I've heard descriptions of how maths and music go together for some people, but for me, they seem to trip completely different parts of my brain. Maths is a process of free-associating possible approaches; tracking each through methodically until it reaches some sort of conclusion, and repeating until you've got somewhere. Music trips my emotions. I can imagine how a sort of pattern-spotting could apply to both, but I find it hard to see music like that, I'm barely beyond "I like it but I don't know why" and "I don't like it but I don't know why".
I am somewhat interested in pop explanations of music theory when it's explained in terms of frequencies and "this is why these notes go together and why these notes don't go together". But I find it impossible to grok explanations that involve learning a bunch of terminology according to how various things were discovered. I need things laid out with "these concepts are fixed because physics, these are cultural, these are an artifact of the notation system, these are basically the same but slightly different, etc" :)
I do feel a cultural affinity for the sort of music which mathematicians stereotypically often like, though, even if my actual exposure to it is small :)
 Come to think of it, that's an interesting observation about maths, that one foundation of actually doing maths, rather than applying previous maths, is generalising between different things that are similar in some way that's hard to explain. This proof and this other proof are the same, but one has 3 and one has 5 -- can I replace 3 with "any odd number" or "any prime number"? The method of solving this integral and that integral are very similar -- can I generalise to a method which works on any related integral? Category theory is this tendency on steroids.
But I don't know if this is something that really good mathematicians are much better at, or just something that you need a minimum amount of.
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