Geometry is not true, it is advantageous.

In the old days when people invented a new function they had something useful in mind.

All that is not thought is pure nothingness; since we can think only thoughts, and all the words we use to speak of things can express only thoughts, to say there is something other than thought is therefore an affirmation which can have no meaning.

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.

Need we add that mathematicians themselves are not infallible?

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.