Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. Both these points would belong to applied mathematics. We start, in pure mathematics, from certain rules of inference, by which we can infer that if one proposition is true, then so is some other proposition. These rules of inference constitute the major part of the principles of formal logic. We then take any hypothesis that seems amusing, and deduce its consequences. If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.
–Bertrand Russell, Recent Work on the Principles of Mathematics, published in International Monthly, Vol. 4 (1901), courtesy of Wikiquote
Grand is the Seen
Grand is the seen, the light, to me—grand are the sky and stars, Grand is the earth, and grand are lasting time and space, And grand their laws, so multiform, puzzling, evolutionary; But grander far the unseen soul of me, comprehending, endowing all those, Lighting the light, the sky and stars, delving the earth, sailing the sea, (What were all those, indeed, without thee, unseen soul? of what amount without thee?) More evolutionary, vast, puzzling, O my soul! More multiform far—more lasting thou than they.
How dare one say it? After the cycles, poems, singers, plays, Vaunted Ionia's, India's—Homer, Shakspere—the long, long times' thick dotted roads, areas, The shining clusters and the Milky Ways of stars—Nature's pulses reap'd, All retrospective passions, heroes, war, love, adoration, All ages' plummets dropt to their utmost depths, All human lives, throats, wishes, brains—all experiences' utterance; After the countless songs, or long or short, all tongues, all lands, Still something not yet told in poesy's voice or print—something lacking, (Who knows? the best yet unexpress'd and lacking.)
L. of G.’s Purport
Not to exclude or demarcate, or pick out evils from their formidable masses (even to expose them,) But add, fuse, complete, extend—and celebrate the immortal and the good. Haughty this song, its words and scope, To span vast realms of space and time, Evolution—the cumulative—growths and generations. Begun in ripen'd youth and steadily pursued, Wandering, peering, dallying with all—war, peace, day and night absorbing, Never even for one brief hour abandoning my task, I end it here in sickness, poverty, and old age. I sing of life, yet mind me well of death: To-day shadowy Death dogs my steps, my seated shape, and has for years— Draws sometimes close to me, as face to face.
More experiences and sights, stranger, than you'd think for; Times again, now mostly just after sunrise or before sunset, Sometimes in spring, oftener in autumn, perfectly clear weather, in plain sight, Camps far or near, the crowded streets of cities and the shopfronts, (Account for it or not—credit or not—it is all true, And my mate there could tell you the like—we have often confab'd about it,) People and scenes, animals, trees, colors and lines, plain as could be, Farms and dooryards of home, paths border'd with box, lilacs in corners, Weddings in churches, thanksgiving dinners, returns of long-absent sons, Glum funerals, the crape-veil'd mother and the daughters, Trials in courts, jury and judge, the accused in the box, Contestants, battles, crowds, bridges, wharves, Now and then mark'd faces of sorrow or joy, (I could pick them out this moment if I saw them again,) Show'd to me—just to the right in the sky-edge, Or plainly there to the left on the hill-tops.
“The Rounded Catalogue Divine Complete”
The devilish and the dark, the dying and diseas'd, The countless (nineteen-twentieths) low and evil, crude and savage, The crazed, prisoners in jail, the horrible, rank, malignant, Venom and filth, serpents, the ravenous sharks, liars, the dissolute; (What is the part the wicked and the loathesome bear within earth's orbic scheme?) Newts, crawling things in slime and mud, poisons, The barren soil, the evil men, the slag and hideous rot.
The commonplace I sing; How cheap is health! how cheap nobility! Abstinence, no falsehood, no gluttony, lust; The open air I sing, freedom, toleration, (Take here the mainest lesson—less from books—less from the schools,) The common day and night—the common earth and waters, Your farm—your work, trade, occupation, The democratic wisdom underneath, like solid ground for all.
A Persian Lesson
For his o'erarching and last lesson the greybeard sufi, In the fresh scent of the morning in the open air, On the slope of a teeming Persian rose-garden, Under an ancient chestnut-tree wide spreading its branches, Spoke to the young priests and students. "Finally my children, to envelop each word, each part of the rest, Allah is all, all, all—immanent in every life and object, May-be at many and many-a-more removes—yet Allah, Allah, Allah is there. "Has the estray wander'd far? Is the reason-why strangely hidden? Would you sound below the restless ocean of the entire world? Would you know the dissatisfaction? the urge and spur of every life; The something never still'd—never entirely gone? the invisible need of every seed? "It is the central urge in every atom, (Often unconscious, often evil, downfallen,) To return to its divine source and origin, however distant, Latent the same in subject and in object, without one exception."
If all things are in common among friends, the most precious is Wisdom. What can Juno give which thou canst not receive from Wisdom? What mayest thou admire in Venus which thou mayest not also contemplate in Wisdom? Her beauty is not small, for the lord of all things taketh delight in her. Her I have loved and diligently sought from my youth up.
–Giordano Bruno, courtesy of Wikiquote