I found that snowflakes were masterpieces of design. No one design was every repeated. When a snowflake melted... Just that much beauty was gone, without leaving any record behind.
Bentley, quoted in Snowflake Bentley by Jacqueline Briggs Martin.
786
 
The average dairy farmer gets up at dawn because he has to go to work in the cow yard. I get up at dawn, too. But it is because I want to find some leaf, hung with dew; or spider web which the dew has made into the most delicate ropes of pearls... I take my camera with me, get down on my knees in the wet grass, and photograph these exquisite bits of nature. Because I do this I can show these lovely things to people who never would have seen them without my help. They will get their daily quart of milk, all right. Other farmers will attend to that. But I think I am giving them something which is just as important.
Bentley, quoted in Snowflake Bentley by Jacqueline Briggs Martin.
785
 
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure even though perhaps also to our bafflement, to wide branches of learning.
Eugene Wagner, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.
388
 
Theories and goals of education don't matter a whit if you don't consider your students to be human beings.
Lou Ann Walker, quoted in The Beacon Book of Quotations by Women, edited by Rosalie Maggio.
389
 
We're brainwashed into being Platonists in elementary school, because it's the easiest way to think about numbers. Nobody wants to tell a fourth-grader the metaphysics of the integer 3, so we've got this idea that 3 is this thing. These are not things. Even if you're a Platonist -- that is, even if you believe that numbers are real in some metaphysical sense, the way trees and Calebs are real, as opposed to mathematically real -- the reason you're convinced of it is we never really think about it. Well, if they are, where are they? What do they look like? What is 3? It's like the speculations that little children have, or adolescents who smoke a lot of pot at 3 o'clock in the morning.
David Foster Wallace, from "Approaching Infinity," by Caleb Crain, Boston Sunday Globe, 26 October, 2003.
1811
 
Everything I did in my life that was worthwhile I caught hell for.
Earl Warren, quoted in The Fourth, and By Far the Most Recent, 637 Best Things Anybody Ever Said, by Robert Byrne.
390
 
Few things help an individual more than to place responsibility upon him and to let him know that you trust him.
Booker T. Washington,
391
 
We are sick with fascination for the useful tools of names and numbers, of symbols, signs, conceptions and ideas. Meditation is therefore the art of suspending verbal and symbolic thinking for a time, somewhat as a courteous audience will stop talking when a concert is about to begin.
Alan Watts,
1575
 
[David Auburn's play "The Proof"] depicts the study of mathematics as a painful joy, not as the geek-making obsession of stereotype, but as human labor, both ennobling and humbling, by people who, like musicians or painters (or playwrights), can envision an elusive beauty in the universe and are therefore both enlivened by its pursuit and daunted by the commitment. It does this not by showing them at work but by showing them trying to live or cope when they can't, won't or simply aren't, and in doing so makes the argument that mathematics is a business for the common heart as well as the uncommon brain.
Bruce Weber, from the review "A common heart and uncommon brain," NewYork Times, 5/24/2000
1182
 
Things, objects, mutely cry to us, "Touch us, taste us, feel us, see us, understand us, learn us, make us more than we are through your association, through your tactile and spiritual intimacy." The use then that we make of matter is gauged by our power, our quality or our energy, to wield it, to adopt it, to share it, to urge it on into the fourth dimension.
Max Weber, quoted in The Fourth Dimension and non-Euclidean Geometry in Modern Art by Linda Dalrymple Henderson.
667
 
Math terminology is designed to eliminate extraneous things and focus on fundamental process, but the method of finding results is far different from these fundamental processes. Mathematical writing doesn't permit any indication of the labor behind the result.
D. Weidman, from "Emotional Perils of Math."
392
 
A mathematician who is not also something of a poet will never be a complete mathematician.
Karl Weierstrass,
393
 
Until very recently it was generally believed, that a… continuous function… always has a first derivative whose value can be indefinite or infinite only at some isolated points. Even in the work of Gauss, Cauchy, Dirichlet, mathematicians who were accustomed to criticize everything in their field most severely, there can not be found, as far as I know, any expression of a different opinion.
Weierstrass, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1121
 
We Germans use instead, following Jacobi, the round /partial for partial derivatives.
Weierstrass, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1126
 
In the future, as in the past, the great ideas [of mathematics] must be simplifying ideas, the creator must always be one who clarifies, for himself, and for others, the most complicated issues of formulas and concepts.
Andre Weil, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.
394
 
...Our students of mathematics would profit much more from a study of Euler's Introductio in Analysin Infinitorum, rather than of the available modern textbooks.
Andre Weil, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1096
 
