While I have heard speculative answers to this question, I do not know one which can be supported. Is there any information explaining why Nobel did not chose to include this topic? Has there even been a serious attempt within the committee to add one or an explanation why they will not?
Let's first mention that the popular myth that Nobel decided not to fund a prize for mathematicians because his wife was cheating on him with a mathematician (often said to be Gösta Mittag-Leffler) is (predictably) not true. In fact, it's trivially false since Nobel was never married! Furthermore, in the correspondence between him and his lover, there is no sign of anything like an affair.
It appears that the reason there is no Nobel Prize in Mathematics is much more dull: Nobel probably simply wasn't that interested in pure mathematics. The other categories are more natural, considering the context: Nobel was personally very much involved in physics and chemistry, so prizes for that were beyond questioning. It was also clear to him that medicine enormously benefits mankind (this is almost the definition of medicine, when you think about it!) It appears that the peace prize was suggested by his secretary and old lover, who would go on to win the prize in 1905. Finally, the prize in literature seems to simply have come from the fact that Nobel was very interested in literature.
There is an alternative theory, however. At the time, the same Mittag-Leffler that is often accused of stealing Nobel's wife had just recently ensured for King Oscar II to create an 'endowment prize for various mathematicians throughout Europe'. Perhaps, this convinced Nobel that no additional prize for mathematicians was needed.
This "oversight" of Mr. Nobel's was rectified in 1980 by the Crafoord Prize in mathematics. Now that there is such a prize, it's unlikely that the Nobel Committee will create another one for mathematics, even though the Crafoord Prize is much less well known,
Mr. Nobel not only created the prizes, but selected the Swedish academies to award them (except for the Peace Prize, which is awarded by the Norwegians, whom he wanted to placate). Perhaps he lacked confidence in the Swedish mathematics academy. He also didn't create a prize in economics, but the Swedish Academy of Science took it upon itself to rectify this.
One more slightly different claim is also that Nobel was not in good terms with Mittag Lefler and when he asked someone if a Nobel in math could ever go to Lefler, the person said yes and so Nobel striked off math from his list (which again some claimed contained math as one of the subjects).
But the most logical explanation that has ever been put forward was that Nobel was not much interested in math as he could not see any tangible applications which served mankind as the others subjects did. And also there existing a good prize for math at that time was probably another reason for him giving math a miss.