[On Archimedes mathematical results:] It is not possible to find in all geometry more difficult and intricate questions, or more simple and lucid explanation... No investigation of yours would succeed in attaining the proof, and yet, once seen you immediately believe you would have discovered it.
Philosophy treats of physics where a more careful knowledge is required because the problems which come under this head are numerous... So the reader of Ctesibius or Archimedes and the other writers of treatises of the same class will not be able to appreciate them unless he has been trained in these subjects by the philosophers.
Marcus Vitruvius Pollio
Surely with as good reason as had Archimedes to have the cylinder, cone and sphere engraved on his tombstone might our distinguished countrymen leave testamentary directions for the cubic eikosiheptagram to be engraved on theirs. Spirit of the Universe! wither are we drifting, and when, where, and how is all this to end?
James Joseph Sylvester
I remember from my school days Archimedes jumping into his bath and displacing water and coming up with his famous principle, and of course Isaac Newton being hit on the head with an apple. In other words, this realm of human knowledge - which is mathematical, essentially - can have a playful visual element to it.
Archimedes said Eureka, Cos in English he weren't too aversed in, when he discovered that the volume of a body in the bath, is equal to the stuff it is immersed in, That is the law of displacement, Thats why ships don't sink, Its a shame he weren't around in 1912, The Titanic would have made him think.
In a manner which matches the fortuity, if not the consequence, of Archimedes' bath and Newton's apple, the [3.6 million year old] fossil footprints were eventually noticed one evening in September 1976 by the paleontologist Andrew Hill, who fell while avoiding a ball of elephant dung hurled at him by the ecologist David Western.
Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this . . . . The imagination in a mathematician who creates makes no less difference than in a poet who invents. . . . Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer.
Jean le Rond d'Alembert
The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated... The importance of this invention is more readily appreciated when one considers that it was beyod the two greatest men of antiquity, Archimedes and Apollonius.
Theology, Mr. Fortune found, is a more accommodating subject than mathematics; its technique of exposition allows greater latitude. For instance when you are gravelled for matter there is always the moral to fall back upon. Comparisons too may be drawn, leading cases cited, types and antetypes analysed and anecdotes introduced. Except for Archimedes mathematics is singularly naked of anecdotes.
Sylvia Townsend Warner
But the owls themselves are not hard to find, silent and on the wing, with their ear tufts flat against their heads as they fly and their huge wings alternately gliding and flapping as they maneuver through the trees. Athena's owl of wisdom and Merlin's companion, Archimedes, were screech owls surely, not this bird with the glassy gaze, restless on the bough, nothing but blood on its mind.
The best lesson from the myths of Newton and Archimedes is to work passionately but to take breaks. Sitting under trees and relaxing in baths lets the mind wander and frees the subconscious to do work on our behalf. Freeman Dyson, a world-class physi- cist and author, agrees: 'I think it's very important to be idle... people who keep themselves busy all the time are generally not creative. So I am not ashamed of being idle.
Did chemistry theorems exist? No: therefore you had to go further, not be satisfied with the quia, go back to the origins, to mathematics and physics. The origins of chemistry were ignoble, or at least equivocal: the dens of the alchemists, their abominable hodgepodge of ideas and language, their confessed interest in gold, their Levantine swindles typical of charlatans and magicians; instead, at the origin of physics lay the strenuous clarity of the West-Archimedes and Euclid.
It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
Spoken of the young Archimedes: . . . [he] was as much enchanted by the rudiments of algebra as he would have been if I had given him an engine worked by steam, with a methylated spirit lamp to heat the boiler; more enchanted, perhaps for the engine would have got broken, and, remaining always itself, would in any case have lost its charm, while the rudiments of algebra continued to grow and blossom in his mind with an unfailing luxuriance. Every day he made the discovery of something which seemed to him exquisitely beautiful; the new toy was inexhaustible in its potentialities.
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.
