I think intelligence is a general idea for one's amount to learn, their memory, problem-solving, etc... . For this, I use 3 main psychologists:
1) Dr. Gardner: He proposed a variety of intelligences: musical, spatial reasoning, mathematical, naturalistc, intrapersonal, verbal, interpersonal, body-kinesthetic, spiritual, moral, and existential intelligences (the last 3 generally aren't talked about as much). (wiki)
2) Dr. Louis Leon Thurstone: He made the law of comparative judgement, and used 7 main traits for intelligence and its testing: verbal comprehension, word fluency, number facility, spatial visualization, associative memory, perceptual speed and reasoning. (wiki)
I don't think that saying it's based solely off of mathematical ability or such is accurate because take savants: they undergo some brain damage and are now amazing at one thing. Let's say, it's music. Perhaps before they were brilliant at math but now they can hardly pass Grade 8 mathematics. Does it seem fair to call them stupid based on their poor mathematical ability, while their musical ability is off the charts?
3) Sigmund Freud: I'm not the biggest fan of psychoanalysis, however, the man does provide a unique way of looking at something, and it would be foolish to say he has contributed nothing to psychology. Freud hypothesized of an id, ego and super-ego (I won't bore you all with this). To put it simply, the id uses the pleasure principle, ego uses reality principle and super-ego uses morality principle, and of course, each experience different types of anxiety. The ego is generally the one that is the busiest (and psychodynamic treatments sometimes focus on the ego using ego analysis), and of course, any reasoanble person would say that the ego needs intelligence. Then again, so does the super-ego using the morality principle, hence, moral intelligence (relating back to Dr.Gardner's theory of multiple intelligences).
I don't think there's really an easy, quick and simple way to say what intelligence is. I personally go with Dr.Gardner and Dr.Thurstone for defining intelligence. It's sort of a beat-around-the-bus type of answer, however, it's either that or a quick, simple one that ignores certain types or includes too many types of intelligences, hence, why I.Q. tests aren't really the best.
Also, there's crystallized and fluid intelligences; fluid is the decision-making when in a new environment, and crystallized is what you've learnt. This is one reason why I think saying intelligence is based only on decision-making is inadequate because you instantly imply that what you've learnt is more or less meaningless, after all, you don't use everything you've learnt in decision-making. Thus, basing it only on decision-making can make one's intelligence seem far lower/higher than it really is.
EDIT: I put (wiki) because I cannot post URLs yet, so just search it in wikipedia.