You should not put too much trust in any unproved conjecture, even if it has been propounded by a great authority, even if it has been propounded by yourself. You should try to prove it or disprove it.

Hilbert once had a student in mathematics who stopped coming to his lectures, and he was finally told the young man had gone off to become a poet. Hilbert is reported to have remarked: 'I never thought he had enough imagination to be a mathematician.'

If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.

Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself

I am too good for philosophy and not good enough for physics. Mathematics is in between.

In order to solve this differential equation you look at it until a solution occurs to you.

Mathematics is not a spectator sport!