No one knows what he is doing so long as he is acting rightly; but of what is wrong one is always conscious.
Johann Wolfgang von GoetheMan knows himself only insofar as he knows the world, becoming aware of it if only within himself, and of himself self only within it. Each new subject, well observed, opens up within us a new organ of thought.
Johann Wolfgang von GoetheMathematics 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.
Johann Wolfgang von Goethe