How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?
One might talk about the sanity of the atom the sanity of space the sanity of the electron the sanity of water- For it is all alive and has something comparable to that which we call sanity in ourselves. The only oneness is the oneness of sanity.
At the Egyptian city of Naucratis there was a famous old god whose name was Theuth; the bird which is called the Ibis was sacred to him, and he was the inventor of many arts, such as arithmetic and calculation and geometry and astronomy and draughts and dice, but his great discovery was the use of letters.
But the whole vital process of the earth takes place so gradually and in periods of time which are so immense compared with the length of our life, that these changes are not observed, and before their course can be recorded from beginning to end whole nations perish and are destroyed.
But by far the greatest obstacle to the progress of science and to the undertaking of new tasks and provinces therein is found in this-that men despair and think things impossible.
The recurrence of a phenomenon like Edison is not very likely. The profound change of conditions and the ever increasing necessity of theoretical training would seem to make it impossible. He will occupy a unique and exalted position in the history of his native land, which might well be proud of his great genius and undying achievements in the interest of humanity.
There is an astonishing imagination, even in the science of mathematics. ... We repeat, there was far more imagination in the head of Archimedes than in that of Homer.
We come no nearer the infinitude of the creative power of God, if we enclose the space of its revelation within a sphere described with the radius of the Milky Way, than if we were to limit it to a ball an inch in diameter. All that is finite, whatever has limits and a definite relation to unity, is equally far removed from the infinite... Eternity is not sufficient to embrace the manifestations of the Supreme Being, if it is not combined with the infinitude of space.
My parents were not scientists. They knew almost nothing about science. But in introducing me simultaneously to skepticism and to wonder, they taught me the two uneasily cohabiting modes of thought that are central to the scientific method.
We could use up two Eternities in learning all that is to be learned about our own world and the thousands of nations that have arisen and flourished and vanished from it. Mathematics alone would occupy me eight million years.