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Many mathematicians will tell you that Nobel omitted mathematics from his prizes to spite the Swedish mathematician Gosta Mittag-Leffler, a rival, and that the Canadian mathematician John Charles Fields created the award that bears his name to correct the omission. But this is a myth that needs debunking. First of all, there is no good evidence of a feud between Nobel and Mittag-Leffler. Nobel omitted mathematics simply because it was not as important to him as other endeavors were.
As for Fields, he proposed his award not as a substitute for the Nobel Prize but as a symbol of international unity. In the aftermath of World War I, the scientific community was fractured by national rivalries. When the International Mathematical Union was first founded, in 1920, it explicitly banned representatives of the former Central Powers. Fields so wanted “to avoid invidious comparisons” among candidates for his award that he suggested it be presented “with a view to encouraging further achievement” rather than just honoring past accomplishments. (This remark would later be used to justify the award’s age limit of 40, though Fields never intended the medal just for the young.)
Source: New York Times