Why is there no Nobel in mathematics?

Nobel prizes were created by the will of Alfred Nobel, a notable Swedish chemist.

One of the most common -and unfounded- 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 because 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).

Further, at the time there existed already a well known Scandinavian prize for mathematicians. If Nobel knew about this prize he may have felt less compelled to add a competing prize for mathematicians in his will.

[...] As professor ordinarius in Stockholm, Mittag-Leffler began a 30-year career of vigorous mathematical activity. In 1882 he founded the Acta Mathematica, which a century later is still one of the world's leading mathematical journals. Through his influence in Stockholm he persuaded King Oscar II to endow prize competitions and honor various distinguished mathematicians all over Europe. Hermite, Bertrand, Weierstrass, and Poincare were among those honored by the King. [...]

Source: "The Mathematics of Sonya Kovalevskaya" by Roger Cooke (Springer-Verlag, New York etc., 1984, II.5.2, p. 90-91:

Here are some relevant facts:

• Nobel never married, hence no ``wife''. (He did have a mistress, a Viennese woman named Sophie Hess.)
• Gosta Mittag-Leffler was an important mathematician in Sweden in the late 19th-early 20th century. He was the founder of the journal Acta Mathematica, played an important role in helping the career of Sonya Kovalevskaya, and was eventually head of the Stockholm Hogskola, the precursor to Stockholms Universitet. However, it seems highly unlikely that he would have been a leading candidate for an early Nobel Prize in mathematics, had there been one - there were guys like Poincare and Hilbert around, after all.
• There is no evidence that Mittag-Leffler had much contact with Alfred Nobel (who resided in Paris during the latter part of his life), still less that there was animosity between them for whatever reason. To the contrary, towards the end of Nobel's life Mittag-Leffler was engaged in ``diplomatic'' negotiations to try to persuade Nobel to designate a substantial part of his fortune to the Hogskola. It seems hardly likely that he would have undertaken this if there was prior bad blood between them. Although initially Nobel seems to have intended to do this, eventually he came up with the Nobel Prize idea - much to the disappointment of the Hogskola, not to mention Nobel's relatives and Fraulein Hess.
• 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....

  However, Sister Mary Thomas a Kempis discovered a letter by R. C. Archibald in the archives of Brown University and discussed its contents in "The Mathematics Teacher" (1966, pp.667-668). Archibald had visited Mittag-Leffler and, on his report, it would seem that M-L *believed* that the absence of a Nobel Prize in mathematics was due to an estrangement between the two men. (This at least is the natural reading, but not the only possible one.)
• A final speculation concerning the psychological element. Would Nobel, sitting down to draw up his testament, presumably in a mood of great benevolence to mankind, have allowed a mere personal grudge to distort his idealistic plans for the monument he would leave behind?

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.