No one likes having offended another person; hence everyone feels so much better if the other person doesn't show he's been offended. Nobody likes being confronted by a wounded spaniel. Remember that. It is much easier patiently - and tolerantly - to avoid the person you have injured than to approach him as a friend. You need courage for that.

Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.

If you want to go down deep you do not need to travel far; indeed, you don't have to leave your most immediate and familiar surroundings.

Is it even always an advantage to replace an indistinct picture by a sharp one? Isn't the indistinct one often what we need?