A very small cause, which escapes us, determines a considerable effect which we cannot ignore, and we say that this effect is due to chance.

It is far better to foresee even without certainty than not to foresee at all.

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know

A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.

Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.