Quotes by Mathematicians - Page 9

On two occasions, I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able to rightly apprehend the kind of confusion of ideas that could provoke such a question.
Charles Babbage
When I consider the small span of my life absorbed in the eternity of all time, or the small part of space which I can touch or see engulfed by the infinite immensity of spaces that I know not and that know me not, I am frightened and astonished to see myself here instead of there … now instead of then.
Blaise Pascal
Whereas Nature does not admit of more than three dimensions ... it may justly seem very improper to talk of a solid ... drawn into a fourth, fifth, sixth, or further dimension.
John Wallis
Let us imagine a number of men in chains, and all condemned to death, where some are killed each day in the sight of the others, and those who remain see their own fate in that of their fellows, and wait their turn, looking at each other sorrowfully and without hope. It is an image of the condition of men.
Pascal
All the labor of all the ages, all the devotion, all the inspiration, all the noonday brightness of human genius are destined to extinction. So now, my friends, if that is true, and it is true, what is the point?
Bertrand Russell
There is much pleasure to be gained from useless knowledge.
Bertrand Russell
Boredom is essentially a thwarted desire for events, not necessarily pleasant ones, but just occurrences such as will enable the victim of ennui to know one day from another. The opposite of boredom, in a word, is not pleasure, but excitement.
Bertrand Russell
Let us return for a moment to Lady Lovelace’s objection, which stated that the machine can only do what we tell it to do. One could say that a man can "inject" an idea into the machine, and that it will respond to a certain extent and then drop into quiescence, like a piano string struck by a hammer. Another simile would be an atomic pile of less than critical size: an injected idea is to correspond to a neutron entering the pile from without. Each such neutron will cause a certain disturbance which eventually dies away. If, however, the size of the pile is sufficiently increased, the disturbance caused by such an incoming neutron will very likely go on and on increasing until the whole pile is destroyed. Is there a corresponding phenomenon for minds, and is there one for machines? There does seem to be one for the human mind. The majority of them seem to be "sub critical," i.e. to correspond in this analogy to piles of sub-critical size. An idea presented to such a mind will on average give rise to less than one idea in reply. A smallish proportion are supercritical. An idea presented to such a mind may give rise to a whole "theory" consisting of secondary, tertiary and more remote ideas. Animals’ minds seem to be very definitely sub-critical. Adhering to this analogy we ask, "Can a machine be made to be super-critical?
Alan Turing
A likely story indeed!" said the Pigeon, in a tone of the deepest contempt. "I've seen a good many little girls in my time, but never one with such a neck as that! No, no! You're a serpent; and there's no use denying it. I suppose you'll be telling me next that you never tasted an egg!""I have tasted eggs, certainly," said Alice, who was a very truthful child; "but little girls eat eggs quite as much as serpents do, you know.""I don't believe it," said the Pigeon; "but if they do, then they're a kind of serpent: that's all I can say.
Lewis Carroll
I lay it down as a fact that if all men knew what others say of them, there would not be four friends in the world.
Blaise Pascal
Let the tree of the Knowledge of Good and Evil fall, soundless in the moldering woods.
Rudy Rucker
If skeptic can weakly force E, then he can force E.
Glenn Shafer
The unity of all science consists alone in its method, not in its material.
Karl Pearson
It becomes the urgent duty of mathematicians, therefore, to meditate about the essence of mathematics, its motivations and goals and the ideas that must bind divergent interests together.
Richard Courant
Cheshire Puss,' she began, rather timidly, as she did not at all know whether it would like the name: however, it only grinned a little wider. 'Come, it's pleased so far,' thought Alice, and she went on. 'Would you tell me, please, which way I ought to go from here?''That depends a good deal on where you want to get to,' said the Cat.'I don't much care where—' said Alice.'Then it doesn't matter which way you go,' said the Cat.'—so long as I get SOMEWHERE,' Alice added as an explanation.'Oh, you're sure to do that,' said the Cat, 'if you only walk long enough.
Lewis Carroll
There is another more psychological obstacle to the full development of love in the modern world, and that is the fear that many people feel of not preserving their individuality in tact. This is a foolish and rather modern terror. Individuality is not an end in itself; it is something that must enter into fructifying contact with the world, and in so doing must lose its separateness. An individuality which is kept in a glass case withers, whereas on e that is freely expended in human contacts becomes enriched.
Bertrand Russell
The whole problem with the world is that fools and fanatics are always so sure of themselves and wiser people so full of doubts.
Bertrand Russell
In every action we must look beyond the action at our past, present and future state, and at others whom it affects, and see the relations of all these things.
Blaise Pascal
Booty Butt, Booty Butt, Booty Butt Cheeks
René Descartes
Eloquence.— We need both what is pleasing and what is real, but that which pleases must itself be drawn from the true.
