The Fields Medal is one of the most prestigious awards in mathematics, often referred to as the "Nobel Prize of Mathematics." It recognizes outstanding mathematical achievement for existing work and the promise of future achievement. The medal is awarded every four years by the International Mathematical Union (IMU) during the International Congress of Mathematicians (ICM). Unlike the Nobel Prize, which has no age limit and is awarded annually in several categories, the Fields Medal is specifically given to mathematicians under the age of 40 on January 1 of the award year, emphasizing the promotion of young talent.
The Fields Medal was established through the vision of Canadian mathematician John Charles Fields (1863–1932), who served as president of the IMU from 1924 to 1926. Fields, a professor at the University of Toronto, was motivated by the need to recognize mathematical excellence internationally, particularly in the aftermath of World War I, to foster international cooperation and highlight mathematics as a universal language. He proposed the creation of a medal and prize fund at the 1924 ICM in Toronto and again in 1928. Fields personally designed the medal and contributed to its funding, but he died in 1932 before it could be instituted.
The first Fields Medals were awarded in 1936 at the Oslo ICM to Lars Ahlfors and Jesse Douglas. Due to World War II, no awards were given in 1940. The tradition resumed in 1950 at the Cambridge ICM, with two recipients, and has continued quadrennially since then, typically awarding two to four medals each time. The age limit of 40 was formalized in 1950 to ensure the award goes to mathematicians at a stage where they can still make significant contributions.
The IMU oversees the selection process, which is highly secretive and rigorous. A committee of eminent mathematicians nominates and votes on candidates, with the final decision kept confidential until the announcement at the ICM. The award has evolved to include a monetary prize, which was CA$15,000 starting in 2006, funded initially by Fields and later by the Norwegian government and other sources.
The Fields Medal features an obverse design by Canadian sculptor R. Tait McKenzie, depicting the ancient Greek philosopher Archimedes awakening the people of Syracuse with a torch, symbolizing the illumination of knowledge. The reverse, designed by Fields himself, shows three children representing the three ancient centers of learning: Athens, Alexandria, and Nalanda, with an inscription from Virgil's Aeneid: "Transire suum pectus mundoque potiri" (to translate the human mind and to rule the world). The medal is cast in 18-karat gold and weighs approximately 169 grams.
Regarded as the highest honor in mathematics, the Fields Medal has been awarded to 64 individuals as of 2022, with notable firsts including Maryam Mirzakhani as the first woman recipient in 2014 and Hugo Duminil-Copin, a French mathematician of Kurdish descent, in 2022. The award criteria focus on groundbreaking contributions across pure and applied mathematics, including fields like algebraic geometry, number theory, topology, and probability. It has significantly influenced the mathematical community by spotlighting innovative work and encouraging interdisciplinary approaches.
The Fields Medal differs from other major math awards like the Abel Prize, which has no age limit and recognizes lifetime achievement, or the Wolf Prize in Mathematics, which is biennial. Its quadrennial cycle aligns with the ICM, making the award ceremony a highlight of global mathematical gatherings.
Sources consulted include the official IMU website, Wikipedia's entry on the Fields Medal, Britannica's overview, and MathWorld's historical summary. For further reading: