History of the Prizes

1. Why No Mathematics Nobel?

When Alfred Nobel established his prizes in 1895 there was no mathematics category. The popular legend that Nobel resented Gösta Mittag-Leffler over a personal grievance is unsubstantiated — Nobel and Mittag-Leffler barely knew each other — but the absence is real. Nobel’s prizes were oriented toward applied benefit to mankind, and pure mathematics did not fit his criteria. The mathematical community has long sought equivalent recognition.

2. John Charles Fields and the 1936 Medal

John Charles Fields (1863–1932) was a Canadian mathematician who organised the 1924 Toronto International Congress of Mathematicians. Aware of the absence of an analogue to the Nobel, he proposed and bequeathed funds for a medal recognising mathematical excellence. He died before the first awards. The first Fields Medals were given at the Oslo ICM in 1936 to Lars Ahlfors (complex analysis) and Jesse Douglas (Plateau’s problem of minimal surfaces).

Fields’ will specified that the medal recognise both existing work and the promise of future achievement. The under-40 age limit, although not in his original wording, evolved as the committee’s interpretation of that promise clause. The prize is now given to up to four laureates every four years at the ICM — the world’s largest mathematics meeting.

3. Niels Henrik Abel

Niels Henrik Abel (1802–1829) was a Norwegian mathematician of extraordinary precocity who, in his short life, settled the question of solubility of the general quintic by radicals (negatively, in 1824, anticipating Galois) and pioneered the theory of elliptic functions and what we now call abelian integrals and abelian groups. He died of tuberculosis at twenty-six, two days before a letter offering him a chair in Berlin reached his lodgings.

The bicentenary of Abel’s birth in 2002 prompted the Norwegian government to establish a major mathematical prize in his name — the Abel Prize. Awarded annually since 2003 by the King of Norway, it carries a purse of 7.5 million NOK (~US$700,000), comparable to a Nobel Prize. It has no age limit and recognises lifetime achievement in mathematics.

4. Two Distinct Cultures

The two prizes have evolved different cultures:

• Fields Medal: every four years, multiple laureates, under 40, emphasis on the trajectory of the laureate’s career, awarded at a working mathematical congress (the ICM), modest cash component.
• Abel Prize: annual, single laureate (occasionally shared), no age limit, emphasis on a lifetime body of work, large cash component, awarded at a state ceremony in Oslo.

Two mathematicians have received both: Jean-Pierre Serre (Fields 1954, inaugural Abel 2003) and John Milnor (Fields 1962, Abel 2011). A handful more have been considered for the Abel Prize after age-disqualifying for the Fields.

5. Other Mathematical Honours

For completeness: the Wolf Prize in Mathematics (Israel, since 1978) recognises lifetime achievement and for many years was the closest thing to a mathematical Nobel; the Chern Medal (since 2010, ICM) is also for lifetime achievement and has no age limit; the Breakthrough Prize in Mathematics(since 2014) is privately funded and carries a US$3 million purse. The Fields and Abel Prizes remain, however, the two awards by which the international mathematical community recognises its very best work.