What Is the Fields Medal? Mathematics' Most Prestigious Prize Explained

The Fields Medal is formally known as the International Medal for Outstanding Discoveries in Mathematics. It was established in 1936 by Canadian mathematician John Charles Fields and is awarded at the International Congress of Mathematicians, held every four years.

Eligibility

Recipients must be under 40 years of age at the time of the award. This age cap — unique among major scientific prizes — was intentional: Fields wanted the award to encourage future mathematical work rather than simply recognize a completed career.

Prize Value

The medal comes with a cash prize of 15,000 Canadian dollars — modest by Nobel standards, but the prestige is incomparable in the mathematical community.

Notable Recipients

John Milnor (1962) for differential topology. Paul Cohen (1966) for proving the independence of the Continuum Hypothesis. Grigori Perelman (2006), who famously declined the medal after proving the Poincaré Conjecture — one of the Millennium Prize Problems. Maryam Mirzakhani (2014) became the first woman to receive the Fields Medal, honored for her work on the dynamics and geometry of Riemann surfaces.