Mathematical discoveries, small or great are never born of spontaneous generation.

In the old days when people invented a new function they had something useful in mind. Now, they invent them deliberately just to invalidate our ancestors' reasoning, and that is all they are ever going to get out of them.

Just as houses are made of stones, so is science made of facts.

Geometry is not true, it is advantageous.

All the scientist creates in a fact is the language in which he enunciates it. If he predicts a fact, he will employ this language, and for all those who can speak and understand it, his prediction is free from ambiguity. Moreover, this prediction once made, it evidently does not depend upon him whether it is fulfilled or not.

It is with logic that one proves; it is with intuition that one invents.

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