The reason Alfred Noble did not issue a prize for mathematics in his will is due to his wife's behavior. It is said that Alfred Noble's wife had an ongoing affair with a prominent asthmatic at the time of his will. Alfred was certain that if he issued a prize for mathematics, that the same professor having an affair with his wife, would win.
It is difficult to determine why Alfred Noble did not dictate a prize for mathematics in his will. It is entirely possible that he belived there was enough existing recognition for outstanding mathematicians or he may equally as likely felt that other, wider disciplines were more deserving fields due to their applicability to human endeavour.
With the exception of medicine, all of the original Nobel prizes are awarded in fields that were of interest to Nobel. They are physics, chemistry, peace, literature and medicine. Although mathematics are used extensively in chemistry and physics, it simply wasn't of sufficient interest for Nobel to consider a prize for it. Rumors that Nobel was jealous of mathematicians of his time have been proven untrue. Perhaps Nobel felt that the mysteries of mathematics had been sufficiently revealed at that time and a prize was not needed. Perhaps he simply didn't see mathematics as anything more than the calculations in his preferred fields. Whatever his reasons, a sixth prize in the field of economics was added in 1969.
Noble didn't choose mathematics for one of his prizes, because it wasn't one of the fields that he was interested in. There could have been many deserving subjects for the noble prize, and Noble picked the subjects that were of the greatest interest to him. Because there is a prize in economics, there is an applied mathematics prize. Perhaps Noble wanted to focus on practical developments rather than abstract theories.