Quotes by Mathematicians - Page 10

For, occupied incessantly with the consideration of the limits prescribed to their power by nature, they [philosophers of former times] became so entirely convinced that nothing was at their disposal except their own thoughts, that this conviction was of itself sufficient to prevent their entertaining any desire of other objects; and over their thoughts they acquired a sway so absolute, that they had some ground on this account for esteeming themselves more rich and more powerful, more free and more happy, than other men who, whatever be the favors heaped on them by nature and fortune, if destitute of this philosophy, can never command the realization of all their desires.
René Descartes
WHAT DOES AN OLD MAN GAIN BY EXERCISINGwhat will he gain by talking on the phonewhat will he gain by going after fame, tell mewhat does he gain by looking in the mirrorNothingeach time he just sinks deeper in the mudIt’s already three or four in the morningwhy doesn’t he try to go to sleepbut no--he won’t stop doing exercisewon’t stop with his famous long-distance callswon’t stop with Bachtt with Beethoventttt with Tchaikovskywon’t stop with the long looks in the mirrorwon’t stop with the ridiculous obsession about continuing to breathepitiful--it would be better if he turned out the lightRidiculous old man his mother says to himyou and your father are exactly alikehe didn’t want to die eithermay God grant you the strength to drive a carmay God grant you the strength to talk on the phonemay God grant you the strength to breathe may God grant you the strength to bury your motherYou fell asleep, you ridiculous old man!but the poor wretch does not intend to sleepLet’s not confuse crying with sleeping
Nicanor Parra
The beauty in the genome is of course that it's so small. The human genome is only on the order of a gigabyte of data...which is a tiny little database. If you take the entire living biosphere, that's the assemblage of 20 million species or so that constitute all the living creatures on the planet, and you have a genome for every species the total is still about one petabyte, that's a million gigabytes - that's still very small compared with Google or the Wikipedia and it's a database that you can easily put in a small room, easily transmit from one place to another. And somehow mother nature manages to create this incredible biosphere, to create this incredibly rich environment of animals and plants with this amazingly small amount of data.
Freeman Dyson
If you don't know where you want to go, then it doesn't matter which path you take.
Lewis Carroll
The art of opposition and of revolution is to unsettle established customs, sounding them even to their source, to point out their want of authority and justice.
Blaise Pascal
How is it you can talk so nicely?' Alice said, hoping to get it into a better temper by a compliment. 'I've been in many gardens before, but none of the flowers could talk.''Put your hand down, and feel the ground,' said the Tiger-lily. 'Then you'll know why.'Alice did so. 'It's very hard,' she said, 'but I don't see what that has to do with it.''In most gardens,' the Tiger-lily said, 'they make the beds too soft - so that the flowers are always asleep.
Lewis Carroll
Aren't you sometimes frightened at being planted out here, with nobody to take care of you?''There's the tree in the middle,' said the Rose:'what else is it good for?''But what could it do, if any danger came?' Alice asked.'It could bark,' said the Rose.
Lewis Carroll
At any rate I'd better be getting out of the wood, for really its coming on very dark. Do you think it's going to rain?'Tweedledum spread a large umbrella over himself and his brother, and looked up into it.'No, I don't think it is,' he said: 'at least - not under here. Nohow.''But it may rain outside?''It may - if it chooses,' said Tweedledee: 'we've got no objection. Contrariwise.
Lewis Carroll
…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…
Gottfried Wilhelm Leibniz
Having knowledge of an unethical act and allowing it to continue can spread a contagion that can affect multiple beings in society
Bertrand Russell
We have in fact, two kinds of morality, side by side: one which we preach, but do not practice, and another which we practice, but seldom preach.
Bertrand Russell
People tend to think that mathematicians always work in sterile conditions, sitting around and staring at the screen of a computer, or at a ceiling, in a pristine office. But in fact, some of the best ideas come when you least expect them, possibly through annoying industrial noise.
Edward Frenkel
The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.
George Pólya
This dog is mine," said those poor children; "that is my place in the sun." Here is the beginning and the image of the usurpation of all the earth.
Blaise Pascal
Advocates of capitalism are very apt to appeal to the sacred principles of liberty, which are embodied in one maxim: The fortunate must not be restrained in the exercise of tyranny over the unfortunate.