We shed as we pick up, like travellers who must carry everything in their arms, and what we let fall will be picked up by those behind. The procession is very long and life is very short. We die on the march. But there is nothing outside the march so nothing can be lost to it. The missing plays of Sophocles will turn up piece by piece, or be written again in another language. Ancient cures for diseases will reveal themselves once more. Mathematical discoveries glimpsed and lost to view will have their time again. You do not suppose, my lady, that if all of Archimedes had been hiding in the great library of Alexandria, we would be at a loss for a corkscrew?
It is the most sweet and comfortable knowledge; to be studying Jesus Christ, what is it but to be digging among all the veins and springs of comfort? And the deeper you dig, the more do these springs flow upon you. How are hearts ravished with the discoveries of Christ in the gospel? what ecstasies, meltings, transports, do gracious souls meet there? Doubtless, Philip's ecstasy, John 1: 25. 'eurekamen Iesoun, ' 'We have found Jesus, ' was far beyond that of Archimedes. A believer could sit from morning to night, to hear discourses of Christ; 'His mouth is most sweet', Cant. [i.e., Song of Solomon] 5: 16.
The house is a normal-sized house, but once you step foot in the door, you are confronted with 'The Dome.' Perfectly round, this room is one continuous curved wall of books. A copper dome sits on top with four stained glass windows fitted tight to allow for natural light to stream in. The four stained glass windows offer portraits of the four greatest mathematicians in history: Newton, Euler, Gauss, and Archimedes, though they are ordered alphabetically from left to right on the dome.
One day at Fenner's (the university cricket ground at Cambridge), just before the last war, G. H. Hardy and I were talking about Einstein. Hardy had met him several times, and I had recently returned from visiting him. Hardy was saying that in his lifetime there had only been two men in the world, in all the fields of human achievement, science, literature, politics, anything you like, who qualified for the Bradman class. For those not familiar with cricket, or with Hardy's personal idiom, I ought to mention that 'the Bradman class' denoted the highest kind of excellence: it would include Shakespeare, Tolstoy, Newton, Archimedes, and maybe a dozen others. Well, said Hardy, there had only been two additions in his lifetime. One was Lenin and the other Einstein.
Almost all genius up to now was one-sided-the result of a sickly constitution. One type had too much sense of the external, the other too much inner sense. Seldom could nature achieve a balance between the two-a complete constitution of genius. Often a perfect proportion arose by chance, but this could never endure because it was not comprehended and fixed by the spirit-they remained fortunate moments. The first genius that penetrated itself found here the exemplary germ of an immeasurable world. It made a discovery which must have been the most remarkable in the history of the world-for with it there begins a whole new epoch for humanity-and true history of all kinds becomes possible for the first time at this stage-for the way that had been traversed hitherto now makes up a proper whole that can be entirely elucidated. That point outside the world is given, and now Archimedes can fulfill his promise.
Solitude, the safeguard of mediocrity, is to genius the stern friend, the cold, obscure shelter where moult the wings which will bear it farther than suns and stars. He who should inspire and lead his race must be defended from travelling with the souls of other men, from living, breathing, reading, and writing in the daily, time-worn yoke of their opinions. "In the morning, - solitude;" said Pythagoras; that Nature may speak to the imagination, as she does never in company, and that her favorite may make acquaintance with those divine strengths which disclose themselves to serious and abstracted thought. 'Tis very certain that Plato, Plotinus, Archimedes, Hermes, Newton, Milton, Wordsworth, did not live in a crowd, but descended into it from time to time as benefactors: and the wise instructor will press this point of securing to the young soul in the disposition of time and the arrangements of living, periods and habits of solitude.
