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Many people have commented over the ages on the similarities between mathematics and music. Leibniz once said that "music is the pleasure the human mind experiences from counting without being aware that it is counting". But the similarity is more than mere numerical. The aesthetics of a musical composition have much in common with the best pieces of mathematics, where themes are established, then mutate and interweave until we find ourselves transformed at the end of the piece to a new place. Just as we listen to a piece of music over and over, finding resonances we missed on first listening, mathematicians often get the same pleasure in rereading proofs, noticing the subtle nuances that make the piece hang together so effortlessly.