Bertrand Russell
Where is an intimate friend who’ll hear the secret from me straight out– of what human beings have been from the moment they began? They are born of toil and molded from the clay of sorrow.They wander the world for a time, then set off.
Omar Khayyám
The mighty Mahmúd, Allah-breathing Lord,That all the misbelieving and black HordeOf Fears and Sorrows that infest the SoulScatters before him with his whirlwind Sword.
Omar Khayyám
To rule by fettering the mind through fear of punishment in another world, is just as base as to use force... Reserve your right to think, for even to think wrongly is better than not to think at all.
Hypatia
The importance of Man, which is the one indispensable dogma of the theologians, receives no support from a scientific view of the future of the solar system.
Bertrand Russell
Science tells us what we can know, but what we can know is little, and if we forget how much we cannot know we become insensitive to many things of very great importance. Theology, on the other hand, induces a dogmatic belief that we have knowledge where in fact we have ignorance, and by doing so generates a kind of impertinent insolence towards the universe. Uncertainty, in the presence of vivid hopes and fears, is painful, but must be endured if we wish to live without the support of comforting fairy tales.
Bertrand Russell
Russell observes that "the merits of democracy are negative: it does not ensure good government, but it prevents certain evils," such as the evil of a small group of individuals achieving a secure monopoly on political power. The chief peril for the politician, Russell insists, is love of power. And politicians can easily yield to the love of power on the pretense that they are pursuing some absolute good.
Bertrand Russell
The problem of finding a collection of “wise” men and leaving the government to them is thus an insoluble one. That is the ultimate reason for democracy.
Bertrand Russell
…   not my own opinion, but my wife’s: Yesterday, when weary with writing, I was called to supper, and a salad I had asked for was set before me. ‘It seems then,’ I said, ‘if pewter dishes, leaves of lettuce, grains of salt, drops of water, vinegar, oil and slices of eggs had been flying about in the air for all eternity, it might at last happen by chance that there would come a salad.’ ‘Yes,’ responded my lovely, ‘but not so nice as this one of mine.
Johannes Kepler
Man, made after God's image, was a nobler creation than twinkling sparks in the sky, or than the larger and more useful lamp of the moon.
David Brewster
We, the atom and I, have been on friendly terms, until recently. I saw in it the key to the deepest secrets of Nature, and it revealed to me the greatness of creation and the Creator.
Max Born
There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.
George Pólya
Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.
Edward Griffith Begle
I don't see how it's doing society any good to have it's members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them.
Paul Lockhart
A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.
George Pólya
...the greater objective (representative) perfection there is in our idea of a thing, the greater also must be the perfection of its cause.
René Descartes
...It is necessary for the average citizen, if he wishes to make a living, to avoid incurring the hostility of certain big men. And these big men have an outlook - religious, moral, and political - with which they expect their employees to agree, at least outwardly.
Bertrand Russell
I await your sentence with less fear than you pass it. The time will come when all will see what I see.
Giordano Bruno
It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing.
Sofia Kovalevskaya
As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
Arthur Cayley
Men seek rest in a struggle against difficulties; and when they have conquered these, rest becomes insufferable.
Blaise Pascal
The determination of the average man is not merely a matter of speculative curiosity; it may be of the most important service to the science of man and the social system. It ought necessarily to precede every other inquiry into social physics, since it is, as it were, the basis. The average man, indeed, is in a nation what the centre of gravity is in a body; it is by having that central point in view that we arrive at the apprehension of all the phenomena of equilibrium and motion.
Adolphe Quetelet
To explain all nature is too difficult a task for any one man or even for any one age
Isaac Newton
The mathematical giant [Gauss], who from his lofty heights embraces in one view the stars and the abysses …
Farkas Bolyai
Consider now the Milky Way. Here also we see an innumerable dust, only the grains of this dust are no longer atoms but stars; these grains also move with great velocities, they act at a distance one upon another, but this action is so slight at great distances that their trajectories are rectilineal; nevertheless, from time to time, two of them may come near enough together to be deviated from their course, like a comet that passed too close to Jupiter. In a word, in the eyes of a giant, to whom our Suns were what our atoms are to us, the Milky Way would only look like a bubble of gas.
