Arthur Stanley Eddington Quotes on Mathematics
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To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the 'cat without a grin' and the 'grin without a cat' are equally set aside as purely mathematical phantasies.
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We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about 'and'.
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Schrodinger's wave-mechanics is not a physical theory, but a dodge - and a very good dodge too.
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Proof is the idol before whom the pure mathematician tortures himself.
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The mathematics is not there till we put it there.