Ralph Waldo Emerson
Reading list (1972 edition) 1. Homer - Iliad, Odyssey 2. The Old Testament 3. Aeschylus - Tragedies 4. Sophocles - Tragedies 5. Herodotus - Histories 6. Euripides - Tragedies 7. Thucydides - History of the Peloponnesian War 8. Hippocrates - Medical Writings 9. Aristophanes - Comedies 10. Plato - Dialogues 11. Aristotle - Works 12. Epicurus - Letter to Herodotus; Letter to Menoecus 13. Euclid - Elements 14. Archimedes - Works 15. Apollonius of Perga - Conic Sections 16. Cicero - Works 17. Lucretius - On the Nature of Things 18. Virgil - Works 19. Horace - Works 20. Livy - History of Rome 21. Ovid - Works 22. Plutarch - Parallel Lives; Moralia 23. Tacitus - Histories; Annals; Agricola Germania 24. Nicomachus of Gerasa - Introduction to Arithmetic 25. Epictetus - Discourses; Encheiridion 26. Ptolemy - Almagest 27. Lucian - Works 28. Marcus Aurelius - Meditations 29. Galen - On the Natural Faculties 30. The New Testament 31. Plotinus - The Enneads 32. St. Augustine - On the Teacher; Confessions; City of God; On Christian Doctrine 33. The Song of Roland 34. The Nibelungenlied 35. The Saga of Burnt Nje¡l 36. St. Thomas Aquinas - Summa Theologica 37. Dante Alighieri - The Divine Comedy;The New Life; On Monarchy 38. Geoffrey Chaucer - Troilus and Criseyde; The Canterbury Tales 39. Leonardo da Vinci - Notebooks 40. Niccole² Machiavelli - The Prince; Discourses on the First Ten Books of Livy 41. Desiderius Erasmus - The Praise of Folly 42. Nicolaus Copernicus - On the Revolutions of the Heavenly Spheres 43. Thomas More - Utopia 44. Martin Luther - Table Talk; Three Treatises 45. Frane§ois Rabelais - Gargantua and Pantagruel 46. John Calvin - Institutes of the Christian Religion 47. Michel de Montaigne - Essays 48. William Gilbert - On the Loadstone and Magnetic Bodies 49. Miguel de Cervantes - Don Quixote 50. Edmund Spenser - Prothalamion; The Faerie Queene 51. Francis Bacon - Essays; Advancement of Learning; Novum Organum, New Atlantis 52. William Shakespeare - Poetry and Plays 53. Galileo Galilei - Starry Messenger; Dialogues Concerning Two New Sciences 54. Johannes Kepler - Epitome of Copernican Astronomy; Concerning the Harmonies of the World 55. William Harvey - On the Motion of the Heart and Blood in Animals; On the Circulation of the Blood; On the Generation of Animals 56. Thomas Hobbes - Leviathan 57. Rene Descartes - Rules for the Direction of the Mind; Discourse on the Method; Geometry; Meditations on First Philosophy 58. John Milton - Works 59. Molie¨re - Comedies 60. Blaise Pascal - The Provincial Letters; Pensees; Scientific Treatises 61. Christiaan Huygens - Treatise on Light 62. Benedict de Spinoza - Ethics 63. John Locke - Letter Concerning Toleration; Of Civil Government; Essay Concerning Human Understanding;Thoughts Concerning Education 64. Jean Baptiste Racine - Tragedies 65. Isaac Newton - Mathematical Principles of Natural Philosophy; Optics 66. Gottfried Wilhelm Leibniz - Discourse on Metaphysics; New Essays Concerning Human Understanding;Monadology 67. Daniel Defoe - Robinson Crusoe 68. Jonathan Swift - A Tale of a Tub; Journal to Stella; Gulliver's Travels; A Modest Proposal 69. William Congreve - The Way of the World 70. George Berkeley - Principles of Human Knowledge 71. Alexander Pope - Essay on Criticism; Rape of the Lock; Essay on Man 72. Charles de Secondat, baron de Montesquieu - Persian Letters; Spirit of Laws 73. Voltaire - Letters on the English; Candide; Philosophical Dictionary 74. Henry Fielding - Joseph Andrews; Tom Jones 75. Samuel Johnson - The Vanity of Human Wishes; Dictionary; Rasselas; The Lives of the Poets
Mortimer J. Adler