Quotes by Mathematicians - Page 11

Eloquence is painted thought, and thus those who, after having painted it, add somewhat more, make a picture, not a portrait.
Blaise Pascal
Preservations are working to save neon signs for future generations, either on-site or in museums. After all, what would America be without a few giant doughnuts around.
Clifford A. Pickover
In America everybody is of the opinion that he has no social superiors, since all men are equal, but he does not admit that he has no social inferiors, for, from the time of Jefferson onward, the doctrine that all men are equal applies only upwards, not downwards.
Bertrand Russell
Freedom of opinion can only exist when the government thinks itself secure.
Bertrand Russell
The objection to propaganda is not only its appeal to unreason, but still more the unfair advantage which it gives to the rich and powerful.
Bertrand Russell
A Vulgar Mechanick can practice what he has been taught or seen done, but if he is in an error he knows not how to find it out and correct it, and if you put him out of his road he is at a stand. Whereas he that is able to reason nimbly and judiciously about figure, force, and motion, is never at rest till he gets over every rub.(from a letter dated 25 May, 1694)
Isaac Newton
The methods of increasing the degree of truth in our beliefs are well known; they consist in hearing all sides, trying to ascertain all the relevant facts, controlling our own bias by discussion with people who have the opposite bias, and cultivating a readiness to discard any hypothesis which has proved inadequate.
Bertrand Russell
But we have reason to think that the annihilation of work is no less a physical impossibility than its creation, that is, than perpetual motion.
George Gabriel Stokes
Nihil est sine ratione.[There is nothing without a reason.]
Gottfried Wilhelm Leibniz
As for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra.
Augustin-Louis Cauchy
Further, the same Arguments which explode the Notion of Luck, may, on the other side, be useful in some Cases to establish a due comparison between Chance and Design: We may imagine Chance and Design to be, as it were, in Competition with each other, for the production of some sorts of Events, and many calculate what Probability there is, that those Events should be rather be owing to the one than to the other.
Abraham de Moivre
The purpose of computation is insight, not numbers.
Richard Hamming
Finally, let them recognise that there are two kinds of people one can call reasonable; those who serve God with all their heart because they know Him, and those who seek Him with all their heart because they do not know Him.
Blaise Pascal
For my part, I prefer the ontological argument, the cosmological argument and the rest of the old stock-in-trade, to the sentimental illogicality that has sprung from Rousseau.
Bertrand Russell
The fact is you cannot be intelligent merely by choosing your opinions. The intelligent man is not the man who holds such-and-such views but the man who has sound reasons for what he believes and yet does not believe it dogmatically. And opinions held for sound reasons have less emotional unity than the opinions of dogmatists because reason is non-party, favouring now one side and now another. That is what people find so unpleasant about it.
Bertrand Russell
The difficulty is that, so long as unreason prevails, a solution of our troubles can only be reached by chance; for while reason, being impersonal, makes universal co-operation possible, unreason, since it represents private passions, makes strife inevitable. It is for this reason that rationality, in the sense of an appeal to a universal and impersonal standard of truth, is of supreme importance to the well-being of the human species.
Bertrand Russell
Mathematics is not a deductive science - that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.
Paul R. Halmos
So how does one go about proving something like this? It's not like being a lawyer, where the goal is to persuade other people; nor is it like a scientist testing a theory. This is a unique art form within the world of rational science. We are trying to craft a "poem of reason" that explains fully and clearly and satisfies the pickiest demands of logic, while at the same time giving us goosebumps.
Paul Lockhart
It's been said before: 'The sleep of reason produces monsters.
Apostolos Doxiadis
People are generally better persuaded by the reasons which they have themselves discovered than by those which have come into the mind of others.
Blaise Pascal
One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.
George Pólya
The Qur’an sought to reform, not to destroy and start from scratch, tosalvage what was useful and then to modify and build on it. The task wasto get the Arabs to think about religion in a novel way, to inculcate in them a new conceptual frame of reference, to transfer them from one worldview to another, and higher, one. This process of transformation took them from traditionalism to individualism, from impulsiveness to discipline, from supernaturalism to science, from intuition to conscious reasoning and, in the end, ideally, harmonized the whole.
Jeffrey Lang
Over a billion people believe in Allah without truly knowing what Allah supposedly stands for or what he really demands of them. And the minority that do understand continue to be Moslems because they have redefined their morality and ethics to fit within the teachings of Islam, which are floridly lacking in morality. They therefore redefine what is good and evil in order to fit their lives into what is preached by Islam, instead of examining Islam to see if it fits within the good life. Backwards thinking, imposed by a backward religion.
