It may be that metaphors don't play a central role in formulating more advanced mathematical concepts, or that if they do, they will need to be of a different nature than those used in more elementary mathematics. Mathematical concepts, once they are developed, acquire a life of their own and are dealt with directly. It's difficult for me to conceive of a metaphor for a real number raised to a complex power, but if there is one, I'd sure like to see it. (Joseph Auslander)