It is my conviction that pure mathematical construction enables us to — Mathematics

"As soon as a thought or word becomes a tool, one can dispense with actually ‘thinking’ it, that is, with going through the logical acts involved in verbal formulation of it. As has been pointed out, often and correctly, the advantage of mathematics—the model of all neo-positivistic thinking—lies in just this ‘intellectual economy.’ Complicated logical operations are carried out without actual performance of the intellectual acts upon which the mathematical and logical symbols are based. … Reason … becomes a fetish, a magic entity that is accepted rather than intellectually experienced."

"Mathematics may be compared to a mill of exquisite workmanship, which grinds your stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat flour from peascods, so pages of formulæ will not get a definite result out of loose data."

"In doing mathematics, I express something personal. It is a source of joy to know that, despite this personal aspect, the fruit of my work can be of interest to other mathematicians."

"If a religion is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one."

"It might have been beans, successful hunts, or victories in battle, but, for millennia, people were using maths to describe things - counting them, measuring them, dividing them up."

"“There’s more to life than mathematics,” Joan said. “But not much more.”"

"Now Art, used collectively for painting, sculpture, architecture and music, is the mediatress between, and reconciler of, nature and man. It is, therefore, the power of humanizing nature, of infusing the thoughts and passions of man into everything which is the object of his contemplation."

"The Good consists in the congruity of a thing with the laws of the reason and the nature of the will, and in its fitness to determine the latter to actualize the former: and it is always discursive. The Beautiful arises from the perceived harmony of an object, whether sight or sound, with the inborn and constitutive rules of the judgment and imagination: and it is always intuitive."

"I believe that the unity of man as opposed to other living things derives from the fact that man is the conscious life of himself. Man is conscious of himself, of his future, which is death, of his smallness, of his impotence; he is aware of others as others; man is in nature, subject to its laws even if he transcends it with his thought."

"Who made you glorious as the gates of heaven Beneath the keen full moon? Who bade the sun Clothe you with rainbows? Who, with living flower Of loveliest blue, spread garlands at your feet? God! let the torrents, like a shout of nations, Answer! and let the ice-plains echo, God! God! sing, ye meadow-streams, with gladsome voice! Ye pine-groves, with your soft and soul-like sounds! And they too have a voice, yon piles of snow, And in their perilous fall shall thunder, God!"

"All Nature seems at work. Slugs leave their lair — The bees are stirring — birds are on the wing — And Winter slumbering in the open air, Wears on his smiling face a dream of Spring! And I the while, the sole unbusy thing, Nor honey make, nor pair, nor build, nor sing."

"Taste is the intermediate faculty which connects the active with the passive powers of our nature, the intellect with the senses; and its appointed function is to elevate the images of the latter, while it realizes the ideas of the former."