Did you ever wonder if the person in the puddle is real, and you're just a reflection of him?
Calvin and Hobbes,
1627
 
The calculus is one of the grandest edifices constructed by mankind.
Cambridge Conference on School Mathematics, quoted in Out of the Mouths of Mathematicians.
618
 
We believe that arithmetic as it has been taught in grade schools until quite recently has such a meagre intellectual content that the oft-noted reaction against the subject is not an unfortunate rebellion against a difficult subject, but a perfectly proper response to a preoccupation with triviality.
Cambridge Conference on School Mathematics Report , quoted in "Teaching Mathematics," by Abe Shenitzer, in Mathematics Tomorrow, by Lynn Arthur Steen.
557
 
People say that what we're all seeking is a meaning for life. I don't think that's what we're really seeking. I think that what we're seeking is an experience of being alive, so that our life experiences on the purely physical plane will have resonances without own innermost being and reality, so that we actually feel the rapture of being alive.
Joseph Campbell, from The Power of Myth
1476
 
You live your life between your ears.
Bebe Moore Campbell, at Westfield State College's 158th Commencement.
510
 
A novel is never anything but a philosophy put into images.
Albert Camus,
996
 
Autumn is a second spring when every leaf is a flower.
Albert Camus,
895
 
The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.
Georg Cantor, quoted in Infinity and the Mind by Rudy Rucker.
524
 
I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not - I do not say divisible - but actually divisible; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.
George Cantor, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.
40
 
All finite cardinal numbers are distinct and simultaneously present in God's intellect.
Georg Cantor, quoted in Godel Meets Einstein: Time Travel in the Godel Universe by Palle Yourgrau.
1058
 
My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. How do I know this? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so to speak, to the first infallible cause of all created things.
Georg Cantor, quoted in Journey Through Genius by William Dunham.
550
 
This view [of the infinite], which I consider to be the sole correct one, is held by only a few. While possibly I am the very first in history to take this position so explicitly, with all of its logical consequences, I know for sure that I shall not be the last!
Georg Cantor, quoted in Journey Through Genius by William Dunham.
549
 
The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.
Georg Cantor, quoted in Understanding the Infinite by Shaughan Lavine.
545
 
The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.
Georg Cantor, quoted in Mind Tools: The Five Levels of Mathematical Reality by Rudy Rucker.
528
 
A set is a Many that allows itself to be thought of as a One.
Georg Cantor, quoted in Infinity and the Mind by Rudy Rucker.
523
 
I entertain no doubts as to the truths of the tranfinites, which I recognized with God"s help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science.
Georg Cantor, quoted in Modern Mathematicians, by Harry Henderson.
485
 
The essence of mathematics is in its freedom.
G. Cantor,
41
 
What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending lader of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers.
Georg Cantor, quoted in Understanding the Infinite by Shaughan Lavine.
543
 
Power series are therefore especially convenient because one can compute with them almost as with polynomials.
C. Caratheodory, quoted in Theory of Complex Functions, by Reinhold Remmert.
482
 
I can't go back to yesterday - because I was a different person then
Lewis Carroll,
1478
 
Contrariwise, if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic.
Lewis Carroll,
1479
 
Sometimes I've believed as many as six impossible things before breakfast.
Lewis Carroll,
1480
 
There are three hundred and sixty-four days when you might get un-birthday presents, and only one for birthday presents, you know.
Lewis Carroll,
1481
 
Who in the world am I? Ah, that's the great puzzle.
Lewis Carroll,
1482
 
"What's one and one and one and one and one and one and one and one and one and one?" "I don't know," said Alice. "I lost count." "She can't do addition," said the Red Queen.
Lewis Carroll, quoted in World of Mathematics, by J.R. Newman.
42
 
"What is the use of a book," thought Alice, "without pictures or conversation?"
Lewis Carroll, from Alice in Wonderland
43
 
For the first time in the history of the world, every human being is now subjected to contact with dangerous chemicals, from the moment of conception until death.
Rachel Carson, quoted in The Harper Book of Quotations, edited by Robert I. Fitzhenry.
626
 
