At the 1924 International Congress of Mathematicians in Toronto, a resolution was adopted that at each ICM, two gold medals should be awarded to recognize outstanding mathematical achievement. Professor J. D. Fields, a Canadian mathematician who was secretary of the 1924 Congress, later donated funds establishing the medals which were named in his honor. Consistent with Fields's wish that the awards recognize both existing work and the promise of future achievement, it was agreed to restrict the medals to mathematicians not over forty at the year of the Congress. In 1966 it was agreed that, in light of the great expansion of mathematical research, up to four medals could be awarded at each Congress.

For more details about the origins of the Fields Medal we recommend the article:

Henry S. Tropp, "The Origins and History of the Fields Medal", Historia Mathematica 3 (1976) 167-181.

The following text by Eberhard Knobloch describes the design of the medal:

Obverse:

The head represents Archimedes facing right.

1. In the field is the word in Greek capitals and
2. the artist's monogram and date RTM, MCNXXXIII.
3. The inscription reads: TRANSIRE SUUM PECTUS MUNDOQUE POTIRI.

The inscriptions mean:

1. "of Archimedes", namely the face of Archimedes.
2. R(obert) T(ait) M(cKenzie), that is the name of the Canadian sculptor who designed the medal. The correct date would read: "MCMXXXIII" or 1933. The second letter M has to be substituted for the false N.
3. "To transcend one's spirit and to take hold of (to master) the world."

Reverse:

The inscription on the tablet reads:

It means: "The mathematicians having congregated from the whole world awarded (this medal) because of outstanding writings." The verb form "tribuere" (the first "e" is a long vowel) is a short form of "tribuerunt".

In the background there is a representation of Archimedes' sphere being inscribed in a cylinder.