Mathematics is the art of giving the same name to different things.
Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.
Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.
It is not order only, but unexpected order, that has value.
Geometry is not true, it is advantageous.
It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.