If I had influence with the good fairy… I should ask that her gift to each child in the world be a sense of wonder so indestructible that it would last throughout life.
Rachel Carson,
840
 
If a child is to keep alive his sense of wonder... he needs the companionship of at least one adult who can share it, rediscovering with him the joy, excitement and mystery of the world we live in.
Rachel Carson, quoted in Listening to Nature by Joseph Cornell.
764
 
There are only two lasting bequests we can hope to give our children. One is roots; the other, wings.
Hodding Carter,
1014
 
Faith implies a continuing search, not necessarily a final answer.
Jimmy Carter,
752
 
We cast this message into the cosmos… Of the 200 billion stars in the Milky Way galaxy, some - perhaps many - may have inhabited planets and space faring civilizations. If one such civilization intercepts Voyager and can understand these recorded contents, here is our message: We are trying to survive our time so we may live into yours. We hope some day, having solved the problems we face, to join a community of Galactic Civilizations. This record represents our hope and our determination and our goodwill in a vast and awesome universe.
Jimmy Carter, from the message on Voyager Spacecraft, 16 June, 1977.
1449
 
I have one life and one chance to make it count for something… I'm free to choose what that something is, and the something I've chosen is my faith. Now, my faith goes beyond theology and religion and requires considerable work and effort. My faith demands - this is not optional - my faith demands that I do whatever I can, wherever I can, whenever I can, for as long as I can with whatever I have to try to make a difference.
Jimmy Carter, from Words I Wish I Wrote by Robert Fulgham
949
 
Learn to do common things uncommonly well.
George Washington Carver,
884
 
How far you go in life depends on your being tender with the young, compassionate with the aged, sympathetic with the striving, and tolerant of the weak and the strong. Because someday in life you will have been all of these.
George Washington Carver,
885
 
God gave them [my inventions] to me; how can I sell them to someone else? If I took that money, I might forget my people.
George Washington Carver,
886
 
Education is the key to unlock the golden door of freedom.
George Washington Carver, quoted in My Soul Looks Back, 'Less I Forget, by Dorothy Winbush Riley.
329
 
How far you go in life depends on your being tender with the young, compassionate with the aged, sympathetic with the striving and tolerant of the weak and strong. Because someday in life you will have been all of these.
George Washington Carver,
1013
 
Well, you wonder why I always dress in black,
Why you never see bright colors on my back,
And why does my appearance seem to have a somber tone.
Well, there's a reason for the things that I have on.
I wear the black for the poor and the beaten down,
Livin' in the hopeless, hungry side of town,
I wear it for the prisoner who has long paid for his crime,
But is there because he's a victim of the times.
I wear the black for those who never read,
Or listened to the words that Jesus said,
About the road to happiness through love and charity,
Why, you'd think He's talking straight to you and me.
Well, we're doin' mighty fine, I do suppose,
In our streak of lightnin' cars and fancy clothes,
But just so we're reminded of the ones who are held back,
Up front there ought 'a be a Man In Black.
I wear it for the sick and lonely old,
For the reckless ones whose bad trip left them cold,
I wear the black in mournin' for the lives that could have been,
Each week we lose a hundred fine young men.
And, I wear it for the thousands who have died,
Believen' that the Lord was on their side,
I wear it for another hundred thousand who have died,
Believen' that we all were on their side.
Well, there's things that never will be right I know,
And things need changin' everywhere you go,
But 'til we start to make a move to make a few things right,
You'll never see me wear a suit of white.
Ah, I'd love to wear a rainbow every day,
And tell the world that everything's OK,
But I'll try to carry off a little darkness on my back,
'Till things are brighter, I'm the Man In Black
Johnny Cash, from "The Man in Black"
1277
 
Godel, Escher, Bach is an entire humanistic education between the covers of a single book. So, for my next visit to a desert island, give me sun, sand, water, and GEB, and I'll live happily ever after.
John L. Casti, Nature
1041
 
