The way in which mathematicians and physicists and historians talk is quite different, and what a physicist means by physical intuition and what a mathematician means by beauty or elegance are things worth thinking about.

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Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.

A mathematician is a person who can find analogies between theorems a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories.