Quotes by Mathematicians - Page 14

Kind words produce their images on men's souls.
Blaise Pascal
The spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didn't bother to remember things. He computed them. You asked him a question, and if he didn't know the answer, he thought for three seconds and would produce and answer.
Paul R. Halmos
And of the fact that every vision of the past is a vision of the blind
Jacques Roubaud
It's a poor sort of memory that only works backwards,' says the White Queen to Alice.
Lewis Carroll
Is Life itself a dream, I wonder?
Lewis Carroll
The twelve jurors were all writing very busily on the slates. "What are they doing?" Alice whispered to the Gryphon. "They can't have anything to put down yet, before the trial's begun.""They're putting down their names," the Gryphon whispered in reply, "for fear they should forget them before the end of the trial.
Lewis Carroll
The 'practical' man, as this word is often used, is one who recognizes only the material needs, who realizes that men must have food for the body, but is oblivious of the necessity of providing food for the mind.
Bertrand Russell
But in practical affairs, particularly in politics, men are needed who combine human experience and interest in human relations with a knowledge of science and technology.
Max Born
Men are so inevitably mad that not to be mad would be to give a mad twist to madness.
Blaise Pascal
I prefer solitude to companions, since there are so few men who are trustworthy, and almost none truly learned. I do not say this because I demand scholarship in all men -- although the sum total of men's learning is small enough; but I question whether we should allow anyone to waste our time. The wasting of time is an abomination.
Girolamo Cardano
The pursuit of science has often been compared to the scaling of mountains, high and not so high. But who amongst us can hope, even in imagination, to scale the Everest and reach its summit when the sky is blue and the air is still, and in the stillness of the air survey the entire Himalayan range in the dazzling white of the snow stretching to infinity? None of us can hope for a comparable vision of nature and of the universe around us. But there is nothing mean or lowly in standing in the valley below and awaiting the sun to rise over Kinchinjunga.
Subrahmanijan Chandrasekhar
Mathematicians enjoy thinking about the simplest possible things, and the simplestpossible things are imaginary.
Paul Lockhart
I see nobody on the road,' said Alice'I only wish I had such eyes,' The King remarked in a fretful tone. 'To be able to see Nobody! And at that distance too! Why it's as much as I can do to see real people, by this light!
Lewis Carroll
So [in mathematics] we get to play and imagine whatever we want and make patterns and ask questions about them. But how do we answer these questions? It’s not at all like science. There’s no experiment I can do ... The only way to get at the truth about our imaginations is to use our imaginations, and that is hard work.
Paul Lockhart
And when we describe it as I shall do, it becomes plain that imagination is a specifically human gift. To imagine is the characteristic act, not of the poet's mind, or the painter's, or the scientist's, but of the mind of man.
Jacob Bronowski
In vain we roared;in vain we triedTo rouse her into laughter:Her pensive glances wandered wideFrom orchestra to rafter -"TIER UPON TIER!" she said,and sighed;And silence followed after.
Lewis Carroll
Scarce was the verdict spoken,When that still calm was broken,A childish form hath burst into the throng;With tears and looks of sadness,That bring no news of gladness,But tell too surely something hath gone wrong!
Lewis Carroll
As far as you can avoid it, do not give grief to anyone. Never inflict your rage on another. If you hope for eternal rest, feel the pain yourself; but don’t hurt others.
Omar Khayyám
If the butterfly wings its way to the sweet light that attracts it, it's only becasue it doesn't know that the fire can consume it.
Giordano Bruno
Let craft, ambition, spite, Be quenched in Reason's night, Till weakness turn to might, Till what is dark be light, Till what is wrong be right!
Lewis Carroll
Truth is the offspring of silence and meditation. I keep the subject constantly before me and wait 'til the first dawnings open slowly, by little and little, into a full and clear light.
Isaac Newton
Intellectually, what is stimulating to a young man is a problem of obvious practical importance. A young man learning economics, for example, ought to hear lectures from individualists and socialists, protectionists and free-traders, inflationists and believers in the gold standard. He ought to be encouraged to read the best books of the various schools, as recommended by those who believe in them. This would teach him to weigh arguments and evidence, to know that no pinion is certainly right, and to judge men by their quality rather than by their consonance with preconceptions.
Bertrand Russell
I received comments on how extraordinary it was that I could keep up speaking for exactly 45 minutes. Indeed, in an age of soundbites lasting some seconds and of quick quotes in the news, all those minutes do seem like an eternity, easy to get lost in. Yet, wait a moment. Television is not the only place where speeches are given. Some hundred thousand teachers teach every day. They all speak 45 minutes, more times a day. They have been doing this for years. Every teacher knows exactly when the time will be over and that by then his speech will need to come to a natural end. It is this tension that determines the success of a lesson. It is a sign of the times that we forget these daily achievements in education. A million students daily attend several ‘live’ lectures and this in secondary education alone. These are high ratings!
