This was supplied by the mean value theorem; and it was Cauchy’s great service to have recognized its fundamental importance… Because of this, we adjudge Cauchy as the founder of exact infinitesimal calculus.
F. Klein, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1117
 
Inner city education must change. Our responsibility is not merely to provide access to knowledge; we must produce educated people.
James Farmer, in Today's Education, April 1969.
117
 
Mathematics serves as a handmaiden for the explanation of the quantitative situations in other subjects, such as economics, physics, navigation, finance, biology and even the arts.
H. F. Fehr, quoted in Out of the Mouths of Mathematicians, By R. Schmalz.
118
 
On the other hand, it is impossible for a cube to be written as a sum of two cubes or a fourth power to be written as a sum of two fourth powers or, in general for any number which is a power greater than the second to be written as a sum of two like powers. For this I have discovered a truly wonderful proof, but the margin is too small to contain it.
P. Fermat, quoted in Excursions in Calculus, by Robert Young.
119
 
How many great theorems can be discovered?
Jessica Ferris, Westfield State College student
1131
 
From a long view of the history of mankind – seen from, say, the thousand years from now – there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics. The American Civil War will pale in provincial insignificance in comparison with this important scientific event of the same decade.
Richard Feynman, quoted in Calculus with Analytic Geometry by George F. Simmons
859
 
I was born not knowing and have only had a little time to change that here and there.
Richard Feynman,
851
 
I learned from her [my mother] that the highest forms of understanding we can achieve are laughter and human compassion.
Richard Feynman, What Do You Care What Other People Think?
925
 
Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry.
Richard Feynman,
872
 
You can know the name of a bird in all the languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird... So let's look at the bird and see what it's doing -- that's what counts. I learned very early the difference between knowing the name of something and knowing something.
Richard Feynman,
850
 
The journey for an education starts with a childhood question.
David L. Finn,
560
 
The effort of the economist is to 'see,' to picture the interplay of economic elements. The more clearly cut these elements appear in his vision, the better; the more elements he can grasp and hold in his mind at once, the better. The economic world is a misty region. The first explorers used unaided vision. Mathematics is the lantern by which what before was dimly visible now looms up in firm bold outlines. The old phantasmagoria disappear. We see better. We also see further.
Irving Fisher, quoted in The World of Mathematics, by J.R. Newman.
122
 
Unc, why do they call them stars when they are really round?
K. C. Fisher, at age 3
121
 
Read in order to live.
Gustave Flaubert,
997
 
With one trillion dollars [one-fifth of the 1996 U.S. National debt], you could buy... a $100,000 house for every family in Kansas, Missouri, Nebraska, Oklahoma, and Iowa AND then you could put a $10,000 car in the garage of each one of those houses AND there would be enough left to build a $10 million library and a $10 million hospital for each of 250 cities in those states AND there would be enough left to build a $10 million dollar school in each of 500 communities in those states AND there would still be enough left to put in the bank, and from the interest alone, pay 10,000 nurses and teachers [indefinitely], plus give a $5,000 bonus to every family in those states.
Lou Jean Fleron,
120
 
Objectivity is the delusion that observations could be made without an observer.
Heinz von Foerster, Quoted in Radical Constructivism: A Way of Knowing and Learning by Ernst von Glasersfeld.
772
 
Mathematicians are like lovers... Grant a mathematician the least principle, and he will draw from it a consequence which you must grant him also, and from this consequence another.
Fontenelle,
123
 
I learned certain things at school that the teachers would say, 'now here's what we're going to learn. You'll learn it, and then I'll tell what you've learned.' Then I'll get out, and I'll be arguing about this point I learned in history, and I realize I know the facts, but I don't have the foggiest idea what I'm talking about. I can tell you all the dates, but I don't know why it's in my head. I don't know why I think it or how I ever reached those conclusions because they don't really go with my ideas at all.
Weinstein Fontini, from Toward Humanist Education.
396
 
