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

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.

Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.

... 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.

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

No mathematician of equal stature has risen from our generation... Hilbert was singularly free from national and racial prejudices; in all public questions, be they political, social or spiritual, he stood forever on the side of freedom.

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.