Religion is an insult to human dignity. With or without it you would have good people doing good things and evil people doing evil things. But for good people to do evil things, that takes religion.
Steven Weinberg,
1358
 
The universe is an enormous direct product of representations of symmetry groups.
Steven Weinberg, quoted in Contemporary Abstract Algebra, by J. Gallian.
395
 
With or without religion, you would have good people doing good things and evil people doing evil things. But for good people to do evil things, that takes religion.
Steven Weinberg, quoted in The New York Times, April 20, 1999 US physicist (1933 - )
1551
 
I think that children have a power to imagine that is almost magical when compared to the adult imagination, and this is something irrevocable that a child loses when he or she becomes bound by logic. We adults continue to have our children"s power of imagination only in our dreams... Of course it"s awfully necessary that children not run their entire lives on the basis of such thinking; they do need to learn how to think logically. But the world will soon teach that to them. And in overabundance. I think we should do everything we can to make it possible for children to hang onto the power to imagine in the almost magical sense for as long as possible.
Joseph Weizenbaum, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz.
471
 
I think that children have a power to imagine that is almost magical when compared to the adult imagination, and this is something irrevocable that a child loses when he or she becomes bound by logic. We adults continue to have our children"s power of imagination only in our dreams... Of course it"s awfully necessary that children not run their entire lives on the basis of such thinking; they do need to learn how to think logically. But the world will soon teach that to them. And in overabundance. I think we should do everything we can to make it possible for children to hang onto the power to imagine in the almost magical sense for as long as possible.
Joseph Weizenbaum, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz.
472
 
I think that children have a power to imagine that is almost magical when compared to the adult imagination, and this is something irrevocable that a child loses when he or she becomes bound by logic. We adults continue to have our children's power of imagination only in our dreams... Of course it's awfully necessary that children not run their entire lives on the basis of such thinking; they do need to learn how to think logically. But the world will soon teach that to them. And in overabundance. I think we should do everything we can to make it possible for children to hang onto the power to imagine in the almost magical sense for as long as possible.
Joseph Weizenbaum, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz.
473
 
Storying, encountering the world, and understanding it contextually, by shaping ideas, facts, experience itself into stories is one of the most fundamental means of making meaning: as such, it is an activity that pervades all learning.
Gordon Wells, quoted in Writing in the Teaching and Learning of Mathematics by J. Meier and T. Rishel.
730
 
Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.
H. G. Wells, quoted in Flaws and Fallacies in Statistics, by Campbell.
398
 
History becomes more and more a race between education and catastrophe.
H. G. Wells,
397
 
We live in a society that completely tends to velarize symbolic forms of representation, algebraic representations, equations, codes, we live in a society that is obsessed with presenting information in this way, teaching information in this way, but through this sort of modality; crochet, other plastic forms of play, people can be engaged with the most abstract, high powered, theoretical ideas, the kind of ideas that normally you have to go to University departments to study in higher mathematics... But you can do it through playing with material objects. One of the ways we have come to do this is that one of the things we are trying to do with the Institute for Figuring and projects like this, is that we are trying to have Kindergarten for Grownups.
Margaret Wertheim, from video clip at http://www.empac.rpi.edu/events/2010/spring/wertheim/
1485
 
Teaching is the royal road to learning.
Jassamyn West, quoted in The Beacon Book of Quotations by Women, edited by Rosalie Maggio.
399
 
Fiction reveals truths that reality obscures.
Jessamyn West,
1634
 
God exists because arithmetic is consistent - the Devil exists because we can't prove it!
Hermann Weyl, quoted in Excursions in Calculus, by Robert M. Young
405
 
Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the universal organ for world-understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation.
Hermann Weyl,
401
 
Much has been written on this the question of the geometry of the honeycomb. The bee's strange social habits and geometric talents could not fail to attract the attention and excite the admiration of their human observers and exploiters. "My house," says the bee in the Arabian Nights, "is constructed according to the laws of a most severe architecture; and Euclid himself could learn from studying the geometry of my cells." Darwin ... spoke of the bees' architecture as "the most wonderful of known instincts" and adds: "Beyond this stage of perfection in architecture natural section (which has replace divine guidance!) could not lead; for the comb of the hive-bee, as far as we can see, is absolutely perfect in economizing labor and wax."
Weyl, Symmetry, 1952.
1230
 
The real aim is simplicity: every natural generalization simplifies since it reduces the assumptions that have to be taken into account.
Hermann Weyl, quoted in the American Mathematical Monthly, December, 2008, p. 883.
1267
 
