“The laws of nature are but the mathematical thoughts of God.”

“The laws of nature are but the mathematical thoughts of God.”

“Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.”

“…if geometry were as much opposed to our passions and present interests as is ethics, we should contest it and violate I but little less, notwithstanding all the demonstrations of Euclid and Archimedes…”

“It seems that mathematical ideas are arranged somehow in strata, the ideas in each stratum being linked by a complex of relations both among themselves and with those above and below. The lower the stratum, the deeper (and in general more difficult) the idea. Thus the idea of an ‘irrational’ is deeper than that of an integer; and Pythagoras’s theorem is, for that reason, deeper than Euclid’s.”

“If the ancients had been able to see it as I see it now, Mr. Palomar thinks, they would have thought they had projected their gaze into the heaven of Plato's ideas, or in the immaterial space of the postulates of Euclid; but instead, thanks to some misdirection or other, this sight has been granted to me, who fear it is too beautiful to be true, too gratifying to my imaginary universe to belong to the real world. But perhaps it is this same distrust of our senses that prevents us from feeling comfortable in the universe. Perhaps the first rule I must impose on myself is this: stick to what I see.”

“Believe me, if Archimedes ever had the grand entrance of a girl as pretty as Gloria to look forward to, he would never have spent so much time calculating the value of Pi. He would have been baking her a Pie! If Euclid had ever beheld a vision of loveliness like the one I see walking into my anti-math class, he would have forgotten all the geometry of lines and planes, and concentrated on the sweet simplicity of soft curves. If Pythagoras had ever had a girl look at him the way Gloria's eyes fix in my direction, he would have given up his calculations on the hypotenuse of right triangles and run for the hills to pick a bouquet of wildflowers.”

“Captain West advanced to meet me, and before our outstretched hands touched, before his face broke from repose to greeting and the lips moved to speech, I got the first astonishing impact of his personality. Long, lean, in his face a touch of race I as yet could only sense, he was as cool as the day was cold, as poised as a king or emperor, as remote as the farthest fixed star, as neutral as a proposition of Euclid. And then, just ere our hands met, a twinkle of--oh--such distant and controlled geniality quickened the many tiny wrinkles in the corner of the eyes; the clear blue of the eyes was suffused by an almost colourful warmth; the face, too, seemed similarly to suffuse; the thin lips, harsh-set the instant before, were as gracious as Bernhardt's when she moulds sound into speech. ”

“Some persons fancy that bias and counter-bias are favorable to the extraction of truth–that hot and partisan debate is the way to investigate. This is the theory of our atrocious legal procedure. But Logic puts its heel upon this suggestion. It irrefragably demonstrates that knowledge can only be furthered by the real desire for it, and that the methods of obstinacy, of authority and every mode of trying to reach a foregone conclusion, are absolutely of no value. These things are proved. The reader is at liberty to think so or not as long as the proof is not set forth, or as long as he refrains from examining it. Just so, he can preserve, if he likes, his freedom of opinion in regard to the propositions of geometry; only, in that case, if he takes a fancy to read Euclid, he will do well to skip whatever he finds with A, B, C, etc., for, if he reads attentively that disagreeable matter, the freedom of his opinion about geometry may unhappily be lost forever.”

“The one created thing which we cannot look at is the one thing in the light of which we look at everything. Like the sun at noonday, mysticism explains everything else by the blaze of its own victorious invisibility. Detached intellectualism is (in the exact sense of a popular phrase) all moonshine; for it is light without heat, and it is secondary light, reflected from a dead world. But the Greeks were right when they made Apollo the god both of imagination and of sanity; for he was both the patron of poetry and the patron of healing. Of necessary dogmas and a special creed I shall speak later. But that transcendentalism by which all men live has primarily much the position of the sun in the sky. We are conscious of it as of a kind of splendid confusion; it is something both shining and shapeless, at once a blaze and a blur. But the circle of the moon is as clear and unmistakable, as recurrent and inevitable, as the circle of Euclid on a blackboard. For the moon is utterly reasonable; and the moon is the mother of lunatics and has given to them all her name.”