Mathematicians From Greece

"Men achieve tranquillity through moderation in pleasure and through the symmetry of life. Want and superfluity are apt to upset them and to cause great perturbations in the soul. The souls that are rent by violent conflicts are neither stable nor tranquil. One should therefore set his mind upon the things that are within his power, and be content with his opportunities, nor let his memory dwell very long on the envied and admired of men, nor idly sit and dream of them. Rather, he should contemplate the lives of those who suffer hardship, and vividly bring to mind their sufferings, so that your own present situation may appear to you important and to be envied, and so that it may no longer be your portion to suffer torture in your soul by your longing for more. For he who admires those who have, and whom other men deem blest of fortune, and who spends all his time idly dreaming of them, will be forced to be always contriving some new device because of his [insatiable] desire, until he ends by doing some desperate deed forbidden by the laws. And therefore one ought not to desire other men's blessings, and one ought not to envy those who have more, but rather, comparing his life with that of those who fare worse, and laying to heart their sufferings, deem himself blest of fortune in that he lives and fares so much better than they. Holding fast to this saying you will pass your life in greater tranquillity and will avert not a few of the plagues of life—envy and jealousy and bitterness of mind."

"A life without a holiday is like a long journey without an inn to rest at."

"The right-minded man, ever inclined to righteous and lawful deeds, is joyous day and night, and strong, and free from care. But if a man take no heed of the right, and leave undone the things he ought to do, then will the recollection of no one of all his transgressions bring him any joy, but only anxiety and self-reproaching."

"Now as of old the gods give men all good things, excepting only those that are baneful and injurious and useless. These, now as of old, are not gifts of the gods: men stumble into them themselves because of their own blindness and folly."

"Fortune is lavish with her favors, but not to be depended on. Nature on the other hand is self-sufficing, and therefore with her feebler but trustworthy [resources] she wins the greater meed] of hope."

"In the weightiest matters we must go to school to the animals, and learn spinning and weaving from the spider, building from the swallow, singing from the birds,—from the swan and the nightingale, imitating their art."

"Of all things the worst to teach the young is dalliance, for it is this that is the parent of those pleasures from which wickedness springs."

"An evil and foolish and intemperate and irreligious life should not be called a bad life, but rather, dying long drawn out."

"For a man petticoat government is the limit of insolence."

"(Democritus said he would rather discover a single demonstration than win the throne of Persia.)"

"Seek after the good, and with much toil shall ye find it; the evil turns up of itself without your seeking it."

"A sensible man takes pleasure in what he has instead of pining for what he has not."

"Men have made an idol of luck as an excuse for their own thoughtlessness. Luck seldom measures swords with wisdom. Most things in life quick wit and sharp vision can set right."

"False men and shams talk big and do nothing."

"My enemy is not the man who wrongs me, but the man who means to wrong me."

"You can tell the man who rings true from the man who rings false, not by his deeds alone, but also by his desires."

"Fame and wealth without wisdom are unsafe possessions."

"The enmity of one's kindred is far more bitter than the enmity of strangers."

"Making money is not without its value, but nothing is baser than to make it by wrong-doing."

"Those who have a well-ordered character lead also a well-ordered life."

"Good means not [merely] not to do wrong, but rather not to desire to do wrong."

"It is better to correct your own faults than those of another."

"There are many who know many things, yet are lacking in wisdom."

"Neither art nor wisdom may be attained without learning."

"The friendship of one wise man is better than the friendship of a host of fools."

"Fools learn wisdom through misfortune."

"One should emulate works and deeds of virtue, not arguments about it."

"Many who have not learned wisdom live wisely, and many who do the basest deeds can make most learned speeches."

"He who does wrong is more unhappy than he who suffers wrong."

"Strength of body is nobility in beasts of burden, strength of character is nobility in men."

"'Tis a grievous thing to be subject to an inferior."

"Men have fashioned an image of Chance as an excuse for their own stupidity. For Chance rarely conflicts with intelligence, and most things in life can be set in order by an intelligent sharpsightedness."

"Not from fear but from a sense of duty refrain from your sins."

"The hopes of the right-minded may be realized, those of fools are impossible."

"Repentance for one's evil deeds is the safeguard of life."

"No one deserves to live who has not at least one good-man-and-true for a friend."

"The most momentous thing in human life is the art of winning the soul to good or to evil."

"Reason is immortal, all else mortal."