My work always tried to unit the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful.
Hermann Weyl, quoted in Freeman Dyson, "Birds and Frogs," Notices of the AMS, Vol. 56, No. 2, February, 2009, p. 213.
1306
 
My own mathematical works are always quite unsystematic, without mode or connection. Expression and shape are almost more to me than knowledge itself. But I believe that, leaving aside my own peculiar nature, there is in mathematics itself, in contrast to the experimental disciplines, a character which is nearer to that of free creative art.
Hermann Weyl,
1316
 
The question for the ultimate foundations and the ultimate meaning of mathematics remains open; we do not know in which direction it will find its final solution nor even whether a final objective answer can be expected at all. "Mathematizing" may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalization.
Hermann Weyl, quoted in Excursions in Calculus, by Robert M. Young.
404
 
Not only in geometry, but to a still more astonishing degree in physics, has it become more and more evident that as soon as we have succeeded in unraveling fully the natural laws which govern reality, we find them to be expressible by mathematical relations of surprising simplicity and architectonic perfection. It seems to me to be one of the chief objects of mathematical instruction to develop the faculty of perceiving this simplicity and harmony.
Hermann Weyl,
402
 
Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or the achievements of mathematics in the last fifty years.
Hermann Weyl, quoted in Excursions in Calculus, by Robert Young.
400
 
In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics.
Hermann Weyl,
1465
 
Aside from the fact that mathematics is the necessary instrument of natural science, purely mathematical inquiry in itself, according to the conviction of many great thinkers, by its special character, its certainty and stringency, lifts the human mind into closer proximity with the divine than is attainable through any other medium. Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means . It is the great achievements of the Greeks to have made the contrast between the finite and the infinite fruitful for the cognition of reality. Coming from the Orient, the religious intuition of the infinite, the aperion, takes hold of the Greek soul. This tension between the finite and the infinite and its conciliation now becomes the driving motive of Greek investigation.
Hermann Weyl, quoted in Naming Infinity (p. 21) by Loren Graham and Jean-Michel Kantor.
1559
 
We say that space is 3-dimensional because the walls of a prison are 2-dimensional.
Hermann Weyl, as remembered by Gerald A. Edgar, from Measure, Topology, and Fractal Geometry.
1719
 
Symmetry, as wide or as narrow as you define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.
Hermann Weyl,
403
 
I don't know if I should care for a man who made life easy; I should want someone who made it interesting.
Edith Wharton, quoted in The Teacher's Quotation Book, edited by Wanda Lincoln and Murray Suid.
630
 
This is because you think of space only in three dimensions... We travel in the fifth dimension. This is something you can understand, Meg. Don't be afraid to try. Was your mother able to explain a tesseract to you?
Mrs. Whatsit, from A Wrinkle in Time by Madeleine L'Engle.
745
 
Mathematics is the science of definiteness, the necessary vocabulary of those who know.
W. J. White, from Memorabilia Mathematica, by R. E. Moritz.
406
 
I wake up every morning determined both to change the world and have one hell of a good time. Sometimes this makes planning the day a little difficult.
E.B. White,
1448
 
Well, Americans:
What, nothin' better to do?
Why don't you kick yourself out?
You're an immigrant too.
Who's usin' who?
What should we do?
Well you can't be a pimp
And a prostitute too.
White Stripes, from "Icky Thump".
1445
 
I wake up every morning determined both to change the world and have one hell of a good time. Sometimes this makes planning the day a little difficult.
E. B. White,
1032
 
Every intellectual revolution which has ever stirred humanity into greatness has been a passionate protest against inert ideas.
Alfred North Whitehead, quoted in A Teacher's Treasury of Quotations, by Bernard E. Farber.
416
 
Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.
Alfred North Whitehead,
415
 
The pursuit of mathematics is a divine madness of the human spirit.
Alfred North Whitehead, from "Mathematics as an Element in the History of Thought," in The World of Mathematics by J.R. Newman.
414
 
Education with inert ideas is not only useless; it is above all things harmful.
Alfred North Whitehead, quoted in Harper Quotes.
413
 
We think of the number "five" as applying to appropriate groups of any entities whatsoever - to five fishes, five children, five apples, five days... We are merely thinking of those relationships between those two groups which are entirely independent of the individual essences of any of the members of either group. This is a very remarkable feat of abstraction; and it must have taken ages for the human race to rise to it
Alfred North Whitehead, from "Mathematics as an Element in the History of Thought," in The World of Mathematics by J.R. Newman.
411
 
