The Field Medal is one of the most prestigious prizes in Mathematics. There is no Nobel Prize in Mathematics.
The Field Medal is awarded every four years on the occasion of the International Congress of Mathematics to recognize outstanding mathematical achievement. The medal is made of gold and shows the face of the brilliant Archimedes. Contrary to other prizes that are usually received by old scientists, the Field Medal can only be won by mathematicians under 40 years of age. This could sound strange, but realize that most important discoveries are usually done by young men and women with a great scientific creativity (that tends to decrease with age).
The proof of the Fermat's Last Theorem was one of the most dificult problems for almost 400 years, until the British mathematician Andrew Wiles solved it. He did a first attempt to give a valid proof in 1993, when he was 40, but there was a little mistake that he could not correct until 1995. Then he was 42, so beyond the age limit of 40 years for receiving the Field Medal! Nevertheless, the International Mathematical Union gave him a silver plaque in recognition of his proof.
In 2006, Grigori Perelman declined the Field Medal. Four years later he also declined a one million dollar prize for solving the Poincaré Conjecture, one of the Millennium Problems.