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.

There are no solved problems; there are only problems that are more or less solved.

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

It is by logic we prove. It is by intuition we discover.

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

Mathematics is the art of giving the same name to different things.

Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.