So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality.

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.

It is not order only, but unexpected order, that has value.

Sociology is the science with the greatest number of methods and the least results.

If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living

Thought must never submit, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, save to the facts themselves, because, for thought, submission would mean ceasing to be.