Quotes by Mathematicians - Page 16

In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide -- a relief from daily life, an anodyne to the practical workaday world.
Paul Lockhart
All right," said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone.
Lewis Carroll
Sarita's been so busy exercising her brain that she hasn't had time for her heart, the poor thing.
Manil Suri
The heart has its order, the mind has its own, which uses principles and demonstrations. The heart has a different one. We do not prove that we ought to be loved by setting out in order the causes of love; that would be absurd.
Blaise Pascal
my first recommendation to people in charge of science education is, more money for public libraries and museums. Public libraries and museums ought to be as common as schools.
Freeman Dyson
When a friend introduced me to a Bach chaconne, he started by describing it by saying that it has 256 measures (256=2^8) divided into 4 sections of 64 measures (64=2^6), and I liked it even before I heard a single note.
James Stein
The Pythagoreans... were fascinated by certain specific ratios, ...The Greeks knew these as the 'golden' proportion and the 'perfect' proportion respectively. They may well have been learned from the Babylonians by Pythagoras himself after having been taken prisoner in Egypt. Ratios lay at the heart of the Pythagorean theory of music.
Graham Flegg
The most successful relationships are ones with a really low negativity threshold. In those relationships, couples allow each other to complain, and work together to constantly repair the tiny issues between them. In such cases, couples don't bottle up their feelings, and little things don't end up being blown completely out of proportion.
Hannah Fry
My tomb shall be in a spot where the north wind may scatter roses over it.
Omar Khayyám
Want for your brother, what you want for yourself.
George Green
Thus nature provides a system for proportioning the growth of plants that satisfies the three canons of architecture. All modules are isotropic and they are related to the whole structure of the plant through self-similar spirals proportioned by the golden mean.
Jay Kappraff
All things can be deadly to us, even the things made to serve us; as in nature walls can kill us, and stairs can kill us, if we do not walk circumspectly.
Blaise Pascal
Those honor nature well, who teach that she can speak on everything.
Blaise Pascal
Nature has made all her truths independent of one another. Our art makes one dependent on the other.
Blaise Pascal
In the modern world, however, love has another enemy more dangerous than religion, and that is the gospel of work and economic success. It is generally held, especially in America, that a man should not allow love to interfere with his career, and that if he does, he is silly. But in this as in all human matters a balance is necessary.
Bertrand Russell
I want to say, in all seriousness, that a great deal of harm is being done in the modern world by belief in the virtuousness of work, and that the road to happiness and prosperity lies in an organised diminution of work.
Bertrand Russell
One of the symptoms of an approaching nervous breakdown is the belief that one’s work is terribly important.
Bertrand Russell
Lust is the source of all our actions, and humanity.
Blaise Pascal
It does appear that some parts of our evolutionary process seem inevitable. It is striking that throughout evolutionary history, the eye evolved independently fifty to a hundred times. This is strong evidence for the fact that the different rolls of the dice that have occurred across different species seem to have produced species with eyes regardless of what is going on around them. Lots of other examples illustrate how some features, if they are advantageous, seem to rise to the top of the evolutionary swamp. This is illustrated every time you see the same feature appearing more than once in different parts of the animal kingdom. Dolphins and bats, for example, use echolocation, but they evolved this trait independently at very different points on the evolutionary tree.
Marcus du Sautoy
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
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
What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn’t really relevant.
Laurent Schwartz
The world of the future will be an even more demanding struggle against the limitations of our intelligence, not a comfortable hammock in which we can lie down to be waited upon by our robot slaves.
Norbert Wiener
I much prefer the sharpest criticism of a single intelligent man to the thoughtless approval of the masses.
Johannes Kepler
It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.
G H Hardy
I would prefer an intelligent hell to a stupid paradise.
Blaise Pascal
A stupid man's report of what a clever man says can never be accurate, because he unconsciously translates what he hears into something he can understand.
Bertrand Russell
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
When we read too fast or too slowly, we understand nothing.
Blaise Pascal
... That little narrative is an example of the mathematician’s art: asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations. There is really nothing else quite like this realm of pure idea; it’s fascinating, it’s fun, and it’s free!
Paul Lockhart
A mathematician, like a painter or a poet, is a maker of poems. If his patterns are more permanent than theirs, it is because they are made with ideas.
G H Hardy
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than their, it is because they are made with ideas.
G H Hardy
Art forms that appeal to [leftists] tend to focus on ... defeat and despair ... as if there were no hope of accomplishing anything through rational calculation.
Theodore J. Kaczynski
Real mathematics must be justified as art if it can be justified at all.
G H Hardy
Art is the imposing of a pattern on experience, and our aesthetic enjoyment is recognition of the pattern.
Alfred North Whitehead
When the qualities that now confer leadership have become universal, there will no longer be leaders and followers, and democracy will have been realized at last.
Bertrand Russell
Souls never die, but always on quitting one abode pass to another. All things change, nothing perishes. The soul passes hither and thither, occupying now this body, now that . . . As a wax is stamped with certain figures, then melted, then stamped anew with others, yet it is always the same wax. So, the Soul being always the same, yet wears at different times different forms.
Pythagoras
It is true that the modern Christian is less robust, but that is not thanks to Christianity; it is thanks to the generations of freethinkers, who from the Renaissance to the present day, have made Christians ashamed of many of their traditional beliefs. It is amusing to hear the modern Christian telling you how mild and rationalistic Christianity really is and ignoring the fact that all its mildness and rationalism is due to the teaching of men who in their own day were persecuted by all orthodox Christians.