The deep study of nature is the most fruitful source of mathematical discoveries.
Jean-Baptist-Joseph Fourier, quoted in Calculus and Analytic Geometry, by Philip Gillett.
551
 
The profound study of nature is the most fertile source of mathematical discovery.
Joseph Fourier, quoted in The Magic of Mathematics, by Theoni Pappas.
491
 
Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.
Joseph Fourier, quoted in Single Variable Calculus, by James Stewart.
124
 
I don't think of all the misery but of the beauty that still remains.
Anne Frank, quoted in Wisdom for the New Millennium edited by Helen Exley.
1066
 
What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of mathematics?
Benjamin Franklin,
125
 
One today is worth two tomorrows.
Benjamin Franklin,
934
 
People who are willing to give up freedom for the sake of short term security deserve neither freedom nor security.
Benjamin Franklin,
926
 
We have already pointed out and will recognize throughout this book the importance of compact sets. All those concerned with general analysis have seen that it is impossible to do without them.
Frechet, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1124
 
I have here a geometer who is a big Cyclops…who has only one eye left, and a new curve, which he is presently computing, could render him totally blind.
Frederick II, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1110
 
A scientist can hardly meet with anything more undesirable than to have the foundation give way just as the work is finished. In this position I was put by a letter from Mr. Bertrand Russell as the work was nearly through the press.
Gottlob Frege,
534
 
In the small matters trust the mind, in the large ones the heart…
Sigmund Freud, from Words I Wish I Wrote by Robert Fulgham
953
 
Man's main task is to give birth to himself.
Eric Fromm,
918
 
Education is the ability to listen to almost anything without losing your temper or your self confidence.
Robert Frost,
922
 
The best way out is through.
Robert Frost, quoted in Wisdom for the New Millennium edited by Helen Exley.
1073
 
I am not a teacher, I am an awakener.
Robert Frost,
126
 
Using mathematics to tell stories and using stories to explain mathematics are two sides of the same coin. They join what should never have separated: the scientist’s and the artist’s ways of uncovering truths about the world.
William Frucht, from the Introduction to Imaginary Numbers: An Anthology of Marvelous Mathematical Stories, Diversions, Poems, and Musings
1045
 
But nothing's better for you [then old, leftover meatloaf]. It's a matter of mental health. I've never heard anybody say he was depressed by eating a cold meatloaf sandwich.
Robert Fulgham, from Uh-Oh
921
 
If you don't play the game, you can't know enough to make the rules. If you are not engaged in the sweaty work of the world, you should not be in charge of the deodorant concession.
Robert Fulgham, from Words I Wish I Wrote
943
 
It has been said that the hottest places in Hell are reserved for those who, in times of moral crisis, maintain their neutrality. And I say the moral crisis of the times is continuous. Knowing and understanding and being are not enough. One must do. To gain the world and give nothing to it is to lose you soul.
Robert Fulgham, from Words I Wish I Wrote
944
 
I'm not often aware that I am happy. But I often remember that I have been happy. Especially when I sit in my kitchen wrapped in an invisible patchwork quilt made of the best moments of yesterdays. These precious things -- these leftovers from living on -- remain to serve as survival rations for the heart and soul. You can't entirely live off them. But life is not worth living without them.
Robert Fulgham, from Uh-Oh.
920
 
When I am working on a problem, I never think about beauty. I only think of how to solve the problem. But when I am finished, if the solution is not beautiful, I know it is wrong.
Buckminster Fuller,
127
 
Wherefore I realized that
All the words in all dictionaries
Are the consequent tools
Of all men"s conscious
And conscientious attempts
To communicate
All their experiences--
Which is of course
To communicate
Universe.
Buckminster Fuller, from "How little I know", excerpted in The Art of Science Writing by D. Worsley and B. Mayer.
742
 
I have great hope for tomorrow. My hope lies in three things: truth, youth, and love.
Buckminister Fuller,
832
 

41 quotes found and displayed.