Blaise Pascal
I wish creatures wouldn't be so easily offended!", "You'll get used to it in time," said the Caterpillar; and it put the hookah into its mouth and began smoking again.
Lewis Carroll
Alice asked the Cheshire Cat who was sitting in a tree "What road do I take?"The cat asked, "Where do you want to go?""I don't know " answered Alice. "Then, said the cat, it really doesn't matter, does it?
Lewis Carroll
Mad Hatter: “Why is a raven like a writing-desk?”“Have you guessed the riddle yet?” the Hatter said, turning to Alice again.“No, I give it up,” Alice replied: “What’s the answer?”“I haven’t the slightest idea,” said the Hatter
Lewis Carroll
And how do you know that you're mad? "To begin with," said the Cat, "a dog's not mad. You grant that?" I suppose so, said Alice. "Well then," the Cat went on, "you see a dog growls when it's angry, and wags it's tail when it's pleased. Now I growl when I'm pleased, and wag my tail when I'm angry. Therefore I'm mad.
Lewis Carroll
It is true that a mathematician who is not somewhat of a poet, will never be a perfect mathematician.
Karl Weierstrass
I will fight for my people, but will they do the same for me?
Mihailo Petrovic
It is part of the pholosophic dullness of our time that there are millions of rational monsters walking about on their hind legs, observing the world through pairs of flexible little lenses, periodically supplying themselves with energy by pushing organic substances through holes in their faces, who see nothing fabulous whatever about themselves.
Martin Gardner
Sometimes the hardest thing in life is to know which bridge to cross and which to burn
Bertrand Russell
and vinegar that makes them sour—and camomile that makes them bitter—and—and barley-sugar and such things that make children sweet-tempered. I only wish people knew that: then they wouldn’t be so stingy about it, you know—
Lewis Carroll
The Caterpillar and Alice looked at each other for some time in silence: at last the Caterpillar took the hookah out of its mouth,
Lewis Carroll
So blind is the curiosity by which mortals are possessed, that they often conduct their minds along unexplored routes, having no reason to hope for success, but merely being willing to risk the experiment of finding whether the truth they seek lies there.
René Descartes
you're entirly bonkers but I'll tell you a secret all the best people are
Lewis Carroll
What a Chimera is man! What a novelty, a monster, a chaos, a contradiction, a prodigy! Judge of all things, an imbecile worm; depository of truth, and sewer of error and doubt; the glory and refuse of the universe.
Blaise Pascal
I was made to learn Latin and Greek, but I resented it, being of opinion that it was silly to learn a language that was no longer spoken. I believe that all the little good I got from years of classical studies I could have got in adult life in a month.
Bertrand Russell
I went to Russia a Communist; but contact with those who have no doubts has intensified a thousandfold my own doubts, not as to Communism in itself, but as to the wisdom of holding a creed so firmly that for its sake men are willing to inflict widespread misery.
Bertrand Russell
...we ought also to consider as false all that is doubtful.
René Descartes
I wish I hadn't cried so much!" said Alice, as she swam about, trying to find her way out. "I shall be punished for it now, I suppose, by being drowned in my own tears! That will be a queer thing, to be sure! However, everything is queer today.
Lewis Carroll
TO MAKE A LONG STORY SHORTTo make a long story shortI leave all my possessionsto the Municipal Slaughterhouseto the Special Unit of the Police Departmentto Lucky Dog LottoSo now if you want you can shoot
Nicanor Parra
Time makes fools of us all. Our only comfort is that greater shall come after us.
Eric Temple Bell
Perhaps the hardest thing in all literature— at least I have found it so: by no voluntary effort can I accomplish it: I have to take it as it comes— is to write anything original. And perhaps the easiest is, when once an original line has been struck out, to follow it up, and to write any amount more to the same tune.
Lewis Carroll
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 great importance.
Bertrand Russell
There is something feeble and a little contemptible about a man who cannot face the perils of life without the help of comfortable myths. Almost inevitably some part of him is aware that they are myths and that he believes them only because they are comforting. But he dare not face this thought! Moreover, since he is aware, however dimly, that his opinions are not rational, he becomes furious when they are disputed.
Bertrand Russell
Political satire became obsolete when Henry Kissinger was awarded the Nobel Peace Prize.
Tom Lehrer
I don’t think this kind of thing [satire] has an impact on the unconverted, frankly. It’s not even preaching to the converted; it’s titillating the converted. I think the people who say we need satire often mean, ‘We need satire of them, not of us.’ I’m fond of quoting Peter Cook, who talked about the satirical Berlin cabarets of the ’30s, which did so much to stop the rise of Hitler and prevent the Second World War.
Tom Lehrer
It is the one of the great secrets of life that those things are most worth doing,we do for others.
