One geometry cannot be more true than another; it can only be more convenient.

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 whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole; it is to intuition that we must look for it.

Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.

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 the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed.

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

How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.