American Mathematician Quotes
Most convincing to me of the spiritual relations between mathematics and music, is my own very personal experience. Composing in an amateurish way, I get exactly the same elevation from a prelude that has come to me at the piano, as I do from a new idea that has come to me in mathematics.
[Science] advances by leaps; and the impulse for each leap is either some new observational resource, or some novel way of reasoning about the observations. Such novel way of reasoning might, perhaps, be considered as a new observation means, since it draws attention to reactions between facts which would previously have been passed by unperceived.