I don't see how you could distinguish those. Even the purest form mathematics involves things like rules and symbols and those have to exist in reality (certainly they are at least as real as any emotion).

My first foray into math involved counting with my fingers.

Sure, it just takes a lot of remembering. But the point is that still that isn't "pure" mental activity. I am still imagining symbols and rules, those exist in reality at least as much as emotions do.