But it seems an irony of creation that man's mind knows how to handle things the better the farther removed they are from the center of his existence. Thus we are cleverest where knowledge matters least.

Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

... numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.

The whole is always more, is more capable of a much greater variety of wave states, than the combination of its parts. ... In this very radical sense, quantum physics supports the doctrine that the whole is more than the combination of its parts.

For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.

You can not apply mathematics as long as words still becloud reality.

A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details.