It is a sin not to know why you are sinning. Pointless sin must be avoided.

I do not think there is any other mental strain comparable to the exertion to which a tournament game subjects the chess master. Working at what seemed to me the most difficult mathematical problems has never exhausted me nearly as much as playing in a chess tournament; and of all intellectual applications mathematical work is surely the hardest. That is why physical fitness is a most important factor in tournament chess and why young players, whose brains can stand the poisons of fatigue much longer than those of older players have a great advantage.

A man whose mind has gone astray should study mathematics.

Victorious warriors win first and then go to war, while defeated warriors go to war first an then seek to win.

Mathematics requires a small dose, not of genius, but of an imaginative freedom which, in a larger dose, would be insanity.