A brief, and sufficiently accurate, description of the intellectual life of the European races during the succeeding two centuries and a quarter up to our own times [that is, from about 1700 to the early 20th century] is that they have been living upon the accumulated capital of ideas provided for them by the genius of the seventeenth century. The men of this epoch inherited a ferment of ideas attendant upon the historical revolt of the sixteenth century, and they bequeathed formed systems of thought touching every aspect of human life. It is the one century which consistently, and throughout the whole range of human activities, provided intellectual genius adequate for the greatness of its occasions.
Alfred North Whitehead, quoted in Calculus Gems, by George Simmons.
409
 
The study of mathematics is apt to commence in disappointment.
Alfred North Whitehead, quoted in Bartlett's Familiar Quotations.
417
 
From the very beginning of his education, the child should experience the joy of discovery.
Alfred North Whitehead,
407
 
To see what is general in what is particular, and what is permanent in what is transitory, is the aim of scientific thought.
Alfred North Whitehead,
412
 
Philosophy is the product of wonder. The effort after the general characterization of the world around us is the romance of human thought.
Alfred North Whitehead, in Nature and Life (1934) Ch. 1
1547
 
Philosophy begins in wonder. And, at the end, when philosophic thought has done its best, the wonder remains.
Alfred North Whitehead, in Modes of Thought (1938) Ch. 3, Lecture 7, p. 232
1548
 
The paradox is now fully established that the utmost abstractions are the true weapons with which to control our thought of concrete fact.
Alfred North Whitehead, quoted in The Art of Mathematics, by Jerry P. King.
408
 
Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of life is to grasp as much as we can out of that infinitude.
Alfred North Whitehead,
410
 
The science of pure mathematics, in its modern developments, may claim to be the most original development of the human spirit.
Alfred North Whitehead, quoted in Bartlett's Familiar Quotations.
418
 
We think in generalities, but we live in detail.
Alfred North Whitehead, from "The Westfield Evening News"
1812
 
One must wager on the future. To save the life of a single child, no effort is superfluous. To make a tired old man smile is to perform an essential task. To defeat injustice and misfortune, if only for one instant, for a single victim, is to invent a new reason to hope.
Elie Wiesel,
888
 
For the dead and the living we must remember.
Elie Wiesel, from the U.S. Holocaust Memorial Museum
968
 
The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it.
Eugene P. Wigner, quoted in The Art of Mathematics, by Jerry P. King.
421
 
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.
Eugene P. Wigner, quoted in The Art of Mathematics, by Jerry P. King
422
 
Probably no branch of mathematics has experienced a more surprising growth than has... topology... Considered as a most specialized and abstract subject in the early 1920's, it is today [1938] an indispensable equipment for the investigation of modern mathematical theories.
Raymond Wilder, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.
419
 
The first seven years I'd worked on this problem [the Taniyama-Shimura conjecture which would prove Fermat's Last Theorem as a consequence]. I loved every minute of it. However hard it had been, there'd been setbacks often, there'd been things that had seemed insurmountable, but it was a kind of private and very personal battle I was engaged in.
Andrew Wiles, from the BBC program "Fermat's Last Theorem" (broadcast in the U.S. on PBS's NOVA as "The Proof"), by Simon Singh and John Lynch.
589
 
At the beginning of September I was sitting here at this desk when suddenly, totally unexpectedly, I had this incredible revelation. It was the most, the most important moment of my working life. Nothing I ever do again will...[Crying]...I'm sorry.
Andrew Wiles, from the BBC program "Fermat's Last Theorem" (broadcast in the U.S. on PBS's NOVA as "The Proof"), by Simon Singh and John Lynch.
588
 
Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the first room and it's dark, completely dark. One stumbles around bumping into the furniture and then gradually you learn where each piece of furniture is, and finally after six months or so you find the light switch, you turn it on suddenly it's all illuminated, you can see exactly where you were.
Andrew Wiles, from the BBC program "Fermat's Last Theorem" (broadcast in the U.S. on PBS's NOVA as "The Proof"), by Simon Singh and John Lynch.
587
 
There's no other problem that will mean the same to me [as Fermat's Last Theorem]. I had this very rare privilege of being able to pursue in my adult life what had been my childhood dream. I know it's a rare privilege but, if one can do this it's more rewarding than anything I could imagine.
Andrew Wiles, from the BBC program "Fermat's Last Theorem" (broadcast in the U.S. on PBS's NOVA as "The Proof"), by Simon Singh and John Lynch.
591
 
