Quotes by Mathematicians - Page 20

How much more of the mosque, of prayer and fasting?Better go drunk and begging round the taverns.Khayyam, drink wine, for soon this clay of yoursWill make a cup, bowl, one day a jar.When once you hear the roses are in bloom,Then is the time, my love, to pour the wine;Houris and palaces and Heaven and Hell-These are but fairy-tales, forget them all.
Omar Khayyám
We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow. An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes. The perfection that the human mind has been able to give to astronomy affords but a feeble outline of such an intelligence.
Pierre-Simon Laplace
An attentive reader will always learn more, and more quickly, from good authors than from life.
Hervé Le Tellier
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
Get your knowledge quickly and then use it. If you can use it you will retain it.
Alfred North Whitehead
A student should not be taught more than he can think about.
Alfred North Whitehead
[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on.
Paul Lockhart
A Puritan twist in our nature makes us think that anything good for us must be twice as good if it's hard to swallow. Learning Greek and Latin used to play the role of character builder, since they were considered to be as exhausting and unrewarding as digging a trench in the morning and filling it up in the afternoon. It was what made a man, or a woman -- or more likely a robot -- of you. Now math serves that purpose in many schools: your task is to try to follow rules that make sense, perhaps, to some higher beings; and in the end to accept your failure with humbled pride. As you limp off with your aching mind and bruised soul, you know that nothing in later life will ever be as difficult.What a perverse fate for one of our kind's greatest triumphs! Think how absurd it would be were music treated this way (for math and music are both excursions into sensuous structure): suffer through playing your scales, and when you're an adult you'll never have to listen to music again. And this is mathematics we're talking about, the language in which, Galileo said, the Book of the World is written. This is mathematics, which reaches down into our deepest intuitions and outward toward the nature of the universe -- mathematics, which explains the atoms as well as the stars in their courses, and lets us see into the ways that rivers and arteries branch. For mathematics itself is the study of connections: how things ideally must and, in fact, do sort together -- beyond, around, and within us. It doesn't just help us to balance our checkbooks; it leads us to see the balances hidden in the tumble of events, and the shapes of those quiet symmetries behind the random clatter of things. At the same time, we come to savor it, like music, wholly for itself. Applied or pure, mathematics gives whoever enjoys it a matchless self-confidence, along with a sense of partaking in truths that follow neither from persuasion nor faith but stand foursquare on their own. This is why it appeals to what we will come back to again and again: our **architectural instinct** -- as deep in us as any of our urges.
Ellen Kaplan
The foundation of reverence is this perception, that the present holds within itself the complete sum of existence, backwards and forwards, that whole amplitude of time, which is eternity.
Alfred North Whitehead
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
A good problem is something you don't know how to solve. That's what makes it a good puzzle and a good opportunity.
Paul Lockhart
In the conditions of modern life the rule is absolute, the race which does not value trained intelligence is doomed.
Alfred North Whitehead
Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.
Paul Lockhart
No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a "mixed number " while 5/2 is an "improper fraction." They're EQUAL for crying out loud. They are the exact same numbers and have the exact same properties. Who uses such words outside of fourth grade?
Paul Lockhart
Every maker of video games knows something that the makers of curriculum don't seem to understand. You'll never see a video game being advertised as being easy. Kids who do not like school will tell you it's not because it's too hard. It's because it's--boring
Seymour Papert
We must be careful not to discourage our twelve-year-olds by making them waste the best years of their lives preparing for examinations.
Freeman Dyson
It is important that students bring a certain ragamuffin, barefoot irreverence to their studies; they are not here to worship what is known, but to question it.
Jacob Bronowski
Vicarious learning from the experiences of others saves making errors yourself, but I regard the study of successes as being basically more important than the study of failures. There are so many ways of being wrong and so few of being right, studying successes is more efficient.
Richard Hamming
...as far as we are capable of knowledge we sin in neglecting to acquire it...
Gottfried Wilhelm Leibniz
Change is scientific, ‘progress’ is ethical. Change is indubitable whereas progress is a matter of controversy.
Bertrand Russell
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.
Charles Sanders Peirce
Neither love without knowledge nor knowledge without love can produce a good life.
