Quotes by Mathematicians - Page 13

We tend to teach mathematics as a long list of rules.You learn them in order and you have to obey them, because if you don't obey them you get a C-.This is not mathematics. Mathematics is the study if things that come out a certain way because there is no other way they could possibly be.
Jordan Ellenberg
True courage is not the brutal force of vulgar heroes but the firm resolve of virtue and reason.
Alfred North Whitehead
Your hand can seize today, but not tomorrow; and thoughts of your tomorrow are nothing but desire. Don’t waste this breath, if your heart isn’t crazy, since "the rest of your life" won’t last forever.
Omar Khayyám
This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.
Emil Artin
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
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
The true spirit of delight the exultation the sense of being more than Man which is the touchstone of the highest excellence is to be found in mathematics as surely as in poetry.
Bertrand Russell
Big whirls have little whirls,That feed on their velocity;And little whirls have lesser whirls,And so on to viscosity.
Lewis Fry Richardson
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations’, are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards.
G H Hardy
It'll be no use their putting their heads down and saying "Come up again, dear!"I shall only look up and say "Who am I then? Tell me that first, and then,if I like being that person, I'll come up: if not, I'll stay down heretill I'm somebody else"--but, oh dear!' cried Alice, with a sudden burstof tears, 'I do wish they WOULD put their heads down! I am so VERY tiredof being all alone here!
Lewis Carroll
Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer?
Henri Poincaré
We have one real candidate for changing the rules; this is string theory. In string theory the one-dimensional trajectory of a particle in spacetime is replaced by a two-dimensional orbit of a string. Such strings can be of any size, but under ordinary circumstances they are quite tiny, ... a value determined by comparing the predictions of the theory for Newton's constant and the fine structure constant to experimental values.
Edward Witten
Since we cannot know all there is to be known about anything, we ought to know a little about everything.
Blaise Pascal
The rule is jam tomorrow and jam yesterday - but never jam today.
Lewis Carroll
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
We see, surrounding the narrow raft illuminated by the flickering light of human comradeship, the dark ocean on whose rolling waves we toss for a brief hour; all the loneliness of humanity amid hostile forces is concentrated on the individual soul, which must struggle alone, with what of courage it can command, against the whole weight of a universe that cares nothing for its hopes and fears. Victory, in this struggle with the powers of darkness, is the true baptism into the glorious company of heroes, the true initiation into the overmastering beauty of human existence.
Bertrand Russell
Education is not to be viewed as something like filling a vessel with water but, rather, assisting a flower to grow in its own way
Bertrand Russell
Common sense is the most widely shared commodity in the world, for every man is convinced that he is well supplied with it.
René Descartes
No, no! The adventures first, explanations take such a dreadful time.
Lewis Carroll
The willingness to reexamine lifelong beliefs because of conflicting data takes enormous courage, and contrasts sharply with recent examples of public discourse in which our political, cultural, and religious leaders have fit data to preconceived theories.
Donal O'Shea
We do not content ourselves with the life we have in ourselves we desire to live an imaginary life in the minds of others and for this purpose we endeavor to shine.
Blaise Pascal
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
I started studying law, but this I could stand just for one semester. I couldn't stand more. Then I studied languages and literature for two years. After two years I passed an examination with the result I have a teaching certificate for Latin and Hungarian for the lower classes of the gymnasium, for kids from 10 to 14. I never made use of this teaching certificate. And then I came to philosophy, physics, and mathematics. In fact, I came to mathematics indirectly. I was really more interested in physics and philosophy and thought about those. It is a little shortened but not quite wrong to say: I thought I am not good enough for physics and I am too good for philosophy. Mathematics is in between.
George Pólya
Time makes fools of us all. Our only comfort is that greater shall come after us.
Eric Temple Bell
If you ask me to tell you anything about the nature of what lies beyond the phaneron… my answer is “How should I know?”… I am not dismayed by ultimate mysteries… I can no more grasp what is behind such questions as my cat can understand what is behind the clatter I make while I type this paragraph.
Martin Gardner
Real life is to most men ... a perpetual compromise between the ideal and the possible.
Bertrand Russell
Two things control man's nature: instinct and experience.
Blaise Pascal
Even if we have a reliable criterion for detecting design, and even if that criterion tells us that biological systems are designed, it seems that determining a biological system to be designed is akin to shrugging our shoulders and saying God did it. The fear is that admitting design as an explanation will stifle scientific inquiry, that scientists will stop investigating difficult problems because they have a sufficient explanation al
William A. Dembski
The deep study of nature is the most fruitful source of mathematical discoveries. By offering to research a definite end, this study has the advantage of excluding vague questions and useless calculations; besides it is a sure means of forming analysis itself and of discovering the elements which it most concerns us to know, and which natural science ought always to conserve.
Joseph Fourier
It is the business of the future to be dangerous.
Alfred North Whitehead
Everything is what it is because it got that way.
D'Arcy Wentworth Thompson
Why don't we want our children to learn to do mathematics? Is it that we don't trust them, that we think it's too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon. Why not about triangles?
Paul Lockhart
Men fear thought as they fear nothing else on earth -- more than ruin, more even than death.
Bertrand Russell
In the conditions of modern life the rule is absolute, the race which does not value trained intelligence is doomed.