Mathematical modeling is about rules - the rules of reality. What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of 'model', is that the mathematical model is an image or picture of reality painted with logical symbols instead of with words, sounds or watercolors. These symbols are then strung together in accordance with a set of rules expressed in a special language, the language of mathematics. A large part of the story told in the 800 pages or so comprising the two volumes of this work is about the grammar of this language. But a piece of the real world encoded into a set of mathematical rules (i.e. a model) is itself an abstraction drawn from the deeper realm of 'the real thing.' Based as it is upon a choice of what to observe and what to ignore, the real-world starting point of any mathematical model must necessarily throw away aspects of this 'real thing' deemed irrelevant for the purposes of the model. So when trying to fathom the meaning of the title of this volume, I invite the reader to regard the word 'rule' as either a noun or a verb - or even to switch back and forth between the two - according to taste.
John Casti, from Reality Rules: 1.
44
 
Where there is great love there are always miracles.
Willa Cather, quoted in Wisdom for the New Millennium edited by Helen Exley.
1074
 
There are some things you lean best in calm, and some in storm.
Willa Cather, quoted in The Beacon Book of Quotations by Women, edited by Rosalie Maggio.
46
 
The dead might as well try to speak to the living as the old to the young.
Willa Cather, quoted in A Teacher"s Treasury of Quotations by Bernard E. Farber.
717
 
Now it is easy to see that differentials of this kind keep the same value if one exchanges the order of differentiation with respect to the several variables.
Cauchy, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1127
 
I received your letter while in bed with fever and gout... But in spite of my illness, I enjoyed the savory fruits of your mind, since I found infinitely admirable that infinitely long hyperbolic solid which is equal to a body finite in all the three dimensions. And having spoken about it to some of my philosophy students, they agreed that it seemed truly marvelous and extraordinary that that could be.
Bonaventure Cavalieri, quoted in "Torricelli's Infinitely Long Solid and Its Philosophical Reception in the Seventeenth Century," by P. Mancosu and E. Vailati, Isis, vol. 82, 1991.
621
 
By a small sample we may judge of the whole piece.
Miguel de Cervantes, from Don Quixote
67
 
If it [the Koch Curve] were given life, it would not be possible to destroy it except by doing away with it all at once, since it would be endlessly reborn of the depths of its triangles, like life in the universe.
E. Cesaro, quoted in Measure, Topology, and Fractal Geometry, by G. Edgar.
465
 
Education don't come by bumping against the school-house.
Selwyn Gurney Champion, quoted in A Teacher's Treasury of Quotations by Bernard E. Farber.
612
 
The birth of a man is the birth of his sorrow. The longer he lives, the more stupid he becomes, because his anxiety to avoid unavoidable death becomes more and more acute. What bitterness! He lives for what is always out of reach! His thirst for survival in the future makes him incapable of living in the present.
Chang-Tzu,
1684
 
It is chiefly through books that we enjoy the intercourse with superior minds... In the best books, great men talk to us, give us their most precious thought, and pour their souls into ours. God be thanked for books.
William Ellery Channing,
994
 
Difficulties are meant to rouse, not discourage. The human spirit is to grow strong by conflict.
William Elery Channing,
1329
 
To be a man is to suffer for others.
Cesar Chavez, quoted in The Night is Dark and I am Far From Home by Jonathan Kozol
1132
 
Well, part of it is a longstanding belief -- it's been in our education establishment at least since the 1930s -- that somehow children should be allowed to discover knowledge for themselves, that they should construct their own knowledge. This has surfaced most recently in connection with mathematics instruction, where the idea is that they need to discover how to add for themselves. Rather than being taught how to add, they should construct this knowledge on their own.
Lynne Cheney, excerpt from Inside Politics, CNN, March 12, 2001.
954
 
Physics and geometry are one family.
Together and holding hands they roam to the limits of outer space...
Surprisingly, Math. has earned its rightful place for man and in the sky;
Fondling flowers with a smile -- just wish nothing is said!
Shiing Shen Chern, quoted in "Interview with Shiing Shen Chern," Notices of the American Mathematical Society, vol. 45, no. 7, August 1998.
716
 