Bertrand Russell
Throughout the Middle Ages, Jews had no part in the culture of Christian countries, and were too severely persecuted to be able to make contributions to civilization, beyond supplying capital for the building of cathedrals and such enterprises. It was only among the Mohammedans, at that period, that Jews were treated humanely, and were able to pursue philosophy and enlightened speculation. Throughout the Middle Ages, the Mohammedans were more civilized and more humane than the Christians. Christians persecuted Jews, especially at times of religious excitement; the Crusades were associated with appalling pogroms. In Mohammedan countries, on the contrary, Jews at most times were not in any way ill treated. Especially in Moorish Spain, they contributed to learning; Maimonides (1135–1204), who was born at Cordova, is regarded by some as the source of much of Spinoza’sphilosophy.Mohammedan civilization in its great days was admirable in the arts and in many technical ways, but it showed no capacity for independent speculation in theoretical matters. Its importance, which must not be under-rated, is as a transmitter. Between ancient and modern European civilization, the dark ages intervened. The Mohammedans and the Byzantines, while lacking the intellectual energy required for innovation, preserved the apparatus of civilization—education, books, and learned leisure. Both stimulated the West when it emerged from barbarism—the Mohammedans chiefly in the thirteenth century, the Byzantines chiefly in the fifteenth.
Bertand Russell
We often hear that mathematics consists mainly of 'proving theorems.' Is a writer's job mainly that of 'writing sentences?
Gian-Carlo Rota
If our logic is to find the common world intelligible, it must not be hostile, but must be inspired by a genuine acceptance such as is not usually to be found among metaphysicians.
Bertrand Russell
Curiosity is only vanity. We usually only want to know something so that we can talk about it.
Blaise Pascal
The first rule of style is to have something to say. The second rule of style is to control yourself when, by chance, you have two things to say; say first one, then the other, not both at the same time.
George Pólya
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
Without these supernova explosions, there are no mist-covered swamps, computer chips, trilobites, Mozart or the tears of a little girl. Without exploding stars, perhaps there could be a heaven, but there is certainly no Earth.
Clifford A. Pickover
Oh threats of Hell and Hopes of Par
Omar Khayyám
If there is anything that can bind the mind of man to this dreary exile of our earthly home and can reconcile us with our fate so that one can enjoy living,—then it is verily the enjoyment of the mathematical sciences and astronomy.
Johannes Kepler
Kind words do not cost much. Yet they accomplish much
Blaise Pascal
Most people would rather die than think and many of them do!
Bertrand Russell
As children', wrote Alice Raikes (Mrs. Wilson Fox) in The Times, January 22, 1932, 'we lived in Onslow Square and used to play in the garden behind the houses. Charles Dodgson used to stay with an old uncle there, and walk up and down, his hands behind him, on the strip of lawn. One day, hearing my name, he called me to him saying, "So you are another Alice. I'm very found of Alices. Would you like to come and see something which is rather puzzling?" We followed him into his house which opened, as ours did, upon the garden, into a room full of furniture with a tall mirror standing across one corner.' "Now", he said giving me an orange, "first tell me which hand you have got that in." "The right" I said. "Now", he said, "go and stand before that glass, and tell me which hand the little girl you see there has got it in." After some perplexed contemplation, I said, "The left hand." "Exactly," he said, "and how do you explain that?" I couldn't explain it, but seeing that some solution was expected, I ventured, "If I was on the other side of the glass, wouldn't the orange still be in my right hand?" I can remember his laugh. "Well done, little Alice," he said. "The best answer I've heard yet." "I heard no more then, but in after years was told that he said that had given him his first idea for Through the Looking-Glass, a copy of which, together with each of his other books, he regularly sent me.
Lewis Carroll
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
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
In all affairs it's a healthy thing now and then to hang a question mark on the things you have long taken for granted.
Bertrand Russell
Surely your gladness need not be the less for the thought that you will one day see a brighter dawn than this.
Lewis Carroll
Gratitude is a species of love, excited in us by some action of the person for whom we have it, and by which we believe that he has done some good to us, or at least that he has had the intention of doing so. Passions, III, 193. XI, 473-474. Trans. John Morris
René Descartes
Might one not say that in the chance combination of nature's production, since only those endowed with certain relations of suitability could survive, it is no cause for wonder that this suitability is found in all species that exist today? Chance, one might say, produced an innumerable multitude of individuals; a small number turned out to be constructed in such fashion that the parts of the animal could satisfy its needs; in another, infinitely greater number, there was neither suitability nor order: all of the later have perished; animals without a mouth could not live, others lacking organs for reproduction could not perpetuate themselves: the only ones to have remained are those in which were found order and suitability; and these species, which we see today, are only the smallest part of what blind fate produced.