Alfred North Whitehead
Probability theory is nothing more than common sense reduced to calculation. -1819
Pierre-Simon Laplace
In the year 1456 ... a Comet was seen passing Retrograde between the Earth and the sun... Hence I dare venture to foretell, that it will return again in the year 1758.
Edmond Halley
What a wonderful and amazing Scheme have we here of the magnificent Vastness of the Universe! So many Suns, so many Earths, and every one of them stock’d with so many Herbs, Trees and Animals, and adorn’d with so many Seas and Mountains! And how must our wonder and admiration be encreased when we consider the prodigious distance and multitude of the Stars?
Christiaan Huygens
It was as though applied mathematics was my spouse, and pure mathematics was my secret lover.
Edward Frenkel
Those who are most sensitive about "politically incorrect" terminology are not the average black ghetto-dweller, Asian immigrant, abused woman or disabled person, but a minority of activists, many of whom do not even belong to any "oppressed" group but come from privileged strata of society.
Theodore J. Kaczynski
Since the future's so iffy, I'll turn my attention to the past.
Manil Suri
The power of reason is thought small in these days, but I remain an unrepentant rationalist. Reason may be a small force, but it is constant, and works always in one direction, while the forces of unreason destroy one another in futile strife. Therefore every orgy of unreason in the end strengthens the friends of reason, and shows afresh that they are the only true friends of humanity.
Bertrand Russell
I've found out so much about electricity that I've reached the point where I understand nothing and can explain no
Pieter van Musschenbroek
The life of Man is a long march through the night, surrounded by invisible foes, tortured by weariness and pain, towards a goal that few can hope to reach, and where none may tarry long. One by one, as they march, our comrades vanish form our sight, seized by the silent orders of omnipotent Death. Very brief is the time in which we can help them, in which their happiness or misery is decided. Be it ours to shed sunshine on their path, to lighten their sorrows by the balm of sympathy, to give them the pure joy of a never-tiring affection, to strengthen failing courage, to instill faith in times of despair.
Bertrand Russell
Each problem that I solved became a rule, which served afterwards to solve other problems.
René Descartes
But as men grow more industrialised and regimented, the kind of delight that is common in children becomes impossible to adults because they are always thinking of the next thing and cannot let themselves be absorbed in the moment. This habit of thinking of the ‘next thing’ is more fatal to any kind of aesthetic excellence than any other habit of mind that can be imagined, and if art, in any important sense, is to survive it will not be by the foundation of solemn academies, but by recapturing the capacity for wholehearted joys and sorrows which prudence and foresight have all but destroyed.
Bertrand Russell
It is a common observation that those who dwell continually upon their expectations are apt to become oblivious to the requirements of their actual situation.
Charles Sanders Peirce
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
[Metaphors] replace genuine uncertainty about the world with semantic ambiguity. A metaphor is a cover-up.
Amos Tversky
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
Our nature consists in motion complete rest is death.
Blaise Pascal
There are considerable mysteries surrounding the strange values that Nature's actual particles have for their mass and charge. For example, there is the unexplained 'fine structure constant' ... governing the strength of electromagnetic interactions, ....
Roger Penrose
I don't think..." then you shouldn't talk, said the Hatter.
Lewis Carroll
The factor in human life provocative of a noble discontent is the gradual emergence of a sense of criticism founded upon appreciation of beauty and of intellectual distinction and of duty.
Alfred North Whitehead
Mathematics, which most of us see as the most factual of all sciences, constitutes the most colossal metaphor imaginable, and must be judged, aesthetically as well as intellectually in terms of the success of this metaphor.
Norbert Wiener
The technologies which have had the most profound effects on human life are usually simple. A good example of a simple technology with profound historical consequences is hay. Nobody knows who invented hay, the idea of cutting grass in the autumn and storing it in large enough quantities to keep horses and cows alive through the winter. All we know is that the technology of hay was unknown to the Roman Empire but was known to every village of medieval Europe. Like many other crucially important technologies, hay emerged anonymously during the so-called Dark Ages. According to the Hay Theory of History, the invention of hay was the decisive event which moved the center of gravity of urban civilization from the Mediterranean basin to Northern and Western Europe. The Roman Empire did not need hay because in a Mediterranean climate the grass grows well enough in winter for animals to graze. North of the Alps, great cities dependent on horses and oxen for motive power could not exist without hay. So it was hay that allowed populations to grow and civilizations to flourish among the forests of Northern Europe. Hay moved the greatness of Rome to Paris and London, and later to Berlin and Moscow and New York.
Freeman Dyson
I would never die for my beliefs because I might be wrong.
Bertrand Russell
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 am perfectly convinced that I have both seen, and heard in a manner which should make unbelief impossible, things called spiritual which cannot be taken by a rational being to be capable of explanation by imposture, coincidence, or mistake.
Augustus De Morgan
When you come to any passage you don't understand, read it again: if you still don't understand it, read it again: if you fail, even after three readings, very likely your brain is getting a little tired. In that case, put the book away, and take to other occupations, and next day, when you come to it fresh, you will very likely find that it is quite easy.
Lewis Carroll
Order and reason, beauty and benevolence, are characteristics and conceptions which we find solely associated with the mind of man.
Karl Pearson