had to be rescheduled to the following year because of the introduction of martial law in Poland on the 13th of December, 1981. Earlier that year, the awards were announced at the ninth General Assembly of the IMU and awarded at the 1983 Warsaw Congress.
7. 1990 – Edward Witten became the first physicist to win the Fields Medal.
8. 1998 – At the International Congress of Mathematicians, the chair of the Fields Medal Committee, Yuri I. Manin, presented Andrew Wiles with the first-ever IMU silver plaque to honor his proof of Fermat’s Last Theorem. Don Zagier called this plaque a “quantized Fields Medal.” Although Wiles was slightly over the age limit for the Fields Medal then, many felt he was a favorite to win the medal.
9. 2006 – Grigori Perelman, who proved the Poincaré conjecture, rejected his Fields Medal and chose not to attend the Congress.
10. 2014 – Maryam Mirzakhani became the first Iranian and the first woman to win the Fields Medal. Also, Manjul Bhargava became the first person of Indian origin, and Artur Avila became the first South American to do so.
11. 2022 – Maryna Viazovska became the first Ukrainian to win the Fields Medal, and June Huh became the first person of Korean origin to do so.

## Terms for Winning the Fields Medal

Unlike the Nobel Prize, the Fields Medal is only awarded every four years. Also, there is an age limit – the recipient must be under 40 on the 1st of January of the year the medal is awarded. It is based on Fields’s wish 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.”

Also, a person can only receive one Fields Medal in their lifetime; winners are ineligible to be awarded medals in the future.

## The Medal of The Fields Medal

Photo Source: By Stefan Zachow for the International Mathematical Union; retouched by King of Hearts – Public Domain

Canadian sculptor R. Tait McKenzie designed the Fields Medal.  It is made of 14kt gold, weighs 169 grams, and has a diameter of 63.5mm.

Its obverse features Archimedes (287-212 BC) and a quote attributed to 1st century AD poet Manilius, reading the following in Latin: “Transire suum pectus mundoque potiri” (“Rise above oneself and grasp the world”).

It also has the year number 1933 written in Roman numerals and contains an error (“MCNXXXIII” instead of “MCMXXXIII”).

The word ΑΡXIMHΔΟΥΣ, or “of Archimedes,” is present in Greek capital letters.

On the medal’s reverse is the following Latin inscription:

CONGREGATI

EX TOTO ORBE

MATHEMATICI

OB SCRIPTA INSIGNIA

TRIBUERE

It translates to: “Mathematicians gathered from the entire world have awarded (this prize) for outstanding writings.

The background represents Archimedes’ tomb, with the carving illustrating his theorem On the Sphere and Cylinder behind an olive branch.

The medal’s rim bears the name of the awardee.

## Significance

The Fields Medal indicates current fertile areas of mathematical research because the winners have usually made contributions that opened up entire fields or integrated technical ideas and tools from various disciplines.

Many winners worked in highly abstract and integrative fields such as algebraic topology and geometry. To some extent, this trend reflects the influence and power of the French consortium of mathematicians, writing under the name of Nicolas Bourbaki since 1939. In their multivolume Éléments de mathématiques, they sought a rigorous, modern, and comprehensive treatment of all mathematics and mathematical foundations.

Nevertheless, individuals have also received medals for their work in more classical mathematics and mathematical physics fields, including solutions to problems that David Hilbert enunciated at the International Congress of Mathematicians in Paris in 1900.

Interestingly, there are large clusters of Fields Medalists within certain research institutions. In fact, almost half of the medalists have held appointments at the Institute for Advanced Study, Princeton, N.J., U.S.

## FAQs

How often is the Fields Medal awarded?

The Fields Medal is awarded every four years on the occasion of the International Congress of Mathematicians for outstanding achievements in mathematics.

What is the age limit to receive the Fields Medal?

The Fields Medal is awarded to mathematicians who are not over 40 years of age.

What is the Fields Medal made of?

The Fields Medal is made of gold and displays the head of Archimedes along with a quotation attributed to him – “Transire suum pectus mundoque potiri” (“Rise above oneself and grasp the world”).

Which country has the most Fields Medals?

Currently, the US has the most Fields Medals (15), followed by the UK (8).

Have any Indians won the Fields Medal?

So far, there are two awardees of Indian origin — Akshay Venkatesh of the Institute for Advanced Study at Princeton (2018) and Manjul Bhargava of the Department of Mathematics at Princeton University (2014).