Mathematicians do not study objects, but the relations between objects.

A small error in the former will produce an enormous error in the latter.

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.

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 is feared, it is above all because it can give no happiness? Man, then, can not be happy through science but today he can much less be happy without it.

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.

Need we add that mathematicians themselves are not infallible?

But for harmony beautiful to contemplate, science would not be worth following.