Why can't somebody give us a list of things that everybody thinks and nobody says, and another list of things that everybody says and nobody thinks? Oliver Wendell Holmes Nothing puzzles me more than time and space; and yet nothing troubles me less, as I never think about them. Charles Lamb The system of Descartes... seemed to give a plausible reason for all those phenomena; and this reason seemed more just, as it is simple and intelligible to all capacities. But in philosophy, a student ought to doubt of the things he fancies he understands too easily, as much as of those he does not understand. Voltaire A marveilous newtrality have these things mathematicall, and also a strange participation between things supernaturall and things naturall. John Dee Like the ski resort full of girls hunting for husbands and husbands hunting for girls, the situation is not as symmetrical as it might seem. Alan MacKay Everything of importance has been said before, by someone who did not discover it. Alfred North Whitehead And Lucy, dear child, mind your arithmetic... What would life be without arithmetic, but a scene of horrors? Syndey Smith, 1835 Then assuredly the world was made, not in time, but simultaneously with time. St. Augustine There was more imagination in the head of Archimedes than in that of Homer. Voltaire In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite. Paul Dirac To Thales the primary question was not 'What do we know?' but 'How do we know it?'. Aristotle Time and again an entirely new philosophical movement arises which finally unmasks the old philosophical problems as pseudo- problems, and which confronts the wicked nonsense of philosophy with the good sense of meaningful, positive, empirical science. And time and again do the despised defenders of 'traditional philosophy' try to explain to the leaders of the latest positivistic assault that the main problem of philosophy is the critical analysis of the appeal to the authority of 'experience' - precisely that 'experience' which every latest discoverer of positivism is, as ever, artlessly taking for granted. Karl Popper, 1935 Certainly he who can digest a second or third fluxion need not, methinks, be squeamish about any point in divinity. George Berkeley, 1734 If a little knowledge is dangerous, where is the man who has so much as to be out of danger? Thomas Henry Huxley, 1877 I never came across one of Laplace's "Thus it plainly appears" without feeling sure that I had hours of hard work before me to fill up the chasm and find out how it plainly appears. Nathanial Bodwitch, 1838 Ignorance is always ready to admire itself. Procure yourself critical friends. Nicolas Boileau, 1674 Everyone is free to set up an opinion and to adduce proofs in support of it. Whether, though, a scientist shall find it worth his while to enter into serious investigations of opinions so advanced is a question which his reason and instinct alone can decide. If these things, in the end, should turn out to be true, I shall not be ashamed of being the last to believe them. Ernst Mach, 1883 I do not see, Sir, that it is reasonable for a man to be angry at another, whom a woman has preferred to him; but angry he is, no doubt; and he is loath to be angry at himself. Samuel Johnson, 1763 The mind of man is more intuitive than logical, and comprehends more than it can coordinate. Vauvenargues, 1746 Never express yourself more clearly than you think. Niels Bohr The mathematician knows some things, no doubt, but not those things one usually wants to get from him. Albert Einstein To guess what to keep and what to throw away takes considerable skill. Actually it is probably merely a matter of luck, but it looks as if it takes considerable skill. Richard Feynman, 1965 Nothing is more dangerous than an idea, when it is the only idea we have. Alain, 1908 The vain presumption of understanding everything can have no other basis than never having understood anything. For anyone who had ever experienced just once the perfect understanding of one single thing, and had truly tasted how knowledge is accomplished, would recognize that of the infinity of other truths he understands nothing. Galileo, 1630 A circumstance which has always appeared wonderful to me, is that such sublime discoveries should have been made by the sole assistance of a quadrant and a little arithmetic. Voltaire Ignoramus, n. A person unacquainted with certain kinds of knowledge familiar to yourself, and having certain other kinds that you know nothing about. Ambrose Bierce, 1890 Court: How old are you? -- Eight. Do you know what you are come here for, child? -- Yes. What are you come here for? -- About my frock. Will you tell me the truth about it? -- Yes. Do you know the difference between what is true and what is false? -- No. Let us try if we cannot go on without her. Call the next witness. The Trial of Mary Wade, 1789 We are like sailors who on the open sea must reconstruct their ship, without ever being able to dismantle it in dry-dock and reconstruct it from its best components. Where a beam is taken away a new one must at once be put there, and for this the rest of the ship is used as support. In this way, by using the old beams and driftwood the ship can be shaped entirely anew, but only by gradual reconstruction. Otto Neurath, 1932 Do I contradict myself? Very well then I contradict myself. I am large, I contain multitudes. Walt Whitman, 1870 Examinations are formidable even to the best prepared, for the greatest fool may ask more than the wisest man can answer. Charles Caleb Colton, 1825 General and abstract ideas are the source of the greatest errors of mankind. Rousseau, 1762 Hope deceives more men than cunning does. Vauvenargues, 1746 The second law of thermodynamics holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation, well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. Arthur Eddington There is frequently more to be learned from the unexpected questions of a child than the discourses of men, who talk in a road, according to the notions and prejudices of their education. John Locke, 1693 I do hate sums. There is no greater mistake than to call arithmetic an exact science. There are hidden laws of number which it requires a mind like mine to perceive. For instance, if you add a sum from the bottom up, and then again from the top down, the result is always different. Mrs. La Touche, 19th c. Invention 13 J. S. Bach From Alexander the Platonic, not frequently nor without necessity to say to any one, or to write in a letter, that I have no leisure; nor continually to excuse the neglect of duties required by our relation to those with