I really dont believe there is a single intelligence. Even if there is a trend that says if you score high in one field you tend to score high in the others as well.....first of all, this may be statically common but is not true in all cases. Second, while they divide up different skills, most of these skills using multiple faculties....I am not convinced that we have A). Identified the distinct cognitive faculties yet, or B). come up with a test that tests the specific faculties in isolation.....and we cant until we understand exactly what they are.
Any skill is going to use multiple faculties, not just one. If you have a strong faculty, it should manifest in your ability for multiple skills, not just one....but I dont believe that there is only one universal faculty....and no, we dont know for sure that Mozart would excel in math....for all we know, a learning dissability could prevent him from understanding geometry, and we wouldnt know if that specific faculty was not essential for his music....just as a crude example, as I am guessing some of the faculties used in math are necessary for music as well, but some faculties needed for music are not needed for math, and likely vice versa. They might share SOME common faculties, but not ALL common faculties.
So, while exceptional faculties will be seen in a spectrum of talents, there are still multiple faculties that work in unison, and if they have not seen wide variance cross category, its because the different categories do not properly isolate the different faculties, NOT because there is only a single faculty called intelligence.