A mathematics teacher is a midwife to ideas.

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

I am intentionally avoiding the standard term which, by the way, did not exist in Euler's time. One of the ugliest outgrowths of the "new math" was the premature introduction of technical terms.

Beauty in mathematics is seeing the truth without effort.

Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice.

A GREAT discovery solves a great problem but there is a grain of discovery in any problem.

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.'