Quotes by Mathematicians - Page 18

Science is my territory, but science fiction is the landscape of my dreams.
Freeman Dyson
Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.
George Pólya
The real difficulty about volcanism is not to see how it can start, but how it can stop.
Harold Jeffreys
Regardless of one's point of view, it's quite easy to see that Darwinism is not in the same league as the hard sciences. For instance, Darwinists will often compare their theory favorably to Einsteinian physics, claiming that Darwinism is just as well established as general relativity. Yet how many physicists, while arguing for the truth of Einsteinian physics, will claim that general relativity is as well established as Darwin’s theory? Zero.
William A. Dembski
Give me the positions and velocities of all the particles in the universe, and I will predict the future.
Marquis Pierre Simon de Laplace
The essential fact which emerges ... is that the three smallest and most active reservoirs ( of carbon in the global carbon cycle), the atmosphere, the plants and the soil, are all of roughly the same size. This means that large human disturbance of any one of these reservoirs will have large effects on all three. We cannot hope either to understand or to manage the carbon in the atmosphere unless we understand and manage the trees and the soil too.
Freeman Dyson
The fundamental claim of intelligent design is straightforward and easily intelligible: namely, there are natural systems that cannot be adequately explained in terms of undirected natural forces and that exhibit features which in any other circumstance we would attribute to intelligence.
William A. Dembski
When the time is ripe for certain things, these things appear in different places in the manner of violets coming to light in early spring.
Farkas Bolyai
There are no foolish questions and no man becomes a fool until he has stopped asking questions.
Charles Proteus Steinmetz
Science, like art, is not a copy of nature but a re-creation of her.
Jacob Bronowski
It is of great advantage to the student of any subject to read the original memoirs on that subject, for science is always most completely assimilated when it is in the nascent state...
James Clerk Maxwell
The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.
Alfred North Whitehead
This seems charmingly paradoxical: scientists seek one truth but often voice many opinions journalists often speak of many truths while voicing a uniform view.
Christopher Essex
The isolated man does not develop any intellectual power. It is necessary for him to be immersed in an environment of other men, whose techniques he absorbs during the first twenty years of his life. He may then perhaps do a little research of his own and make a very few discoveries which are passed on to other men. From this point of view the search for new techniques must be regarded as carried out by the human community as a whole, rather than by individuals.
Alan Turing
Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths.
Bertrand Russell
Discover the force of the skies O Men: once recognised it can be put to use.
Johannes Kepler
I used to measure the skies, now I measure the shadows of Earth.Although my mind was sky-bound, the shadow of my body lies
Johannes Kepler
If our brains were simple enough for us to understand them, we'd be so simple that we couldn't.
Ian Stewart
It is our task, both in science and in society at large, to prove the conventional wisdom wrong and to make our unpredictable dreams come true
Freeman Dyson
It is not what the man of science believes that distinguishes him, but how and why he believes it. His beliefs are tentative, not dogmatic; they are based on evidence, not on authority or intuition.
Bertrand Russell
When things get too complicated, it sometimes makes sense to stop and wonder: Have I asked the right question?
Enrico Bombieri
Big whirls have little whirls,That feed on their velocity;And little whirls have lesser whirls,And so on to viscosity.
Lewis Fry Richardson
Maybe you who condemn me are in greater fear than I who am condemned.
Giordano Bruno
The thing is, it's very dangerous to have a fixed idea. A person with a fixed idea will always find some way of convincing himself in the end that he is right
Atle Selberg
We ought not to ask why the human mind troubles to fathom the secrets of the universe. The diversity of the phenomena of nature is so great, and the treasures hidden in the skies so rich, precisely in order that the human mind shall never be lacking in fresh nourishment.
Johannes Kepler
I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted.
Alan Turing
Science is what you know, philosophy is what you don't know
Bertrand Russell
What goes up must come down.
Isaac Newton
But in my opinion, all things in nature occur mathematically.
René Descartes
Even if the open windows of science at first make us shiver after the cozy indoor warmth of traditional humanizing myths, in the end the fresh air brings vigor, and the great spaces have a splendor of their own.
Bertrand Russell
We know very little, and yet it is astonishing that we know so much, and still more astonishing that so little knowledge can give us so much power.
Bertrand Russell
If I have seen further it is by standing on the shoulders of Giants.
Isaac Newton
There are men and gods, and beings like Pythagoras.
Pythagoras
What do you suppose is the use of a child without any meaning? Even a joke should have some meaning-- and a child's more imporant than a joke, I hope. You couldn't deny that, even if you tried with both hands.
Lewis Carroll
The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.
