Fields Medal is highly regarded as the Nobel prize for mathematics, although its rules and the prize's monetary value are quite distinct of those of the Nobel prize.
The award is named after the Canadian mathematician John Charles Fields who chaired the Committee in charge of organizing the 1924 International Congress of Mathematicians to be held in Toronto.
As mentioned in the minutes of the Committee's meeting of 24 February 1931, this body "resolved that the sum of $2,500 should be set apart for two medals to be awarded in connection with successive International Mathematical Congresses through an international committee appointed for such purpose initially by the executive of the International Mathematical Congress, but later by the International Mathematical Union". The idea was rapidly supported by the major mathematical societies of France, Germany, Italy, Switzerland and the United States, and the medal, in spite of Field's intentions, became known as the Fields Medal when it was awarded for the first time in Oslo in 1936.
The Fields Medal is awarded every four years on the occasion of the International Congress of Mathematicians to recognize outstanding mathematical achievement for existing work and for the promise of future achievement.
A candidate's 40th birthday must not occur before January 1st of the year of the Congress at which the Fields Medals are awarded.
The Fields Medal Committee is asked to choose at least two, with a strong preference for four, Fields Medallists, and to have regard in its choice to representing a diversity of mathematical fields.
If a former student (Ph.D. thesis only) of a Committee member is seriously considered, such a member shall not continue to serve on the Committee for its final decision.
The monetary value of the Fields Prize is presently Can$15,000 (about US$11'800, or €9,100), microscopically out of scale of its reputation as the Nobel Prize in Mathematics.
As specified by Fields, the medal must "contain at least 200 dollars worth of gold and be of a fair size".
In the chaos of World War II, the medal itself proved invaluable for the Finnish Lars Ahlfors, one of the two first laureates in 1936. In 1945, he was allowed to leave Finland with only 10 crowns. He smuggled out his Fields Medal and pawned it, enabling him to reach his wife in Zürich, Switzerland.
Alexander Grothendieck, 1966 laureate, did not attend his own Fields Medal ceremony in Moscow, in protest against Soviet policies. By 1970, growing more and more discontent with the role of scientists in society, their eagerness to take military funding and generally with world politics, Grothendieck retreated from the scientific "milieu". In 1988, he refused the Crafoord Prize awarded by the Swedish Academy, on the grounds that not only his pension would be more than sufficient to meet his material needs, but above all because to "participate in the game of 'prizes' and 'awards' would also mean giving [his] own approval to" the declining "ethics of the scientific community (at least among mathematicians)". Later on, he supposedly left his home in France and his whereabouts are unknown.
Grigori Perelman, 2006 laureate, was the first person to decline the coveted prize. He has also refused a major European maths prize, reportedly on the grounds that he did not feel the awarding committee was sufficiently qualified to evaluate his work. According to news articles, Perelman became disenchanted with the ethical standards in the realm of mathematics, is unwilling to play the self-promoting game, and opted out of a successful career to live poorly with his mother in Saint Petersburg, Russia.