It was a Monday morning, September 19th and I was trying to convince myself that it [a key reduction in his proof of the Taniyama-Shimura conjecture, which would prove Fermat's Last Theorem as a consequence] didn't work, just seeing exactly what the problem was. Suddenly, totally unexpectedly, I had this incredible revelation. I, I realised what was holding me up was exactly what would resolve the problem I'd had in my Iwasawa theory attempt three years earlier. It was the most, the most important moment of my working life. It was so indescribably beautiful, it was so simple and so elegant and I just stared in disbelief for twenty minutes. Then during the day I walked round the department, I'd keep coming back to my desk and looking to see if it was still there. It was still there... My original approach to the problem from three years before would make it exactly work. So out of the ashes seemed to rise the true answer to the problem. So the first night I went back and slept on it, I checked through it again the next morning and by 11 o'clock I satisfied. I went down and told my wife, "I've got it, I think I've got it, I've found it." It was so unexpected, she, I think she thought I was talking about a children's toy or something, said, "Got what?" And I said, "I've fixed my proof, I, I've got it."
Andrew Wiles, from the BBC program "Fermat's Last Theorem" (broadcast in the U.S. on PBS's NOVA as "The Proof"), by Simon Singh and John Lynch.
674
 
Nothing should be overlooked in fighting for better education. Be persistent and ornery; this will be good for the lethargic educational establishment and will aid the whole cause of public education.
Roy Wilkins, quoted in My Soul Looks Back, 'Less I Forget, by Dorothy Winbush Riley.
420
 
Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure. It is our light, not our darkness, that most frightens us. We ask ourselves, who am I to be brilliant, gorgeous, talented and fabulous? Actually, who are you not to be? You are a child of God. Your playing small doesn't serve the world. We were born to make manifest the glory of God that is within us. It's not just in some of us; it's in everyone. And as we let our own light shine, we unconsciously give other people permission to do the same. As we are liberated from our own fear, our presence automatically liberates others.
Marianne Williamson,
1772
 
Confront the dark parts of yourself, and work to banish them with illumination and forgiveness. Your willingness to wrestle with your demons will cause your angels to sing. Use the pain as fuel, as a reminder of your strength.
August Wilson, (American Writer, 1945-2005)
1768
 
They say that every snowflake is different. If that were true, how could the world go on? How could we ever get up off our knees? How could we ever recover from the wonder of it?
Jeanette Winterson,
1455
 
I put the relation of a fine teacher to a student just below the relation of a mother to her son and I don't think I could say more than this.
Thomas Wolfe, quoted in Teaching Is..., by Merrill Harmin and Tom Gregory.
423
 
I estimated that just today, across the world, we spent about 106 average world lifetimes teaching people how to calculate by hand. That's an amazing amount of human endeavor.
Conrad Wolfram, from "Teaching Kids Real Math With Computers," July 2010, TedGlobal talk.
1784
 
Math has been liberated from calculating. But that math liberation has not gotten into education yet.
Conrad Wolfram, from "Teaching Kids Real Math With Computers," July 2010, TedGlobal talk.
1764
 
What I am really suggesting here is we have a unique opportunity here to make math more practical and more conceptual simultaneously. I can't think of any other subject where that's recently been possible. It's usually some kind of choice between vocational and intellectual. But I think we can do both at the same time [with computers].
Conrad Wolfram, from "Teaching Kids Real Math With Computers," July 2010, TedGlobal talk.
1746
 
We are many, but are we much?
John Wooden,
1374
 
Discipline yourself and others won't need to.
John Wooden,
1377
 
Make each day your masterpiece.
John Wooden,
1376
 
What is right is more important than who is right.
John Wooden,
1375
 
Truth is life.
Frank Lloyd Wright, quoted in the Ken Burns' documentary "Frank Llyod Wright."
778
 
It [the Larkin Building in Buffalo, New York] was an essay in the third dimension.
Frank Llyod Wright, quoted in the Ken Burns' documentary "Frank Llyod Wright."
779
 
On this simple unit-system [of building blocks] ruled on the low table-top all these forms were combined by the child into imaginative patter. Design was recreation! ...The virtue of all this lay in the awakening of the childmind to rhythmic structure in Nature - giving the child a sense of innate cause-and-effect otherwise far beyond child-comprehension.
Frank Llyod Wright, quoted in A Mathematical Mystery Cruise, by Ivars Peterson.
424
 
Geometry is the grammar, so to speak, of the form. It is its architectural principle. But there is a psychic correlation between the geometry of the form and our associated ideas which constitutes its symbolic value. There resides a certain "spell power" in any geometric form which seems more or less a mystery, and is, as we say, the soul of the thing.
Frank Lloyd Wright,
1334
 

88 quotes found and displayed.