Lewis Carroll
I revered our theology, and aspired as much as any one to reach heaven: but being given assuredly to understand that the way is not less open to the most ignorant than to the most learned, and that the revealed truths which lead to heaven are above our comprehension, I did not presume to subject them to the impotency of my reason; and I thought that in order competently to undertake their examination, there was need of some special help from heaven, and of being more than man.
René Descartes
In some strange way, any new fact or insight that I may have found has not seemed to me as a “discovery” of mine, but rather something that had always been there and that I had chanced to pick up.
Subrahmanijan Chandrasekhar
A chorus of voices exhorts kids to study science. No one stops to ask whether it is inhumane to force adolescents to spend the bulk of their time studying subjects most of them hate. When skilled workers are put out of a job by technical advances and have to undergo “retraining,” no one asks whether it is humiliating for them to be pushed around in this way. It is simply taken for granted that everyone must bow to technical necessity, and for good reason: If human needs were put before technical necessity there would be economic problems, unemployment, shortages or worse. The concept of “mental health” in our society is defined largely by the extent to which an individual behaves in accord with the needs of the system and does so without showing signs of stress.
Theodore J. Kaczynski
Progress is the exploration of our own error. Evolution is a consolidation of what have always begun as errors. And errors are of two kinds: errors that turn out to be true and errors that turn out to be false (which are most of them). But they both have the same character of being an imaginative speculation. I say all this because I want very much to talk about the human side of discovery and progress, and it seems to me terribly important to say this in an age in which most non-scientists are feeling a kind of loss of nerve.
Jacob Bronowski
But if it be true, as every prospect assures us, that the human race shall not again relapse into its ancient barbarity; if every thing ought to assure us against that pusillanimous and corrupt system which condemns man to eternal oscillations between truth and falsehood, liberty and servitude, we must, at the same time, perceive that the light of information is spread over a small part only of our globe; and the number of those who possess real instruction, seems to vanish in the comparison with the mass of men consigned over to ignorance and prejudice. We behold vast countries groaning under slavery, and presenting nations in one place, degraded by the vices of civilization, so corrupt as to impede the progress of man; and in others, still vegetating in the infancy of its early age. We perceive that the exertions of these last ages have done much for the progress of the human mind, but little for the perfection of the human species; much for the glory of man, somewhat for his liberty, but scarcely any thing yet for his happiness. In a few directions, our eyes are struck with a dazzling light; but thick darkness still covers an immense horison.
Nicolas de Condorcet
Progress imposes not only new possibilities for the future but new restrictions.
Norbert Wiener
Now, in the modern money economy everything in the nature of a social-economic occurrence consists in human actions and behaviour.
Oskar Morgenstern
...the facts of economic life cannot be comprehensively described in terms of statistics.
Oskar Morgenstern
Our knowledge of dynamic processes is necessarily inferior to our ability to describe stationary conditions.
Oskar Morgenstern
It is natural that the appearance of pollution should have taken by surprise an economic science which has delighted in playing around with all kinds of mechanistic models. Curiously, even after the event economics gives no signs of acknowledging the role of natural resources in the economic process. Economists still do not seem to realize that, since the product of the economic process is waste, waste is an inevitable result of that process and ceteris paribus increases in greater proportion than the intensity of economic activity.
Nicholas Georgescu-Roegen
Let us remember that the automatic machine is the precise economic equivalent of slave labor. Any labor which competes with slave labor must accept the economic consequences of slave labor.
Norbert Wiener
No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; … [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.
G H Hardy
Ultimately, classroom teachers are the targets of this anger, as they are the public face of the education system. As a group, teachers work very hard with limited resources. They are called upon to equalize the inequities our society creates, and to offer not just equal educational opportunities, but equal educational outcomes to all children.
Christopher Danielson
Hold your tongue!’ said the Queen, turning purple. ‘I won’t!’ said Alice. ‘Off with her head!’ the Queen shouted at the top of her voice. Nobody moved. ‘Who cares for you?’ said Alice (she had grown to her full size by this time). ‘You’re nothing but a pack of cards!’ At this the whole pack rose up into the air, and came flying down upon her; she gave a little scream, half of fright and half of anger, and tired to beat them off, and found herself lying on the bank, with her head in the lap of her sister, who was gently brushing away some dead leaves that had fluttered down from the trees upon her face. ‘Wake up, Alice dear!’ said her sister. ‘Why, what a long sleep you’ve had!’ So Alice got up and ran off, thinking while she ran, as well she might, what a wonderful dream it had been. Lewis Carroll, Alice’s Adventure in Wonderland, 1865
Lewis Carroll
Religious toleration, to a certain extent, has been won, because people have ceased to consider religion so important as it was once thought to be. But in politics and economics, which have taken the place formerly occupied by religion, there is a growing tendency to persecution, which is not by any means confined to one party.
Bertrand Russell