Quotes by Mathematicians - Page 4

Nihil est sine ratione.[There is nothing without a reason.]
Gottfried Wilhelm Leibniz
Ah take the cash and let the credit go.
Omar Khayyám
Contradiction is not a sign of falsity nor the lack of contradiction a sign of truth.
Blaise Pascal
I believe that ideas such as absolute certitude, absolute exactness, final truth, etc. are figments of the imagination which should not be admissible in any field of science... This loosening of thinking seems to me to be the greatest blessing which modern science has given to us. For the belief in a single truth and in being the possessor thereof is the root cause of all evil in the world.
Max Born
A likely story indeed!" said the Pigeon, in a tone of the deepest contempt. "I've seen a good many little girls in my time, but never one with such a neck as that! No, no! You're a serpent; and there's no use denying it. I suppose you'll be telling me next that you never tasted an egg!""I have tasted eggs, certainly," said Alice, who was a very truthful child; "but little girls eat eggs quite as much as serpents do, you know.""I don't believe it," said the Pigeon; "but if they do, then they're a kind of serpent: that's all I can say.
Lewis Carroll
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
[Benjamin Peirce's] lectures were not easy to follow. They were never carefully prepared. The work with which he rapidly covered the blackboard was very illegible, marred with frequent erasures, and not infrequent mistakes (he worked too fast for accuracy). He was always ready to digress from the straight path and explore some sidetrack that had suddenly attracted his attention, but which was likely to have led nowhere when the college bell announced the close of the hour and we filed out, leaving him abstractedly staring at his work, still with chalk and eraser in his hands, entirely oblivious of his departing class.
William Elwood Byerly
With me, everything turns into mathematics.
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
The last advance of reason is to recognize that it is surpassed by innumerable things it is feeble if it cannot realize that.
Blaise Pascal
Rightness of limitation is essential for growth of reality.Unlimited possibility and abstract creativity can procure nothing. The limitation, and the basis arising from what is already actual, are both of them necessary and interconnected.
Alfred North Whitehead
Oh, come with old Khayyàm, and leave the Wise To talk; one thing is certain, that Life flies; One thing is certain, and the Rest is Lies; The Flower that once has blown forever dies.
Omar Khayyám
If I have ever made any valuable discoveries it has been owing more to patient attention than to any other talent.
Isaac Newton
Most people would die sooner than think in fact they do.
Bertrand Russell
A time will come when men will stretch out their eyes. They should see planets like our Earth.
Christopher Wren
Cruel, Clever Cat.Sally, having swallowed cheese,Directs down holes the scented breeze,Enticing thus with baited breathNice mice to an untimely death.
Geoffrey Taylor
Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.
Andrew John Wiles
Desire urges me on, while fear bridals me.
Giordano Bruno
Enjoy your own life without comparing it with that of another.
Marquis de Condorcet
Ever since Plato most philosophers have considered it part of their business to produce ‘proofs’ of immortality and the existence of God. They have found fault with the proofs of their predecessors — Saint Thomas rejected Saint Anselm's proofs, and Kant rejected Descartes' — but they have supplied new ones of their own. In order to make their proofs seem valid, they have had to falsify logic, to make mathematics mystical, and to pretend that deepseated prejudices were heaven-sent intuitions.
Bertrand Russell
Some of the finest moral intuitions come to quite humble people. The visiting of lofty ideas doesn't depend on formal schooling. Think of those Galilean peasants.
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
As a philosopher, if I were speaking to a purely philosophic audience I should say that I ought to describe myself as an Agnostic, because I do not think that there is a conclusive argument by which one can prove that there is not a God. On the other hand, if I am to convey the right impression to the ordinary man in the street I think that I ought to say that I am an Atheist, because, when I say that I cannot prove that there is not a God, I ought to add equally that I cannot prove that there are not the Homeric gods.
Bertrand Russell
Happiness, as is evident, depends partly upon external circumstances and partly upon oneself.
Bertrand Russell
[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher in popular estimation.
G H Hardy
Progress is the exploration of our own error. Evolution is a consolidation of what have always begun as errors. And errors are of two kinds: errors that turn out to be true and errors that turn out to be false (which are most of them). But they both have the same character of being an imaginative speculation. I say all this because I want very much to talk about the human side of discovery and progress, and it seems to me terribly important to say this in an age in which most non-scientists are feeling a kind of loss of nerve.
Jacob Bronowski
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
I think the essence of wisdom is emancipation, as far as possible, from the tyranny of the here and now.
