Any philosophy worth taking seriously would have to be built upon a firm foundation of unyielding despair.

Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.

A democrat need not believe that the majority will always reach a wise decision. He should however believe in the necessity of accepting the decision of the majority, be it wise or unwise, until such a time that the majority reaches another decision.

I must, before I die, find some way to say the essential thing that is in me, that I have never said yet -- a thing that is not love or hate or pity or scorn, but the very breath of life, fierce and coming from far away, bringing into human life the vastness and the fearful passionless force of non-human things.

... the word "theory" ... was originally an Orphic word, which Cornford interprets as "passionate sympathetic contemplation" ... For Pythagoras, the "passionate sympathetic contemplation" was intellectual, and issued in mathematical knowledge ... To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural.

The mind is a strange machine which can combine the materials offered to it in the most astonishing ways.

The power of thought, the vast regions it can master.