There is nothing more frightful than for a teacher to know only what his scholars are intended to know.

Science has been seriously retarded by the study of what is not worth knowing and of what is not knowable.

Thou art in the end what thou art. Put on wigs with millions of curls, set thy foot upon ell-high rocks. Thou abidest ever--what thou art.

Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight.

While man's desires and aspirations stir he cannot choose but err.

A man's name is not like a mantle which merely hangs about him...but a perfectly fitting garment, which, like the skin, has grown over him, at which one cannot rake and scrape without injuring the man himself.

There is nothing so terrible as activity without insight.