Bertrand Russell
This principle of nature being very remote from the conceptions of Philosophers, I forbore to describe it in that book, least I should be accounted an extravagant freak and so prejudice my Readers against all those things which were the main designe of the book.
Isaac Newton
Science is what you know, philosophy is what you don't know
Bertrand Russell
The charm of fame is so great, that we like every object to which it is attached, even death.
Blaise Pascal
The orbit of every planet is an ellipse with the sun at one of the two foci.
Johannes Kepler
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
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
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
To know that we know what we know, and to know that we do not know what we do not know, that is true knowledge.
Nicolaus Copernicus
All mankind's unhappiness derives from one thing: his inability to know how to remain in repose in one room.
Blaise Pascal
Perchance you who pronounce my sentence are in greater fear than I who receive it.
Giordano Bruno
For the inexperienced, however, it is very difficult to distinguish passionate love from mere sex hunger; especially is this the case with well-brought-up girls, who have been taught that they could not possibly like to kiss a man unless they loved him.
Bertrand Russell
A child develops best when, like a young plant, he is left undisturbed in the same soil. Too much travel, too much variety of impressions, are not good for the young, and cause them as they grow up to become incapable of enduring fruitful monotony.
Bertrand Russell
All this of Pot and Potter - Tell me then Who is the Potter pray and who the Pot?
Omar Khayyám
The world of being is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life. The world of existence is fleeting, vague, without sharp boundaries, without any clear plan or arrangement, but it contains all thoughts and feelings, all the data of sense, and all physical objects, everything that can do either good or harm, everything that makes any difference to the value of life and the world. According to our temperaments, we shall prefer the contemplation of the one or of the other.
Bertrand Russell
Kind words do not cost much. Yet they accomplish much
Blaise Pascal
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
My tomb shall be in a spot where the north wind may scatter roses over it.
Omar Khayyám
With mathematics we stand precisely at that intersection of bondage and freedom that is the essence of the human itself.
Hermann Weyl
... This is a major theme in mathematics: things are what you want them to be. You have endless choices; there is no reality to get in your way.On the other hand, once you have made your choices then your new creations do what they do, whether you like it or not. This is the amazing thing about making imaginary patterns: they talk back!
Paul Lockhart
Physicists believe that the Gaussian law has been proved in mathematics while mathematicians think that it was experimentally established in physics.
Henri Poincaré
Let it not be said that I have said nothing new. The arrangement of the material is new.
Blaise Pascal
0 thou who didst with pitfall and with gin Beset the road I was to wander in Thou wilt not with predestin'd evil round Enmesh and then impute my fall to sin.
Omar Khayyám
There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else — but persistent.
Raoul Bott
A book of Verses underneath the Bough A Jug of Wine a Loaf of Bread - and Thou Beside me singing in the Wilderness - Oh Wilderness were Paradise enow!
Omar Khayyám
The solution which I am urging is to eradicate the fatal disconnection of subjects which kills the vitality of our modern curriculum. There is only one subject-matter for education, and that is LIfe in all its manifestations. Instead of this single unity, we offer children--Algebra, from which nothing follows; Geometry, from which nothing follows; Science, from which nothing follows; History, from which nothing follows; a Couple of Languages, never mastered; and lastly, most dreary of all, Literature, represented by plays of Shakespeare, with philological notes and short analyses of plot and character to be in substance committed to memory. Can such a list be said to represent Life, as it is known in the midst of living it? The best that can be said of it is, that it is a rapid table of contents which a deity might run over in his mind while he was thinking of creating a world, and has not yet determined how to put it together
Alfred North Whitehead
The mathematical giant [Gauss], who from his lofty heights embraces in one view the stars and the abysses …
Farkas Bolyai
Love knows no limit to its endurance, no end to its trust, no fading of its hope; it can outlast anything. Love still stands when all else has fallen.
Blaise Pascal
One must care about a world one will not see.
Bertrand Russell
Running overtime is the one unforgivable error a lecturer can make. After fifty minutes (one microcentury as von Neumann used to say) everybody's attention will turn elsewhere.
Gian-Carlo Rota
It's frightening to think that you might not know something, but more frightening to think that, by and large, the world is run by people who have faith that they know exactly what is going on.
Amos Tversky
Oh threats of Hell and Hopes of Par
Omar Khayyám
He lived far from the gods, but in his mind he was at home with them.
Pythagoras