See Conway and Guy The Book of Numbers, New York: Springer-Verlag, 1996
There is perhaps some strong similarity between musical composition and mathematical thinking. People might suppose that a mathematical proof is conceived as a logical progression, where each step follows upon the ones that have preceded it. Yet the conception of a new argument is hardly likely actually to proceed in this way. There is a globality and seemingly vague conceptual content that is necessary in the construction of a mathematical argument and this can bear little relation to the time that it would seem to take in order fully to appreciate a serially presented proof.Penrose, Roger, The Emperor's New Mind, p576-577