Robbert Dijkgraaf
What you learn from others you can use to follow.What you learn for yourself you can use to lead.
Richard Hamming
When we were little," the Mock Turtle went on at last, more calmly, though still sobbing a little now and then, "we went to school in the sea. The master was an old Turtle - we used to call him Tortoise -""Why did you call him Tortoise, if he wasn't one?" Alice asked."We called him Tortoise because he taught us," said the Mock Turtle angrily: "really you are very dull!
Lewis Carroll
What if at school you had to take an art class in which you were only taught how to pain a fence? What if you were never shown the paintings of Leonardo da Vinci and Picasso? Would that make you appreciate art? Would you want to learn more about it? I doubt it...Of course this sounds ridiculous, but this is how math is taught.
Edward Frenkel
It is mathematics which reveals every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever then has the effrontery to study physics while neglecting mathematics, should know from the start that he will never make his entry into the portals of wisdom.
Thomas Bradwardine
I think actually if you take the analogy with other areas of engineering, and increasingly of science and even mathematics, you can see people do not have to learn the vast number of formulae they used to learn. Instead, they have to learn to use the computer effectively. This frees them, I feel, to understand concepts and the foundations while they’re learning the mechanics of the application of the theory.
C.A.R. Hoare
It's much easier, after all, to learn mathematics from someone who's made a few mistakes. It's impossible to learn it from someone who always gets it right.
John C. Lennox
In all the works on pedagogy that ever I read — and they have been many, big, and heavy — I don't remember that any one has advocated a system of teaching by practical jokes, mostly cruel. That, however, describes the method of our great teacher, Experience.
Charles Sanders Peirce
God instituted prayer to communicate to creatures the dignity of causality.
Blaise Pascal
A word is used "correctly" when the average hearer will be affected by it in the way intended. This is a psychological, not a literary, definition of "correctness". The literary definition would substitute, for the average hearer, a person of high education living a long time ago; the purpose of this definition is to make it difficult to speak or write correctly.
Bertrand Russell
Where would you be without etymology'? Lea asked sarcastically.'I think I might find words a little less interesting,' said Mr Ruche.
Denis Guedj
When I use a word,' Humpty Dumpty said in a rather scornful tone, 'it means just what I choose it to mean - neither more nor less.
Lewis Carroll
Be silent or let thy words be worth more than silence.
Pythagoras
[Metaphors] replace genuine uncertainty about the world with semantic ambiguity. A metaphor is a cover-up.
Amos Tversky
Fables should be taught as fables, myths as myths, and miracles as poetic fancies. To teach superstitions as truths is a most terrible thing. The child mind accepts and believes them, and only through great pain and perhaps tragedy can he be in after years relieved of them. In fact, men will fight for a superstition quite as quickly as for a living truth — often more so, since a superstition is so intangible you cannot get at it to refute it, but truth is a point of view, and so is changeable.
Hypatia
When two men of science disagree, they do not invoke the secular arm; they wait for further evidence to decide the issue, because, as men of science, they know that neither is infallible. But when two theologians differ, since there is no criteria to which either can appeal, there is nothing for it but mutual hatred and an open or covert appeal to force.
Bertrand Russell
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.
Siméon Denis Poisson
William James used to preach the 'will to believe.' For my part, I should wish to preach the 'will to doubt' ... what is wanted is not the will to believe, but the wish to find out, which is the exact opposite.
Bertrand Russell
Every time we let ourselves believe for unworthy reasons, we weaken our powers of self-control, of doubting, of judicially and fairly weighing evidence. We all suffer severely enough from the maintenance and support of false beliefs and the fatally wrong actions which they lead to, and the evil born when one such belief is entertained is great and wide.
William Kingdon Clifford
I wish to propose for the reader's favourable consideration a doctrine which may, I fear, appear wildly paradoxical and subversive. The doctrine in question is this: that it is undesirable to believe a proposition when there is no ground whatever for supposing it true.
Bertrand Russell
It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence.
William Kingdon Clifford
The fact that an opinion has been widely held is no evidence whatever that it is not utterly absurd; indeed in view of the silliness of the majority of mankind, a widely spread belief is more likely to be foolish than sensible.
Bertrand Russell
A time will come when men will stretch out their eyes. They should see planets like our Earth.
Christopher Wren
Nature  …   has made it impossible for us to have any communication from this earth with the other great bodies of the universe, in our present state; and it is highly possible that he has likewise cut off all communication betwixt the other planets, and betwixt the different systems.… We observe, in all of them, enough to raise our curiosity, but not to satisfy it  …   It does not appear to be suitable to the wisdom that shines throughout all nature, to suppose that we should see so far, and have our curiosity so much raised  …   only to be disappointed at the end  …   This, therefore, naturally leads us to consider our present state as only the dawn or beginning of our existence, and as a state of preparation or probation for farther advancement.…
Colin Maclaurin
The world is full of magical things patiently waiting for our wits to grow sharper.