Bertrand Russell
Thus, by science I mean, first of all, a worldview giving primacy to reason and observation and a methodology aimed at acquiring accurate knowledge of the natural and social world. This methodology is characterized, above all else, by the critical spirit: namely, the commitment to the incessant testing of assertions through observations and/or experiments — the more stringent the tests, the better — and to revising or discarding those theories that fail the test. One corollary of the critical spirit is fallibilism: namely, the understanding that all our empirical knowledge is tentative, incomplete and open to revision in the light of new evidence or cogent new arguments (though, of course, the most well-established aspects of scientific knowledge are unlikely to be discarded entirely).. . . I stress that my use of the term 'science' is not limited to the natural sciences, but includes investigations aimed at acquiring accurate knowledge of factual matters relating to any aspect of the world by using rational empirical methods analogous to those employed in the natural sciences. (Please note the limitation to questions of fact. I intentionally exclude from my purview questions of ethics, aesthetics, ultimate purpose, and so forth.) Thus, 'science' (as I use the term) is routinely practiced not only by physicists, chemists and biologists, but also by historians, detectives, plumbers and indeed all human beings in (some aspects of) our daily lives. (Of course, the fact that we all practice science from time to time does not mean that we all practice it equally well, or that we practice it equally well in all areas of our lives.)
Alan Sokal
I believe that we do not know anything for certain, but everything probably.
Christiaan Huygens
Since we cannot know all there is to be known about anything, we ought to know a little about everything.
Blaise Pascal
What is wanted is not the will to believe, but the will to find out, which is the exact opposite.
Bertrand Russell
I do not pretend to be able to prove that there is no God. I equally cannot prove that Satan is a fiction. The Christian god may exist; so may the gods of Olympus, or of ancient Egypt, or of Babylon. But no one of these hypotheses is more probable than any other: they lie outside the region of even probable knowledge, and therefore there is no reason to consider any of them.
Bertrand Russell
There cannot be a language more universal and more simple, more free from errors and obscurities...more worthy to express the invariable relations of all natural things [than mathematics]. [It interprets] all phenomena by the same language, as if to attest the unity and simplicity of the plan of the universe, and to make still more evident that unchangeable order which presides over all natural causes
Joseph Fourier
From the house of unbeliefto true religionis a single breath;From the world of doubtto certaintyis a single breath;Enjoy this precious single breath,for the harvestof our whole livesis that same one breath.
Omar Khayyám
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
There are two objectionable types of believers: those who believe the incredible, and those who believe that 'belief' must be discarded and replaced by 'the scientific method'.
Max Born
No religion except ours has taught that man is born in sin none of the philosophical sects has admitted it none therefore has spoken the truth
Blaise Pascal
Gravity explains the motions of the planets, but it cannot explain who sets the planets in motion.
Isaac Newton
There are three sources of belief: reason, custom, inspiration.
Blaise Pascal
what is the use of a book,' thought Alice, 'without pictures or conversations?'"- Lewis Carroll, Alice in Wonderland, Ch. 1
Lewis Carroll
The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there" all along I just couldn't see it. And now I can! This is really what keeps me in the math game-- the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods.
Paul Lockhart
And ever, as the story drainedThe wells of fancy dry,And faintly strove that weary oneTo put the subject by,"The rest next time--" "It is next time!"The Happy voice cry.Thus grew the tale of Wonderland
Lewis Carroll
Then you should say what you mean," the March Hare went on. "I do," Alice hastily replied; "at least--at least I mean what I say--that's the same thing, you know." "Not the same thing a bit!" said the Hatter. "You might just as well say that "I see what I eat" is the same thing as "I eat what I see"!
Lewis Carroll
To make a man a saint, it must indeed be by grace; and whoever doubts this does not know what a saint is, or a man.
Blaise Pascal
Perchance you who pronounce my sentence are in greater fear than I who receive it.
Giordano Bruno
If we submit everything to reason our religion will be left with nothing mysterious or supernatural. If we offend the principles of reason our religion will be absurd and ridiculous . . . There are two equally dangerous extremes: to exclude reason, to admit nothing but reason.
Blaise Pascal
Every particle of dust on a patch of earthWas a sun-cheek or brow of the morning star;Shake the dust off your sleeve carefully--That too was a delicate, fair face.
Omar Khayyám
Here with a Loaf of Bread beneath the Bough,A Flask of Wine, a Book of Verse - and ThouBeside me singing in the Wilderness -And Wilderness is Paradise enow.
Omar Khayyám
One! two! and through and throughThe vorpal blade went snickersnack!He left it dead, and with its headHe went galumphing back.
Lewis Carroll
A book of verses underneath the boughA flask of wine, a loaf of bread and thouBeside me singing in the wildernessAnd wilderness is paradise now.