Henri Poincaré
As I write this entry, I touch a saber-tooth tiger skull in my office. Without stars there could be no skulls
Clifford A. Pickover
Mortal as I am, I know that I am born for a day. But when I follow at my pleasure the serried multitude of the stars in their circular course, my feet no longer touch the earth.
Ptolemy
I know that I am mortal by nature, and ephemeral; but when I trace at my pleasure the windings to and fro of the heavenly bodies I no longer touch the earth with my feet: I stand in the presence of Zeus himself and take my fill of ambrosia
Ptolemy
In Labor movements generally, success through violence can hardly be expected except in circumstances where success without violence is attainable.
Bertrand Russell
If [a man] spent his money, say, in giving parties for his friends, they (we may hope) would get pleasure, and so would all those upon whom he spent money, such as the butcher, the baker, and the bootlegger. But if he spends it (let us say) upon laying down rails for surface cars in some place where surface cars turn out not to be wanted, he has diverted a mass of labor into channels where it gives pleasure to no one. Nevertheless, when he becomes poor through failure of his investment he will be regarded as a victim of undeserved misfortune, whereas the gay spendthrift, who has spent his money philanthropically, will be despised as a fool and a frivolous person.
Bertrand Russell
The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea.
George Pólya
You're enough to try the patience of an oyster!
Lewis Carroll
Now the New Year reviving old Desires,The thoughtful Soul to Solitude retires.
Omar Khayyám
All men's miseries derive from not being able to sit quiet in a room alone.
Blaise Pascal
How vast those Orbs must be, and how inconsiderable this Earth, the Theatre upon which all our mighty Designs, all our Navigations, and all our Wars are transacted, is when compared to them. A very fit consideration, and matter of Reflection, for those Kings and Princes who sacrifice the Lives of so many People, only to flatter their Ambition in being Masters of some pitiful corner of this small Spot.
Christiaan Huygens
The last thing one knows when writing a book is what to put first.
Blaise Pascal
One obvious palliative of the evils of democracy in its present form would be to encourage much more publicity and initiative on the part of civil servants. They ought to have the right, and, on occasion, the duty, to frame Bills in their own names, and set forth publicly the arguments in their favor.
Bertrand Russell
A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science:'The probability of an event is the reason we have to believe that it has taken place, or that it will take place.''The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible' (equally like to happen).From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary. Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.
George Boole
The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.
Eric Temple Bell
Men fear thought as they fear nothing else on earth -- more than ruin -- more even than death.... Thought is subversive and revolutionary,destructive and terrible,thought is merciless to privilege,established institutions,and comfortable habit.Thought looks into the pit of hell and is not afraid.Thought is great and swift and free,the light of the world, and the chief glory of man.
Bertrand Russell
The philosophers make still another objection: "What you gain in rigour," they say, "you lose in objectivity. You can rise toward your logical ideal only by cutting the bonds which attach you to reality. Your science is infallible, but it can only remain so by imprisoning itself in an ivory tower and renouncing all relation with the external world. From this seclusion it must go out when it would attempt the slightest application.
Henri Poincaré
Pure analysis puts at our disposal a multitude of procedures whose infallibility it guarantees; it opens to us a thousand different ways on which we can embark in all confidence; we are assured of meeting there no obstacles; but of all these ways, which will lead us most promptly to our goal? Who shall tell us which to choose? We need a faculty which makes us see the end from afar, and intuition is this faculty. It is necessary to the explorer for choosing his route; it is not less so to the one following his trail who wants to know why he chose it.
Henri Poincaré
…every feeling is the perception of a truth...
Gottfried Wilhelm Leibniz
The mind leans on [innate] principles every moment, but it does not come so easily to distinguish them and to represent them distinctly and separately, because that demands great attention to its acts, and the majority of people, little accustomed to think, has little of it.
Gottfried Wilhelm Leibniz
The mind is not only capable of knowing [innate ideas], but further of finding them in itself; and if it had only the simple capacity to receive knowledge…it would not be the source of necessary truths…
Gottfried Wilhelm Leibniz
For the [innate] general principles enter into our thoughts, of which they form the soul and the connection. They are as necessary thereto as the muscles and sinews are for walking, although we do not at all think of them.
Gottfried Wilhelm Leibniz