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.

Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that by their very nature refer to the infinite. This is his glory.

We must learn a new modesty. We have stormed the heavens, but succeeded only in building fog upon fog, a mist which will not support anybody who earnestly desires to stand upon it. What is valid seems so insignificant that it may be seriously doubted whether anlaysis is at all possible.

Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind.

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.