Bertrand Russell
If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is an intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense. If, however, the existence of such a teapot were affirmed in ancient books, taught as the sacred truth every Sunday, and instilled into the minds of children at school, hesitation to believe in its existence would become a mark of eccentricity and entitle the doubter to the attentions of the psychiatrist in an enlightened age or of the Inquisitor in an earlier time.
Bertrand Russell
If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful. Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary.
Paul Lockhart
Order and reason, beauty and benevolence, are characteristics and conceptions which we find solely associated with the mind of man.
Karl Pearson
Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.
Paul Lockhart
There is a certain standard of grace and beauty which consists in a certain relation between our nature... and the thing which pleases us.
Blaise Pascal
The creative personality is always one that looks on the world as fit for change and on himself as an instrument for change. Otherwise, what are you creating for? If the world is perfectly all right the way it is, you have no place in it. The creative personality thinks of the world as a canvas for change and of himself as a divine agent of change.
Jacob Bronowski
The conservatives are fools: They whine about the decay of traditional values, yet they enthusiastically support technological progress and economic growth. Apparently it never occurs to them that you can't make rapid, drastic changes in the technology and the economy of a society without causing rapid changes in all other aspects of the society as well, and that such rapid changes inevitably break down traditional values.
Theodore J. Kaczynski
Give me but a firm spot on which to stand, and I shall move the earth.
Archimedes
The psychology of adultery has been falsified by conventional morals, which assume, in monogamous countries, that attraction to one person cannot coexist with affection for another. Everybody knows that this is untrue.
Bertrand Russell
In most gardens they make the beds too soft – so that the flowers are always asleep.
Lewis Carroll
The problem of political theory is how to combine that degree of individual initiative which is necessary for progress, with the degree of social cohesion which is necessary for survival.
Bertrand Russell
To be sure I was!' Humpty Dumpty said gaily, as she turned it round forhim. 'I thought it looked a little queer. As I was saying, that SEEMSto be done right--though I haven't time to look it over thoroughly justnow--and that shows that there are three hundred and sixty-four dayswhen you might get un-birthday presents--'Certainly,' said Alice.And only ONE for birthday presents, you know. There's glory for you!'I don't know what you mean by "glory,"' Alice said.Humpty Dumpty smiled contemptuously. 'Of course you don't--till I tellyou. I meant "there's a nice knock-down argument for you!"'But "glory" doesn't mean "a nice knock-down argument,"' Alice objected.When _I_ use a word,' Humpty Dumpty said in rather a scornful tone, 'itmeans just what I choose it to mean--neither more nor less.'The question is,' said Alice, 'whether you CAN make words mean so manydifferent things.'The question is,' said Humpty Dumpty, 'which is to be master--that'sall.
Lewis Carroll
No Ghost of any common sense begins a conversation
Lewis Carroll
There is nothing we can now call our own, for what we call so is the effect of art; crimes are made by decrees of the senate, or by the votes of the people; and as here-to-fore we are burdened by vices, so now we are oppressed by laws.
Blaise Pascal
All of humanity's problems stem from man's inability to sit quietly in a room alone.
Blaise Pascal
With mathematics we stand precisely at that intersection of bondage and freedom that is the essence of the human itself.
Hermann Weyl
A surrogate activity is an activity that is directed toward an artificial goal that the individual pursues for the sake of the “fulfillment” that he gets from pursuing the goal, not because he needs to attain the goal itself. For instance, there is no practical motive for building enormous muscles, hitting a little ball into a hole or acquiring a complete series of postage stamps. Yet many people in our society devote themselves with passion to bodybuilding, golf or stamp-collecting. Some people are more “other-directed” than others, and therefore will more readily attach importance to a surrogate activity simply because the people around them treat it as important or because society tells them it is important. That is why some people get very serious about essentially trivial activities such as sports, or bridge, or chess, or arcane scholarly pursuits, whereas others who are more clear-sighted never see these things as anything but the surrogate activities that they are, and consequently never attach enough importance to them to satisfy their need for the power process in that way.
Theodore J. Kaczynski
73. ...There is no law that says we have to go to work every day and follow our employer’s orders. Legally there is nothing to prevent us from going to live in the wild like primitive people or from going into business for ourselves. But in practice there is very little wild country left, and there is room in the economy for only a limited number of small business owners. Hence most of us can survive only as someone else’s employee.
Theodore J. Kaczynski
The degree of personal freedom that exists in a society is determined more by the economic and technological structure of the society than by its laws or its form of government. Most of the Indian nations of New England were monarchies, and many of the cities of the Italian Renaissance were controlled by dictators. But in reading about these societies one gets the impression that they allowed far more personal freedom than our society does.In part this was because they lacked efficient mechanisms for enforcing the ruler’s will: There were no modern, well-organised police forces, no rapid long-distance communications, no surveillance cameras, no dossiers of information about the lives of average citizens. Hence it was relatively easy to evade control.
Theodore J. Kaczynski
But, said Alice, if the world has absolutely no sense, who's stopping us from inventing one?
Lewis Carroll
United States: the country where liberty is a statue.
Nicanor Parra
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 habits; thought is anarchic and lawless, indifferent to authority, careless of the well-tried wisdom of the ages. 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