Chance ... must be something more than the name we give to our ignorance..

The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things..

Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though th….

Les faits ne parlent pas. Facts do not speak..

A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mat….

If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science….

The task of the educator is to make the child's spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppress….

The mind uses its faculty for creativity only when experience forces it to do so..

Talk with M. Hermite. He never evokes a concrete image, yet you soon perceive that the more abstract entities are to him like living creatures..

One does not ask whether a scientific theory is true, but only whether it is convenient..

I entered an omnibus to go to some place or other. At that moment when I put my foot on the step the idea came to me, without anything in my former t….

A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of ….

To invent is to discern, to choose..

Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work..

All that is not thought is pure nothingness; since we can think only thoughts, and all the words we use to speak of things can express only thoughts,….

The subliminal self is in no way inferior to the conscious self. It knows how to choose and to divine..

When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the ….

It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produ….

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

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

Point set topology is a disease from which the human race will soon recover..