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Mathematics is really a field of inventions and research where we find interesting problems some of which we can solve and others which remain open. I'm sorry to ask this question because I see it is better suited for the meta but at the same time I think that this is a question which may encourage people to research and learn more about Mathematics history.

My question is this: Why is there no Nobel Prize in mathematics yet it is one of the most important fields in science in terms of research?

Note: I hope find out the real reason why Mathematics is not a category for the Nobel Prize.

Thank you for any help.

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    $\begingroup$ One story says that Nobel's wife (lover, girlfriend, ...) had an affair with a mathematician, which soured the benefactor to the idea of funding a prize in mathematics. However that is apparently bunk: skeptics.stackexchange.com/questions/18635/… $\endgroup$ – Simon S Aug 10 '15 at 22:33
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    $\begingroup$ Having read some biographical material on Nobel, my impression is that he didn't consider mathematics of sufficient direct, practical importance , compared to the sciences for which he established awards. (The "popular" reason is a canard and is one of those stories that accreted to the Prize's history later. I could also be snide and say, "Whaddaya expect, he was an engineer !", but I won't do that... :p ) $\endgroup$ – colormegone Aug 10 '15 at 22:47
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    $\begingroup$ This has nothing to do with number theory. $\endgroup$ – davidlowryduda Aug 11 '15 at 0:05
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    $\begingroup$ That is a false claim. Number theory has only some of the interesting open problems of mathematics. $\endgroup$ – davidlowryduda Aug 11 '15 at 0:18
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    $\begingroup$ Try that other place to ask: hsm.stackexchange.com but of course check the duplicate question first! $\endgroup$ – GEdgar Aug 11 '15 at 0:51
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Nobel wanted to reward the most important discovery or invention for the benefit of mankind in his last will. He must have been very down to earth engineer. He assumed that the information about inventions and discoveries could be verified quickly and rewarded the next year, a provision that has been modified. Mathematics was perhaps considered less problematic to such a practical mind. The relevant part of his last will:

The whole of my remaining realizable estate shall be dealt with in the following way: the capital, invested in safe securities by my executors, shall constitute a fund, the interest on which shall be annually distributed in the form of prizes to those who, during the preceding year, shall have conferred the greatest benefit on mankind. The said interest shall be divided into five equal parts, which shall be apportioned as follows: one part to the person who shall have made the most important discovery or invention within the field of physics; one part to the person who shall have made the most important chemical discovery or improvement; one part to the person who shall have made the most important discovery within the domain of physiology or medicine; one part to the person who shall have produced in the field of literature the most outstanding work in an ideal direction; and one part to the person who shall have done the most or the best work for fraternity between nations, for the abolition or reduction of standing armies and for the holding and promotion of peace congresses. The prizes for physics and chemistry shall be awarded by the Swedish Academy of Sciences; that for physiological or medical work by the Caroline Institute in Stockholm; that for literature by the Academy in Stockholm, and that for champions of peace by a committee of five persons to be elected by the Norwegian Storting. It is my express wish that in awarding the prizes no consideration whatever shall be given to the nationality of the candidates, but that the most worthy shall receive the prize, whether he be a Scandinavian or not.

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Alfred Nobel just didn't think it was a subject worth giving a prize for. http://www.nobelprize.org/faq/questions_in_category.php?id=2

Just for your information, there also is no Nobel Prize for civil or electrical engineering (so it's not like he was discriminating solely against mathematics).

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    $\begingroup$ Although it might be said that electrical engineering within his lifetime was not the field we've come to think of it as in the past 75 years or so. $\endgroup$ – colormegone Aug 10 '15 at 22:52
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    $\begingroup$ You are every systematic about misspelling the guy's name! $\endgroup$ – Mariano Suárez-Álvarez Aug 11 '15 at 0:27

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