A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.
David HilbertHowever unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes.
David HilbertMathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
David HilbertOne must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs
David HilbertBesides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof.
David Hilbert