A mathematics teacher is a midwife to ideas.

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.'

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

The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing.

The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is feasible.

Look around when you have got your first mushroom or made your first discovery: they grow in clusters.

Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements.