Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.

Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.... The two propositions: "The earth turns round" and "it is more convenient to suppose the earth turns round" have the same meaning; there is nothing more in the one than in the other.

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.

Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.

Geometry is the art of correct reasoning from incorrectly drawn figures.

Often when works at a hard question, nothing good is accomplished at the first attack. Then one takes a rest, long or short, and sits down anew to the work. During the first half-hour, as before, nothing is found, and then all of a sudden the decisive idea presents itself to the mind.

Thought is only a flash between two long nights, but this flash is everything.