Gian-Carlo Rota
Must a name mean something?" Alice asked doubtfully.Of course it must," Humpty Dumpty said with a short laugh; "my name means the shape I am - and a good handsome shape it is, too. With a name like yours, you might be any shape, almost.
Lewis Carroll
Our great democracies still tend to think that a stupid man is more likely to be honest than a clever man, and our politicians take advantage of this prejudice by pretending to be even more stupid than nature made them.
Bertrand Russell
Be what you would seem to be - or, if you'd like it put more simply - never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.
Lewis Carroll
Why it's simply impassible!Alice: Why, don't you mean impos
Lewis Carroll
We are not the stuff that abides, but patternsthat perpetuate themselves.
Norbert Wiener
He no longer loves the person whom he loved ten years ago. I quite believe it. She is no longer the same, nor is he. He was young, and she also; she is quite different. He would perhaps love her yet, if she were what she was then.
Blaise Pascal
Men spend their time in following a ball or a hare it is the pleasure even of kings.
Blaise Pascal
... who can forget the amazement of a child balancing an adult on a see-saw, simply by being placed at the right position. How could this be? Where did all that extra force come from!?The only wonder nowadays is that a physics student is unlikely to produce a satisfactory answer to this question. Perhaps we will be offered a few mumblings about moments, force times distance, laws of the lever perhaps even the "principle of virtual work". But we probably won't get an answer that seems to explain where that extra force comes from; and it is highly unlikely that we will get an answer that begins by establishing principles about rigid bodies, even though the rigidity of the lever is an absolute necessity for it to work.In fact, the whole path from Newton's Laws, which basically concern "point masses", to bodies whose shape and extent are significant, is often rather dubiously traversed, even though elementary physics courses blithely pose such problems of the most diverse sorts.
Michael Spivak
For many years I have been saying that I would like to write a book (or series of books) called Physics for Mathematicians. Whenever I would tell people that, they would say, “Oh good, you're going to explain quantum mechanics, or string theory, or something like that”. And I would say, “Well that would be nice, but I can't begin to do that now; first I have to learn elementary physics, so the first thing I will be writing will be Mechanics for Mathematicians”. So then people would say, “Ah, so you're going to be writing about symplectic structures”, or something of that sort. And I would have to say, “No, I'm not trying to write a book about mathematics for mathematicians, I'm trying to write a book about physics for mathematicians”; …… it's elementary mechanics that I don't understand. … I mean, for example, that I don't understand this – lever.... Most of us know the law of the lever, but this law is simply a quantitative statement of exactly how amazing the lever is, and doesn't give us a clue as to why it is true, how such a small force at one end can exert such a great force at the other. Now physicists all agree that Newton's Three Laws are the basis from which all of mechanics follows, but if you ask for an explanation of the lever in terms of these three laws, you will almost certainly not get a satisfactory answer.
Michael Spivak
Probability theory is nothing more than common sense reduced to calculation. -1819
Pierre-Simon Laplace
Everything is what it is because it got that way.
D'Arcy Wentworth Thompson
My work has always tried to unite the True with the Beautiful and when I had to choose one or the other, I usually chose the Beautiful.
Hermann Weyl
And every science, when we understand it not as an instrument of power and domination but as an adventure in knowledge pursued by our species across the ages, is nothing but this harmony, more or less vast, more or less rich from one epoch to another, which unfurls over the course of generations and centuries, by the delicate counterpoint of all the themes appearing in turn, as if summoned from the void.
Alexandre Grothendieck
Science is a river with two sources, the practical source and the theoretical source.
Alfred North Whitehead
If I have been able to see further than others, it is because I have stood on the shoulders of giants
Isaac Newton
It may be asked how I know that there are any Reals. If this hypothesis is the sole support of my method of inquiry, my method of inquiry must not be used to support my hypothesis. The reply is this: 1. If investigation cannot be regarded as proving that there are Real things, it at least does not lead to a contrary conclusion; but the method and the conception on which it is based remain ever in harmony. No doubts of the method, therefore, necessarily arise from its practice, as is the case with all the others. 2. The feeling which gives rise to any method of fixing belief is a dissatisfaction at two repugnant propositions. But here already is a vague concession that there is some one thing which a proposition should represent. Nobody, therefore, can really doubt that there are Reals, for, if he did, doubt would not be a source of dissatisfaction. The hypothesis, therefore, is one which every mind admits. So that the social impulse does not cause men to doubt it. 3. Everybody uses the scientific method about a great many things, and only ceases to use it when he does not know how to apply it. 4. Experience of the method has not led us to doubt it, but, on the contrary, scientific investigation has had the most wonderful triumphs in the way of settling opinion. These afford the explanation of my not doubting the method or the hypothesis which it supposes; and not having any doubt, nor believing that anybody else whom I could influence has, it would be the merest babble for me to say more about it. If there be anybody with a living doubt upon the subject, let him consider it.
