Fields Medal

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 (ICM) 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. In the remaining years (1990, 1994, and 2002), part of the text of the ICM lecture itself has been quoted. The most recent awarding of the Fields Medal at the 2026 International Congress of the International Mathematical Union was in Philadelphia.

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. He retains this distinction.

In 1966, Alexander Grothendieck boycotted the ICM, held in Moscow, to protest against Soviet military actions taking place in Eastern Europe. Léon Motchane, founder and director of the Institut des hautes études scientifiques, attended and accepted Grothendieck's 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 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. 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 Poincaré conjecture, refused his Fields Medal, stating "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo." He did not attend the congress.

In 2014, Maryam Mirzakhani became the first Iranian as well as the first woman to win the Fields Medal, Artur Avila became the first South American, and Manjul Bhargava became the first person of Indian origin to do so.

Medal

The medal was designed by the Canadian sculptor R. Tait McKenzie. It is made of 14KT gold, has a diameter of 63.5mm, and weighs 169g.

• On the obverse is Archimedes and a quote attributed to 1st century AD poet Manilius, which reads in Latin: Transire suum pectus mundoque potiri ("To surpass one's understanding and master the world"). The year number 1933 is written in Roman numerals and contains an error (MCNXXXIII rather than MCMXXXIII). In capital Greek letters the word Ἀρχιμηδους, or "of Archimedes," is inscribed.
• On the reverse is the inscription:

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 2⁄3.)

The rim bears the name of the prizewinner.

Female recipients

The Fields Medal has had three female recipients: Maryam Mirzakhani from Iran in 2014, Maryna Viazovska from Ukraine in 2022, and Hong Wang from China in 2026.

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. In the 2005–2010 TV series Numbers, the leading character, mathematics professor Charlie Eppes, is portrayed as a Fields nominee. The series also references the popular myth concerning the absence of a Nobel Prize in mathematics, with a character jokingly claiming it was excluded because of a mathematician's romantic prowess with Alfred Nobel's fiancée.