Music and math have a very close relationship that stretches back thousands of years, to the very origins of music and civilization. In fact, it’s unfortunate that we don’t teach these connections to kids in school because that might make them see mathematics in a new light.
There are a lot of connections between Mathematics and Music that are hard to describe to people that haven’t studied them at a high level. I’d say the most interesting and obvious connection between the two of them is the study of the sheer intricacies of patterns–at least that’s what excites me most about them both. Mathematics has entire fields devoted to the study of patterns, functions, quantities, and shapes. Music is the patterns, functions, colours and shapes of sound.
Music involves creating patterns of sound. Mathematics can be described as the study of patterns. So you can study everything in music — melody, harmony, rhythm, timbre — from several different mathematical perspectives, including geometry, number theory, trigonometry, differential calculus, combinatorics and signal processing. Also, the electrical and electronic tools used to make modern music are based on a mathematical understanding of how music works.
There is definitely a correlation between musical precociousness and mathematical understanding, it just hasn’t been studied yet.