"ἐν ὀργῇ μήτε τι λέγειν μήτε πράσσειν"

"ἀλλήλοις θ᾽ ὁμιλεῖν, ὡς τοὺς μὲν φίλους ἐχθροὺς μὴ ποιῆσαι, τοὺς δ᾽ ἐχθροὺς φίλους ἐργάσασθαι. ἴδιόν τε μηδὲν ἡγεῖσθαι."

"Τὴν δ' ἀνθρώπου ψυχὴν διῃρῆσθαι τριχῆ, εἴς τε νοῦν καὶ φρένας καὶ θυμόν. νοῦν μὲν οὖν καὶ θυμὸν εἶναι καὶ ἐν τοῖς ἄλλοις ζῴοις, φρένας δὲ μόνον ἐν ἀνθρώπῳ."

"Dear youths, I warn you cherish peace divine, And in your hearts lay deep these words of mine."

"By the air which I breathe, and by the water which I drink, I will not endure to be blamed on account of this discourse."

"I was Euphorbus at the siege of Troy."

"It has fallen to the lot of one people, the ancient Greeks, to endow human thought with two outlooks on the universe neither of which has blurred appreciably in more than two thousand years. ...The first was the explicit recognition that proof by deductive reasoning offers a foundation for the structure of number and form. The second was the daring conjecture that nature can be understood by human beings through mathematics, and that mathematics is the language most adequate for idealizing the complexity of nature into appreciable simplicity. Both are attributed by persistent Greek tradition to Pythagoras in the sixth century before Christ. ...there is an equally persistent tradition that it was Thales... who first proved a theorem in geometry. But there seems to be no claim that Thales... proposed the inerrant tactic of definitions, postulates, deductive proof, theorem as a universal method in mathematics. ...in attributing any specific advance to Pythagoras himself, it must be remembered that the Pythagorean brotherhood was one of the world's earliest unpriestly cooperative scientific societies, if not the first, and that its members assigned the common work of all by mutual consent to their master."

"It seems to me that they do well to study mathematics, and it is not at all strange that they have correct knowledge about each thing, what it is. For if they knew rightly the nature of the whole, they were also likely to see well what is the nature of the parts. About geometry, indeed, and arithmetic and astronomy, they have handed us down a clear understanding, and not least also about music. For these seem to be sister sciences; for they deal with sister subjects, the first two forms of being."

"If someone associates with a true Pythagorean, what will he will get from him, and in what quantity? I would say: statesmanship, geometry, astronomy, arithmetic, harmonics, music, medicine, complete and god-given prophecy, and also the higher rewards — greatness of mind, of soul, and of manner, steadiness, piety, knowledge of the gods and not just supposition, familiarity with blessed spirits and not just faith, friendship with both gods and spirits, self-sufficiency, persistence, frugality, reduction of essential needs, ease of perception, of movement, and of breath, good color, health, cheerfulness, and immortality."

"The concept of a harmonious universe ordered according to "the Great Chain of Being" — a chain that connects the continuum of matter, body, mind, soul and spirit — stands as one of the most fundamental ideas of western thought. … It continues to be a profound influence upon the deepest strata of our thought. And yet a major rift has appeared in the consciousness of our time because the theme of harmonia has not been translated into the realm of human conduct. The challenge of our time may be to revive it, and make divine harmony "the great theme" of the next millennium. Any success we have in accomplishing this will be based, in large part, on the achievements of Pythagoras."

"It is important to recognize that the materialist, scientific paradigm that dominates the late twentieth century world and provides the basis for its dominant institutions, has its basis in the life and work of Pythagoras, one of the most significant representatives of the perennial philosophy and a founder of the magical tradition. This spirit, which gave rise to our world view, is a spirit that must be recaptured if our civilization is to flourish. The choice is a clear one to many, and was summed up in a book title by the late Pythagorean and futurist Buckminster Fuller, Utopia or Oblivion."

"At the dawn of our century, scientists were proclaiming that our understanding of the world was almost complete. Only one or two small problems in physics remained to be solved. One of these problems had to do with black body radiation and was solved by Max Planck. His solution, however, formed the foundation for quantum mechanics which was to sweep aside almost the whole edifice of fundamental assumptions in physics, and with it our understanding of the world. A hundred years later we are faced with a similar situation. The mechanistic viewpoint that began to dominate our world view in the seventeenth century has almost completed its hegemony. This paradigm, as historian Hugh Kearney points out, stems from only one of three main systems of thought that flowed from Greek thought into the modern world, each of which has dominated our world view at different points in our history. … In spite of the dominance of mechanistic thought in the contemporary world, a perplexing residue of the magical tradition still survives in the form of several issues, solutions to which do not appear possible within the context of a purely mechanical view of the world."