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Portrait of The Fields Medal

Science · Mathematics

The Fields Medal

1936 – present

Mathematics — prizes and honours

Mathematics' most famous award, given every four years at the International Congress of Mathematicians to between two and four mathematicians who must be under 40 on 1 January of the award year. It was endowed by the Canadian mathematician John Charles Fields and first awarded in Oslo in 1936. The medal bears the head of Archimedes and the Latin motto transire suum pectus mundoque potiri — "to rise above oneself and grasp the world". Because of the age limit it is not a lifetime-achievement prize, and the cash attached, C$15,000, is trivial beside its prestige.

How to spot them

  • ▸Awarded every four years at the International Congress of Mathematicians
  • ▸Recipients must be under 40 — the reason Andrew Wiles never received one
  • ▸The obverse shows Archimedes; the motto is 'to rise above oneself and grasp the world'
  • ▸First given in Oslo in 1936; the endowment came from a Canadian mathematician
  • ▸Two women have won it before 2026: Maryam Mirzakhani in 2014 and Maryna Viazovska in 2022

Key facts

A quadrennial award restricted to mathematicians under the age of 40 (1936)

The age limit is its defining and most-asked-about feature

The head of Archimedes on the obverse, with a motto about rising above oneself

transire suum pectus mundoque potiri — designed by the Canadian sculptor Robert Tait McKenzie

Declined in 2006 by a reclusive Russian who had proved the Poincaré conjecture (2006)

Grigori Perelman, the only person ever to refuse it

The first woman to win it, an Iranian professor at Stanford who died of cancer in 2017 (2014)

Maryam Mirzakhani, honoured for work on Riemann surfaces and moduli spaces

A 1998 silver plaque given to a laureate who was too old to receive the real thing (1998)

Andrew Wiles, 41 when he completed the proof of Fermat's Last Theorem

Stolen from a Kurdish-Iranian laureate's briefcase in Rio within minutes of the 2018 ceremony (2018)

Caucher Birkar's medal; a replacement was presented days later

Four winners announced in Philadelphia in July 2026, including only the third woman (2026)

Yu Deng, John Pardon, Jacob Tsimerman and Hong Wang

A 1966 laureate honoured for showing the continuum hypothesis to be independent (1966)

Paul Cohen, whose method of forcing settled the first of Hilbert's problems

Key ideas

  • The age limit under 40 is interpreted as under 40 on 1 January of the year of the Congress, and is meant to recognise promise as well as achievement.
  • The International Mathematical Union also awards the Abacus Medal (formerly the Nevanlinna Prize), the Gauss Prize, the Chern Medal and the Leelavati Prize at the same ceremony.

Quick-fire facts

  • •Endowed by John Charles Fields (1863–1932) and first awarded at the Oslo Congress in 1936, to Lars Ahlfors and Jesse Douglas
  • •Between two and four are awarded every four years; the recipient must be under 40 on 1 January of that year
  • •The medal is struck in 14-carat gold and carries a cash award of C$15,000
  • •The obverse shows Archimedes and the motto transire suum pectus mundoque potiri; the reverse refers to the mathematicians of the world assembled to honour outstanding work
  • •Grigori Perelman declined the medal in 2006 — the only person to do so
  • •Maryam Mirzakhani became the first woman to win it in 2014; she died in 2017 aged 40
  • •Maryna Viazovska, honoured in 2022 for sphere packing in dimensions 8 and 24, was the second
  • •The 2026 medals went to Yu Deng, John Pardon, Jacob Tsimerman and Hong Wang at the ICM in Philadelphia; Hong Wang is the third woman to receive it
  • •Caucher Birkar, a Kurdish refugee who became a Cambridge professor, had his medal stolen in Rio in 2018 minutes after receiving it
  • •Jean-Pierre Serre, awarded in 1954 at 27, remains the youngest recipient
  • •Other British winners include Michael Atiyah (1966), Simon Donaldson (1986), Richard Borcherds and Timothy Gowers (1998), and James Maynard (2022)

Drill it — 9 cards

1 / 9new card

Sources