Twice two makes four seems to me simply a piece of insolence. Twice two makes four is a pert coxcomb who stands with arms akimbo barring your path and spitting. I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too.
The years of searching in the dark for a truth that one feels but cannot express, the intense desire and the alternations of confidence and misgiving until one breaks through to clarity and understanding, are known only to him who has experienced them himself.
But twice-two-makes-four is for all that a most insupportable thing. Twice-two-makes-four is, in my humble opinion, nothing but a piece of impudence. Twice-two-makes-four is a farcical, dressed-up fellow who stands across your path with arms akimbo and spits at you.
Consider the concepts referred to in the words 'where', 'when', 'why', 'being', to the elucidation of which innumerable volumes of philosophy have been devoted. We fare no better in our speculations than a fish which should strive to become clear as to what is water.
What's all this whining about the environment? They're always talking about 'stop the clearcuts.' I mean do the math people. If we were out of trees then we wouldn't have any clearcuts to be complaining about now would we?
But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.