whom we live, by alleging urgent occupations. Marcus Aurelius, Meditations The intellectuals' chief cause of anguish are one another's works. Jacques Barzun, 1959 all ignorance toboggans into know and trudges up to ignorance again. e.e.cummings, 1959 The test of interesting people is that subject matter doesn't matter. Louis Kronenberger, 1954 The perplexity of life arises from there being too many interesting things in it for us to be interested properly in any of them. G. K. Chesterton, 1909 He who serves two masters has to lie to one. Portuguese Proverb That knowledge which stops at what it does not know, is the highest knowledge. Chuang Tzu, 4th c. B.C. Intelligence is characterized by a natural incomprehension of life. Henri Bergson, 1907 Knowledge is two-fold, and consists not only in the affirmation of what is true, but in the negation of that which is false. Charles Caleb Colton, 1825 If I cannot brag of knowing something, then I brag of not knowing it. R. W. Emerson, 1866 Human beings take more pleasure in their representation than in the thing, or rather we must say: Human beings take pleasure in a thing only insofar as they conceive it. It must suit their turn of mind. And try as they may to raise their way of conceiving things ever so high above the common run, try as they may to purify it ever so much, it nevertheless commonly remains but one way of conceiving things: that is, an attempt to bring many objects into a certain comprehensible relation that, strictly speaking, they do not have, and hence the inclination to hypotheses, theories, terminologies, and systems - which we cannot condemn, since they must necessarily spring from the organization of our being. Johann Wolfgang von Goethe Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, 1891 The first mark of intelligence, to be sure, is not to start things; the second mark of intelligence is to pursue to the end what you have started. Panchatantra, c. 5th c. The sole cause of all human misery is the inability of people to sit quietly in their rooms. Blaise Pascal, 1670 Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena. Leonhard Euler, 1748 The shortest path between two truths in the real domain passes through the complex domain. Jacques Hadamard Such is the advantage of a well-constructed language that its simplified notation often becomes the source of profound theories. P. S. Laplace 6accdae13eff7i3l9n4o4qrr4s8t12ux. Isaac Newton, 1676 I hope that posterity will judge me kindly, not only as to the things which I have explained, but also as to those which I have intentionally omitted so as to leave to others the pleasure of discovery. Rene Descartes, 1637 It is easier to square a circle than to get round a mathematician. A. De Morgan, 1840 There is no excellent beauty that has not some strangeness in the proportion. Francis Bacon In conclusion I wish to say that in working at the problem here dealt with I have had the loyal assistance of my friend and colleague M. Besso, and that I am indebted to him for several valuable suggestions. Albert Einstein, 1905 You had, by the way, overestimated the meaningfulness of my observations again: I was not aware that they had the meaning that an energy tensor for gravitation was dispensable. If I understand it correctly, my inadvertent statement now implies that planetary motion would satisfy conservation laws just by chance, as it were. What is certain is that I was not aware of this consequence of my comments and cannot grasp the argument even now. Michele Besso, 1918 I see I have made myself a slave to Philosophy, but if I get free of Mr. Linus's business I will resolutely bid adew to it eternally, excepting for what I do for my private satisfaction or leave to come out after me. For I see a man must either resolve to put out nothing new or to become a slave to defend it. Isaac Newton, 1677 There wanted not some beams of light to guide men in the exercise of their Stocastick faculty. John Owen, 1662 I should consider that I know nothing about physics if I were able to explain only how things might be, and were unable to demonstrate that they could not be otherwise. Rene Descartes, 1640 Of all the communities available to us there is not one that I would devote myself to, except for the society of true searchers, which has very few living members at any time. Albert Einstein, 1949 The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn. Isaac Newton, 1687 I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated...geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics. Carl Gauss, 1817 Among the great men who have philosophized about [the action of the tides], the one who surprised me most is Kepler. He was a person of independent genius, [but he] became interested in the action of the moon on the water, and in other occult phenomena, and similar childishness. Galileo, 1632 Taking mathematics from the beginning of the world to the time of Newton, what he has done is much the better half. Gottfried Leibniz, 1688 I will sette as I doe often in woorke use, a paire of paralleles, or [twin] lines of one lengthe, thus = , bicause noe 2. thynges, can be moare equalle. Robert Recorde, 1557 That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles. Euclid, c. 300 B.C. One of the chief peculiarities of this treatise is the doctrine that the true electric current, on which the electromagnetic phenomena depend, is not the same thing as the current of conduction, but that the time-variation of the electric displacement must [also] be taken into account... James Clerk Maxwell, 1873 Your manuscript is both good and original. However, that which is good is not original, and that which is original is not good. Samuel Johnson "That is another of your odd notions," said the Prefect, who had the fashion of calling everything 'odd' that was beyond his comprehension, and thus lived amid an absolute legion of 'oddities'. Edgar Allan Poe I knew when seven justices could not take up a quarrel, but when the parties were met themselves, one of them thought but of an If, as, 'If you said so, then I said so;' and they shook hands and swore brothers. Your If is the only peacemaker; much virtue in If. Shakespeare I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal A work of art is never finished, merely abandoned. Leonardo da Vinci S'io credessi che mia risposta fosse a persona che mai tornasse al mondo, questa fiamma staria senza piu scosse. Ma per cio che giammai di questo fondo non torno vivo alcun, s'i'odo il vero, senza tema d'infamia ti rispondo. Dante, 1302Return to MathPages Main Menu
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