Six Nobel Prizes are awarded each year, one in each of the following categories: literature, physics, chemistry, peace, economics and medicine. Notably absent from this list is an award for Mathematics. The reason for this conspicuous omission has been subject of extensive speculations, some of which are discussed below.
One of the most common reasons as to why Nobel decided against a Nobel prize in math is that [a woman he proposed to/his wife/his mistress] [rejected him beacuse of/cheated him with] a famous mathematician. Gosta Mittag-Leffler is often claimed to be the guilty party.
There is no historical evidence to support the story.
For one, Mr. Nobel was never married.
There are more credible reasons as to why there is no Nobel prize in math. Chiefly among them is simply the fact he didn't care much for mathematics, and that it was not considered a practical science from which humanity could benefit (a chief purpose for creating the Nobel Foundation).
Here are some relevant facts:
According to the very interesting study by Elisabeth Crawford, ``The Beginnings of the Nobel Institution'', Cambridge Univ. Press, 1984, pages 52-53:
``Although it is not known how those in responsible positions at the Hogskola came to believe that a *large* bequest was forthcoming, this indeed was the expectation, and the disappointment was keen when it was announced early in 1897 that the Hogskola had been left out of Nobel's final will in 1895. Recriminations followed, with both Pettersson and Arrhenius [academic rivals of Mittag-Leffler in the administration of the Hogskola] letting it be known that Nobel's dislike for Mittag-Leffler had brought about what Pettersson termed the `Nobel Flop'. This is only of interest because it may have contributed to the myth that Nobel had planned to institute a prize in mathematics but had refrained because of his antipathy to Mittag-Leffler or --in another version of the same story-- because of their rivalry for the affections of a woman....''
Nobel, an inventor and industrialist, did not create a prize in mathematics simply because he was not particularly interested in mathematics or theoretical science. His will speaks of prizes for those ``inventions or discoveries'' of greatest practical benefit to mankind. (Probably as a result of this language, the physics prize has been awarded for experimental work much more often than for advances in theory.)
However, the story of some rivalry over a woman is obviously much more amusing, and that's why it will probably continue to be repeated.
Whatever the case, the mathematicians of the world decided to fight back. At the 1924 International Congress of Mathematicians (ICM) in Toronto, a resolution was adopted that at each ICM, two gold medals should be awarded to recognize outstanding mathematical achievement. A hyperlinked list of all Fields medal laureates can be found here.
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