Pierre-Louis Moreau De Maupertuis
God is not an alternative to science as an explanation, he is not to be understood merely as a God of the gaps, he is the ground of all explanation: it is his existence which gives rise to the very possibility of explanation, scientific or otherwise. It is important to stress this because influential authors such as Richard Dawkins will insist on conceiving of God as an explanatory alternative to science – an idea that is nowhere to be found in theological reflection of any depth. Dawkins is therefore tilting at a windmill - dismissing a concept of God that no serious thinker believes in anyway. Such activity is not necessarily to be regarded as a mark of intellectual sophistication.
John C. Lennox
If it has been revealed to man that the Almighty made him out of the dust of the earth, and breathed into his nostrils the breath of life, it is in vain to tell a Christian that man was originally a speck of albumen, and passed through the stages of monads and monkeys, before he attained his present intellectual preeminence. If it be a received truth that the Creator has repeatedly interposed in the government of the universe and displayed his immediate agency in miraculous interpositions, it is an insult to any reader to tell him that the being slumbers on his throne and rules under a "primal arrangement in his counsels," and "by a code of laws of unbending operation.
David Brewster
It is a more rational belief that man may become a brute than that a brute may become a man; and it is an easier faith that plants and animals may dwindle down into an elemental atom, than that this atom should embrace in its organization, and evolve, all the noble forms of vegetable, animal, and intellectual life.
David Brewster
Liberation from the tyranny of the body contributes to greatness, but just as much to greatness in sin as to greatness in virtue.
Bertrand Russell
The whole conception of 'sin' is one which I find very puzzling, doubtless owing to my sinful nature.
Bertrand Russell
All that alcohol does for them is to liberate the sense of sin, which reason suppresses in saner moments.
Bertrand Russell
[It] is hardly possible to maintain seriously that the evil done by science is not altogether outweighed by the good. For example, if ten million lives were lost in every war, the net effect of science would still have been to increase the average length of life.
G H Hardy
... for systems belonging to the singular part of the stability boundary a small change of the parameters is more likely to send the system into the unstable region than into the stable region. This is a manifestation of a general principle stating that all good things (e.g. stability) are more fragile than bad things. It seems that in good situations a number of requirements must hold simultaneously, while to call a situation bad even one failure suffices.
Vladimir I. Arnold
The world is full of injustice, and those who profit by injustice are in a position to administer rewards and punishments. The rewards go to those who invent ingenious justifications for inequality, the punishments to those who try to remedy it.
Bertrand Russell
It is possible that mankind is on the threshold of a golden age; but, if so,it will be necessary first to slay the dragon that gaurds the door,and this dragon is religion
Bertrand Russell
No one knows loneliness like an atheist. When an average person feels isolated, he can call through the depths of his soul to One who knows him and sense an answer. An atheist cannot allow himself that luxury, for he has to crush the urge and remind himselfof its absurdity.
Jeffrey Lang
...The existence or non-existence of an undefined 'god' are quite poin
Herman Bondi
I am not religious in any sense; in fact, I consider myself an atheist.
Subrahmanijan Chandrasekhar
Religion divides us, while it is our human characteristics that bind us to each other.
Hermann Bondi
I agree with Pierre Bayle and with Unamuno that when cold reason contemplates the world it finds not only an absence of God, but good reasons for supposing that there is no God at all. From this perspective, from what Unamuno called the 'tragic sense of life', from this despair, faith comes to the rescue, not only as something nonrational but in a sense irrational. For Unamuno the great symbol of a person of faith was his Spanish hero Don Quixote. Faith is indeed quixotic. It is absurd. Let us admit it. Let us concede to everything! To a rational mind the world looks like a world without God. It looks like a world with no hope for another life. To think otherwise, to believe in spite of appearances, is surely a kind of madness. The atheist sees clearly that windmills are in fact only windmills, that Dulcinea is just a poor country bumpkin with a homely face and an unpleasant smell. The atheist is a Sarah, justifiably laughing in her old age at Abraham's belief that God will give them a son.What can be said in reply? How can a fideist admit that faith is a kind of madness, a dream fed by passionate desire, and yet maintain that one is not mad to make the leap?
Martin Gardner
Nothing can penetrate the loneliness of the human heart except the highest intensity of the sort of love the religious teachers have preached.
Bertrand Russell
A strange mystery it is that Nature, omnipotent but blind, in the revolutions of her secular hurryings through the abysses of space, has brought forth at last a child subject still to her power but gifted with sight, with knowledge of good and evil, with the capacity of judging all the works of his unthinking mother.
Bertrand Russell
Naturalism is the view that the physical world is a self-contained system that works by blind, unbroken natural laws. Naturalism doesn't come right out and say there's nothing beyond nature. Rather, it says that nothing beyond nature could have any conceivable relevance to what happens in nature. Naturalism's answer to theism is not atheism but benign neglect. People are welcome to believe in God, though not a God who makes a difference in the natural order.
William A. Dembski
The idea that things must have a beginning is really due to the poverty of our imagination.
Bertrand Russell