Free math (Available here Monday through Friday). But you must bring your own container, and you must fill it with much or little according to its capacity and the amount of work that you are willing to do. The learning assistant (sometimes euphemistically called a "teacher") will provide expertise, advice, guidance, and will set an example. But in the final analysis it is you who must do the work needed for your learning... Here it is -- this wonderful stuff called math. If you want it, come and get it. If you don't want it, kindly step out of the way -- as not to impede the progress of those who do. The choice is yours.
L.M. Christolphe, Jr.,
1159
 
You create your own universe as you go along.
Winston S. Churchill,
1730
 
Man will occasionally stumble over the truth, but usually manages to pick himself up, walk over or around it, and carry on.
Winston Churchill,
1732
 
If you're going through hell, keep going.
Winston Churchill,
1054
 
A room without books is like a body without a soul.
Cicero,
991
 
Knowledge is the only instrument of production that is not subject to diminishing returns.
John Bates Clark, from "Overhead Costs in Modern Industry," Journal of Political Economy, October 1927.
1156
 
Statistics are no substitute for judgment.
Henry Clay, quoted in Flaws and Fallacies in Statistics, by Campbell.
47
 
You don't have to teach people to be human. You have to teach them how to stop being inhuman.
Eldridge Cleaver, quoted in My Soul Looks Back, 'Less I Forget', by Dorothy Winbush Riley.
48
 
The price of hating other human beings is loving oneself less.
Eldridge Cleaver,
1697
 
If we had a ham, we could have ham and eggs, if we had the eggs.
Andrew Clifford's Grandmother,
49
 
By the end of the first month of the 1995 session, each Senator will have made more money than any person who works 40 hours a week at minimum wage for the entire year.
Bill Clinton, President's State of the Union Address, 25 January, 1995.
50
 
The title which I most covet is that of teacher. The writing of a research paper and the teaching of freshman calculus, and everything in between, falls under this rubric. Happy is the person who comes to understand something and then gets to explain it.
Marshall Cohen, from the Cornell University Department of Mathematics Annual Report, 1991-92.
52
 
The schools are a great theater in which we play out the conflicts in the culture.
David Cohen and Barbara Neufeld,
51
 
Over the years, I've asked children to tell me who they are--by saying whatever words they wish to say, or drawing whatever picture will enable them to forsake words for a visual statement…To my constant surprise, the variety of responses is enormous. Even when I am in a particular neighborhood--and therefore the national, regional, social, and racial characteristics are the same for child after child--I find astonishing differences in the choices made by children as they prepare to present themselves through one perspective or another.
Robert Coles, from The Spiritual Life of Children.
770
 
The chapters that follow are the result of a kind of fieldwork - a teacher's conversations with his students over many years in many classrooms... [I] want to acknowledge an enormous debt to the students, who have taught me so much. My book's title is autobiographical: one keeps learning by teaching.
Robert Coles, from The Call of Stories.
53
 
We hate some persons because we do not know them; and we will not know them because we hate them.
Charles Caleb Colton,
893
 
The first law of ecology is that everything is related to everything else.
Barry Commoner, quoted in The Harper Book of Quotations, edited by Robert I. Fitzhenry.
627
 
Learning without thought is labor lost; thought without learning is perilous.
Confucius, quoted in A Teacher's Treasury of Quotations, by Bernard E. Farber.
54
 
I am proudest, though, of discovering a whole new world of numbers, which Donald Knuth named "surreal numbers." I wish I'd invented that name… When I discovered them, I went around in a permanent daydream for six weeks thinking about how the explorer Hernando Cortez looked out over the Pacific and saw a world that no Westerner had ever seen before. Nobody had ever seen what I saw before… It was an amazing new world.
John Horton Conway,
1512
 
People often have the misconception that what someone like Einstein did is complicated. No, the truly earthshattering ideas are simple ones. But these ideas often have a sublety of some sort, which stops people from thinking of them. The simple idea involves a question nobody had thought of asking.
John H. Conway, from "The Power of Mathematics".
1393
 