Charles Sanders Peirce
To satisfy our doubts . . . it is necessary that a method should be found by which our beliefs may be determined by nothing human, but by some external permanency -- by something upon which our thinking has no effect. . . . Our external permanency would not be external, in our sense, if it was restricted in its influence to one individual. It must be something which affects, or might affect, every man. And, though these affections are necessarily as various as are individual conditions, yet the method must be such that the ultimate conclusion of every man shall be the same. Such is the method of science. Its fundamental hypothesis, restated in more familiar language, is this: There are Real things, whose characters are entirely independent of our opinions about them; those Reals affect our senses according to regular laws, and, though our sensations are as different as are our relations to the objects, yet, by taking advantage of the laws of perception, we can ascertain by reasoning how things really and truly are; and any man, if he have sufficient experience and he reason enough about it, will be led to the one True conclusion. The new conception here involved is that of Reality. It may be asked how I know that there are any Reals. If this hypothesis is the sole support of my method of inquiry, my method of inquiry must not be used to support my hypothesis. The reply is this: 1. If investigation cannot be regarded as proving that there are Real things, it at least does not lead to a contrary conclusion; but the method and the conception on which it is based remain ever in harmony. No doubts of the method, therefore, necessarily arise from its practice, as is the case with all the others. 2. The feeling which gives rise to any method of fixing belief is a dissatisfaction at two repugnant propositions. But here already is a vague concession that there is some one thing which a proposition should represent. Nobody, therefore, can really doubt that there are Reals, for, if he did, doubt would not be a source of dissatisfaction. The hypothesis, therefore, is one which every mind admits. So that the social impulse does not cause men to doubt it. 3. Everybody uses the scientific method about a great many things, and only ceases to use it when he does not know how to apply it. 4. Experience of the method has not led us to doubt it, but, on the contrary, scientific investigation has had the most wonderful triumphs in the way of settling opinion. These afford the explanation of my not doubting the method or the hypothesis which it supposes; and not having any doubt, nor believing that anybody else whom I could influence has, it would be the merest babble for me to say more about it. If there be anybody with a living doubt upon the subject, let him consider it.
Charles Sanders Peirce
That is the essence of science: ask an impertinent question, and you are on the way to the pertinent answer.
Jacob Bronowski
A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.
Euclid
We are nature's unique experiment to make the rational intelligence prove itself sounder than the reflex. Knowledge is our destiny
Jacob Bronowski
One of the most curious consequences of quantum physics is that a particle like an electron can seemingly be in more than one place at the same time until it is observed, at which point there seems to be a random choice made about where the particle is really located. Scientists currently believe that this randomness is genuine, not just caused by a lack of information. Repeat the experiment under the same conditions and you may get a different answer each time.
Marcus du Sautoy
Personally I do not agree with sex being brought into science at all. The idea of 'women and science' is entirely irrelevant. Either a woman is a good scientist, or she is not; in any case she should be given opportunities, and her work should be studied from the scientific, not the sex, point of view
Hertha Ayrton
To understand this new frontier, I will have to try to master one of the most difficult and counterintuitive theories ever recorded in the annals of science: quantum physics. Listen to those who have spent their lives immersed in this world and you will have a sense of the challenge we face. After making his groundbreaking discoveries in quantum physics, Werner Heisenberg recalled, "I repeated to myself again and again the question: Can nature possibly be so absurd as it seemed to us in these atomic experiments?" Einstein declared after one discovery, "If it is correct it signifies the end of science." Schrödinger was so shocked by the implications of what he'd cooked up that he admitted, "I do not like it and I am sorry I had anything to do with it." Nevertheless, quantum physics is now one of the most powerful and well-tested pieces of science on the books. Nothing has come close to pushing it off its pedestal as one of the great scientific achievements of the last century. So there is nothing to do but to dive headfirst into this uncertain world. Feynman has some good advice for me as I embark on my quest: "I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that?' because you will get 'down the drain,' into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.
Marcus du Sautoy
Scientists rightly resist invoking the supernatural in scientific explanations for fear of committing a god-of-the-gaps fallacy (the fallacy of using God as a stop-gap for ignorance). Yet without some restriction on the use of chance, scientists are in danger of committing a logically equivalent fallacy-one we may call the “chance-of-the-gaps fallacy.” Chance, like God, can become a stop-gap for ignorance.
William A. Dembski
eorum omnium actiones in se invicem
Isaac Newton