Omar Khayyám
Wake! For the Sun, who scatter'd into flightThe Stars before him from the Field of Night,Drives Night along with them from Heav'n,and strikesThe Sultan's Turret with a Shaft of Light
Omar Khayyám
I sent my Soul through the Invisible, Some letter of that After-life to spell: And by and by my Soul return'd to me, And answer'd: 'I Myself am Heav'n and Hell
Omar Khayyám
Twas brillig, and the slithy toves Did gyre and gimble in the wabe;All mimsy were the borogoves,And the mome raths outgrabe."Beware the Jabberwock, my son The jaws that bite, the claws that catch!Beware the Jubjub bird, and shun The frumious Bandersnatch!"He took his vorpal sword in hand; Long time the manxome foe he sought—So rested he by the Tumtum tree, And stood awhile in thought.And, as in uffish thought he stood, The Jabberwock, with eyes of flame,Came whiffling through the tulgey wood, And burbled as it came!One, two! One, two! And through and through The vorpal blade went snicker-snack!He left it dead, and with its head He went galumphing back."And hast thou slain the Jabberwock? Come to my arms, my beamish boy!O frabjous day! Callooh! Callay!" He chortled in his joy.'Twas brillig, and the slithy toves Did gyre and gimble in the wabe;All mimsy were the borogoves,And the mome raths outgrabe.
Lewis Carroll
The last thing one discovers in composing a work is what to put first.
Blaise Pascal
The Moving Finger writes; and, having writ,Moves on: nor all thy Piety nor WitShall lure it back to cancel half a Line,Nor all thy Tears wash out a Word of it.
Omar Khayyám
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
Put a man on the brink of the abyss and - in the unlikely event that she doesn't fall into it - he will become a mystic or a madman... Which is probably the same thing!
Apostolos Doxiadis
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
If there be light, then there is darkness; if cold, heat; if height, depth; if solid, fluid; if hard, soft; if rough, smooth; if calm, tempest; if prosperity, adversity; if life, death.
Pythagoras
If, years later, I do use the slit detector to observe which way the electron went, it will mean that many years earlier the electron must have passed through one slit or the other. But if I don't use the "slit detector," then the electron must have passed through both slits. This is, of course, extremely weird. My actions at the beginning of the twenty-first century can change what happened thousands of years ago when the electron began its journey. It seems that just as there are multiple futures, there are also multiple pasts, and my acts of observation in the present can decide what happened in the past. As much as it challenges any hope of ever really knowing the future, quantum physics asks whether I can ever really know the past. It seems that the past is also in a superposition of possibilities that crystallize only once they are observed.
Marcus du Sautoy
The Victorian Age, for all its humbug, was a period of rapid progress, because men were dominated by hope rather than fear. If we are again to have progress, we must again be dominated by hope.
Bertrand Russell
...Usually i’d sit back and just enjoy the view for what it was because it’s not often you come across something so ridiculously out of place, a girl like you, on the subway, it’s like spotting a unicorn at the zoo.I reasoned how to pull this off, to get you, to say hi, to ask your name, what your voice sounded like, if you had a cute smile because i like cute smiles. In ten minutes I had a thousand thoughts of you and you had no clue...
Stephan K. Garcia
Yo no nací dichoso. De niño, mi himno favorito era: «Cansado del mundo y con el peso de mis pecados». A los cinco años yo pensaba que si había de vivir setenta no había pasado aún más que la catorceava parte de mi vida vital, y me parecía casi insoportable la enorme cantidad de aburrimiento que me aguardaba. En la adolescencia la vida me era odiosa, y estaba continuamente al borde del suicidio, del cual me libré gracias al deseo de saber más matemáticas. Hoy, por el contrario, gusto de la vida, y casi estoy por decir que cada año que pasa la encuentro más gustosa. Esto es debido, en parte, a haber descubierto cuáles eran las cosas que deseaba más y haber adquirido gradualmente muchas de ellas. En parte es debido también a haberme desprendido, felizmente, de ciertos deseos (la adquisición del conocimiento indudable acerca de algo) como esencialmente inasequibles. Pero en la mayor parte se debe a la preocupación, cada día menor, de mí mismo.
Bertrand Russell
If all our happiness is bound up entirely in our personal circumstances it is difficult not to demand of life more than it has to give.
Bertrand Russell
To like many people spontaneously and without effort is perhaps the greatest of all sources of personal happiness.
Bertrand Russell