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This is the first time I have come across a use of but to mean and without having a negative context. If the usage is correct, how would it be different from being used after a context with not only or not, and how would the meaning change if and were used instead of but also?
My brother is talented in many different ways. He is a mathematical genius but also has great musical ability.
But contrasts where and equates. In your example, the use of but suggests that there might be something exceptional about being a mathematical genius as well as having great musical ability. And would have made the combination of the two sound normal.
The second sentence means exactly the same thing as "He is not only a mathematical genius but also has great musical ability," a sentence with which you are familiar. In fact, because "not only" and "but" are redundant, we can elide the "not only" (although we don't have to). My personal preference is to use "not only" in these sentences.
The construction but also would typically be used in sentences where the two things being mentioned are not exactly of the same kind. For example:
The book is a little cryptic but also easy to understand at times.
and also would be used in sentences where the two parts mentioned are of similar kind:
The burger is pretty warm and also tasty