It's not what is poured into a student that counts, but what is planted.
Linda Conway,
1026
 
I'd always been first, second, or third in every subject, but when puberty hit me, I couldn't care less. I hung around with the kids who weren't interested in anything, the back-of-the-class types, because they were interesting characters. (I've had that trouble ever since. I like interesting characters.)
John Horton Conway,
1511
 
Custodial education does not have as its objective the education of youth but rather social control over them. It suppresses rather than stimulates their intellectual and physical energies.
John Conyers, quoted in My Soul Looks Back, 'Less I Forget', by Dorothy Winbush Riley.
55
 
Perhaps there will be prattlers who, although completely ignorant of mathematics, nevertheless take it upon themselves to pass judgment on mathematical questions, and on account of some passage in Scripture, badly distorted to their purpose, will dare to censure and assail what I have presented here.
Copernicus,
982
 
To the world you may be one person, but to one person you may be the world.
Heather Cortez,
1025
 
After an unbroken tradition of many centuries, mathematics has ceased to be generally considered as an integral part of culture in our era of mass education.
Richard Courant, in his introduction to Morris Kline's Mathematics in Western Culture.
1413
 
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.
Courant and Robbins, from What is Mathematics?
56
 
Starting in the seventeenth century, the general theory of extreme values -- maxima and minima -- has become one of the systematic integrating principles of science.
Richard Courant and Herbert Robbins, from What is Mathematics?
749
 
With an absurd oversimplification, the "invention" of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part.
Richard Courant and Herbert Robbins, from What is Mathematics?
617
 
What is the eternal and ultimate problem of a free society? It is the problem of the individual who thinks that one man cannot possibly make a difference in the destiny of that society.
Norman Cousins, from Words I Wish I Wrote by Robert Fulgham
946
 
The tragedy of life is not death, but what we let die inside us while we live.
Norman Cousins, from Words I Wish I Wrote by Robert Fulgham
945
 
Infinity converts the possible into the inevitable.
Norman Cousins, quoted in To Infinity and Beyond by Eli Maor.
647
 
In our times, geometers are still exploring those new Wonderlands, partly for the sake of their applications to cosmology and other branches of science, but much more for the sheer joy of passing through the looking glass into a land where the familiar lines, planes, triangles, circles and spheres are seen to behave in strange but precisely determined ways.
H.S.M. Coxeter,
1196
 
In our times, geometers are still exploring those new Wonderlands, partly for the sake of their applications to cosmology and other branches of science, but much more for the sheer joy of passing through the looking glass into a land where the familiar lines, planes, triangles, circles and spheres are seen to behave in strange but precisely determined ways.
H.S.M. Coxeter,
791
 
"I am never bored." [When asked about his longevity.]
H.S.M. Coxeter,
863
 
The effect of the discovery of hyperbolic geometry on our ideas of truth and reality has been so profound.
H.S.M. Coxeter, quoted in Euclidean and Non-Euclidean Geometries by Greenberg.
1036
 
...scientific power is like inherited wealth: attained without discipline. You read what others have done, and you take the next step. You can do it very young...there is no mastery, old scientists are ignored. There is no humility before nature...Its a form of inherited wealth. And you know what assholes congenitally rich people are.
Michael Creichton, (Ian Malcom) from Jurrasic Park.
57
 
People think the brain is mysterious but not the weather. Why is that? We don't yet have a clear understanding of how raindrops form but we do know how individual neurons and synapses work.
Francis Crick, quotes in the 13 April, 2004 New York Times.
1471
 
The Islamic artist was not only versed in mathematics in the geometrical sense, but mathematics was integral to his art as it was a 'universal' structure supporting the intuitive insights that characterize all true art.
Keith Critchlow, from the introduction to Islamic Patterns: An Analytical and Cosmological Approach.
1325
 
Life is not easy for any of us. But what of that? We must have perseverance and above all confidence in ourselves. We must believe that we are gifted for something, and that this thing, at whatever cost, must be attained.
Marie Currie, quoted in Wisdom for the New Millennium edited by Helen Exley.
1075
 

95 quotes found and displayed.