Bertrand Russell
If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.
Henri Poincaré
On the other hand it is possible that human control over the machines may be retained. In that case the average man may have control over certain private machines of his own, such as his car of his personal computer, but control over large systems of machines will be in the hands of a tiny elite -- just as it is today, but with two difference. Due to improved techniques the elite will have greater control over the masses; and because human work will no longer be necessary the masses will be superfluous, a useless burden on the system. If the elite is ruthless the may simply decide to exterminate the mass of humanity. If they are humane they may use propaganda or other psychological or biological techniques to reduce the birth rate until the mass of humanity becomes extinct, leaving the world to the elite. Or, if the elite consist of soft-hearted liberals, they may decide to play the role of good shepherds to the rest of the human race. They will see to it that everyone's physical needs are satisfied, that all children are raised under psychologically hygienic conditions, that everyone has a wholesome hobby to keep him busy, and that anyone who may become dissatisfied undergoes "treatment" to cure his "problem." Of course, life will be so purposeless that people will have to be biologically or psychologically engineered either to remove their need for the power process or to make them "sublimate" their drive for power into some harmless hobby. These engineered human beings may be happy in such a society, but they most certainly will not be free. They will have been reduced to the status of domestic animals.
Ted Kaczynski
When we look ahead to 2018, we should expect big steps forward in science to come once again from changes in style rather than from marginal improvements in technology.
Freeman Dyson
Since the future's so iffy, I'll turn my attention to the past.
Manil Suri
If we examine our thoughts, we shall find them always occupied with the past and the future.
Blaise Pascal
The poem or the discovery exists in two moments of vision: the moment of appreciation as much as that of creation; for the appreciator must see the movement, wake to the echo which was started in the creation of the work. In the moment of appreciation we live again the moment when the creator saw and held the hidden likeness. When a simile takes us aback and persuades us together, when we find a juxtaposition in a picture both odd and intriguing, when a theory is at once fresh and convincing, we do not merely nod over someone else's work. We re-enact the creative act, and we ourselves make the discovery again......Reality is not an exhibit for man's inspection, labeled: "Do not touch." There are no appearances to be photographed, no experiences to be copied, in which we do not take part. We re-make nature by the act of discovery, in the poem or in the theorem. And the great poem and the deep theorem are new to every reader, and yet are his own experiences, because he himself re-creates them. They are the marks of unity in variety; and in the instant when the mind seizes this for itself, in art or in science, the heart misses a beat.
Jacob Bronowski
If teaching is reduced to mere data transmission, if there is no sharing or excitement and wonder, if teachers themselves are passive recipients of information and not creators of new ideas, what hope is there for their students?
Paul Lockhart
The last thing we discover in composing a work is what to put down first.
Blaise Pascal
We know too much and feel too little. At least, we feel too little of those creative emotions from which a good life springs.
Bertrand Russell
[Beware of] the fallacy of misplaced concreteness [mistaking an abstraction for concrete reality, for actuality] In the inescapable flux, there is something that abides; in the overwhelming permanence, there is an element that escapes into flux. Permanence can be snatched only out of flux; and the passing moment can find its adequate intensity only by its submission to permanence.Error is the price we pay for progress.In the real world it is more important that a proposition be interesting than that it be true. The importance of truth is that it adds to interest.Creativity is the universal of universals characterizing ultimate matter of fact. It is that ultimate principle by which the many, which are the universe disjunctively, become the one actual occasion, which is the universe conjunctively. It lies in the nature of things that the many enter into complex unity.The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, "Seek simplicity and distrust it."It requires a very unusual mind to undertake the analysis of the obvious.[From various of Whitehead's books, not only PR]
Alfred North Whitehead
When I was a boy I felt that the roll of rhyme in poetry was to compel one to find the un-obvious- because of the necessity of finding a word which rhymes. This forces novel associations, and almost guarantees deviations from routine chains or trains of thought. It becomes, paradoxically, a sort of automatic mechanism of originality.
Stanislaw Ulam
The question that will decide our destiny is not whether we shall expand into space. It is: shall we be one species or a million? A million species will not exhaust the ecological niches that are awaiting the arrival of intelligence.
Freeman Dyson
Let me here remind you that the essence of dramatic tragedy is not unhappiness. It resides in the solemnity of the remorseless working of things. This inevitableness of destiny can only be illustrated in terms of human life by incidents which in fact involve unhappiness. For it is by them that the futility of escape can be made evident in the drama. This remorseless inevitableness is what pervades scientific thought. The laws of physics are the decrees of fate.
Alfred North Whitehead