Fuzzy logic lacks every feature that the pioneers of modern logic wanted logic for; it sacrifices what have traditionally been regarded as the crucuail advantages of formalism -- precise, formal rules of inference, the security offered by consistentcy and completeness results.
Susan Haack, from Deviant Logic, Fuzzy Logic, 1996.
754
 
While, traditionally, logic has corrected or avoided it, fuzzy logic compromises with vagueness; it is not just a logic of vagueness, it is -- from what Frege"s point of view would have been a contradiction in terms -- a vague logic.
Susan Haack, from Deviant Logic, Fuzzy Logic, 1996.
755
 
If fuzzy logic is construed, as Zadeh and co. suggest it should be, as a nonclassical theory of truth-preserving inferences, fuzzy technology does not rely on it, and so the successes of that technology cannot be claimed to its credit. If, on the other hand, fuzzy logic is construed as an attempt to represent the mental processes through which people go when making adjustments to kiln thermostats, air-conditionaers, etc., there is a connection with fuzzy technology. But, of course, so construed, fuzzy logic is not, after all, an attempt to represent truth-preserving inferences, and is not, after all, a theory in the same domain as classical logic; in fact, so construed, it is obviously not properly describable as a "logic" at all.
Susan Haack, from Deviant Logic, Fuzzy Logic, 1996.
756
 
The shortest path between two assertions about the reals passes through the complexes.
J. Hadamard, quoted in Theory of Complex Functions, by Reinhold Remmert.
148
 
Practical application is found by not looking for it, and one can say that the whole progress of civilization rests on that principle.
Jacques Hadamard, quoted in Euclidean and Non-Euclidean Geometries by Greenberg
875
 
Anyone, anywhere along the line, can fill in the details and check them. The fact that a computer can run through more details in a few hours than a human could ever hope to do in a lifetime does not change the basic concept of mathematical proof. What has changed is not the theory but the practice of mathematics.
Wofgang Haken, quoted in From Here to Infinity, by Ian Stewart.
585
 
The universe is not only queerer than we suppose but queerer than we can suppose.
J.B.S. Haldane, quoted in Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, by Manfred Schroder.
566
 
It’s hard for me to get used to the absence of pressure. I always pushed myself under pressure, and of course, I blamed the world. The world is putting on the pressure. Well, now I’m beginning to realize that the world is not putting on the pressure. If I never published anything, not even an elementary textbook, if I never again answered a letter, if I never did anything any more except drink my beer and watch the telly, nobody would, I think, think any the worse of me. But I keep putting myself under a little pressure and keep doing these small piddling jobs.
Paul Halmos, quoted in “In touch with God: An interview with Paul Halmos,” by Don Albers, College Mathematics Journal, vol. 35, no. 1, January 2004, pp. 2- 14
868
 
Learning mathematics is always extraordinarily hard work. I can’t easily read mathematics. I can’t listen to lectures. The only thing I enjoy is a kind of mathematical gossip, when people sit in easy chairs with their feet up on something and tell me their mathematics; then I can learn.
Paul Halmos, quoted in In touch with God: An interview with Paul Halmos, by Don Albers, College Mathematics Journal, vol. 35, no. 1, January 2004, pp. 2- 14
867
 
It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.
Paul Halmos, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz
451
 
Mathematics is not a deductive science -- that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.
Paul R. Halmos, from I Want to Be a Mathematician
1148
 
A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant.
Paul Halmos,
151
 
Mathematics - this may surprise or shock some - is never deductive in its creation. The mathematician at work makes vague guesses, visualizes broad generalizations, and jumps to unwarranted conclusions. He arranges and rearranges his ideas, and he becomes convinced of their truth long before he can write down a logical proof... The deductive stage, writing the result down, and writing its rigorous proof are relatively trivial once the real insight arrives; it is more like the draftsman's work not the architect's.
Paul Halmos, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.
150
 
A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one.
Paul Halmos, quoted in Contemporary Abstract Algebra, by J. Gallian.
149
 
The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method, the method in which the teacher plays a role of an omniscient but largely uncommunicative referee between the learner and the facts.
Paul Halmos, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz
450
 
Teachers of elementary mathematics in the USA frequently complain that all calculus books are bad. That is a case in point. Calculus books are bad because there is no such subject as calculus; it is not a subject because it is many subjects. What we call calculus nowadays is the union of a dab of logic and set theory, some axiomatic theory of complete ordered fields, analytic geometry and topology, the latter in both the "general" sense (limits and continuous functions) and the algebraic sense (orientation), real-variable theory properly so called (differentiation), the combinatoric symbol manipulation called formal integration, the first steps of low-dimensional measure theory, some differential geometry, the first steps of the classical analysis of the trigonometric, exponential, and logarithmic functions, and, depending on the space available and the personal inclination of the author, some cook-book differential equations, elementary mechanics, and a small assortment of applied mathematics. Any one of these is hard to write a good book on; the mixture is impossible.
Paul Halmos, quoted in Excursions in Calculus, by Robert Young.
152
 
To be able to be caught up into the world of thought - that is educated.
Edith Hamilton, quoted in The Beacon Book of Quotations by Women, edited by Rosalie Maggio.
153
 
This above all: To thine own self be true, And it must follow, as the night the day, Thou canst not then be false to any man.
Hamlet,
936
 
The purpose of computing is insight, not numbers!
R. W. Hamming, quoted in "Mathematics and Modern Technology" by R.S. Pinkham, in The American Mathematical Monthly, vol. 103, no. 7, Aug.-Sept.1996, pp. 539-545.
154
 
People usually consider walking on water or in thin air a miracle. But I think the real miracle is not to walk either on water or in thin air, but to walk on earth. Every day we are engaged in a miracle which we don't even recognize: a blue sky, white clouds, green leaves, the black, curious eyes of a child -- our own two eyes. All is a miracle.
Thich Nhat Hanh,
1018
 
Paul Erdos has a theory that God has a book containing all the theorems of mathematics with their absolutely most beautiful proofs, and when he wants to express particular appreciation of a proof he exclaims, 'This is from the book!'
Ross Hansberger, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.
155
 
Here was a man who could work out modular equations and theorems of complex multiplication, to orders unheard of, whose mastery of continued fractions was, on the formal side at any rate, beyond that of any mathematician in the world, who had found for himself the functional equation of the Zeta-function, and the dominant terms of many of the most famous problems in the analytic theory of numbers; and he had never heard of a doubly periodic function or of Cauchy's theorem, and he had indeed but the vaguest idea of what a function of a complex variable was. His ideas as to what constituted a mathematical proof were of the most shadowy description. All his results, new or old, right or wrong, had been arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account.
G.H. Hardy, from The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel
880
 
A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
G. H. Hardy,
158
 
Hardy's New Year's Resolutions:
1. Prove the Riemann hypothesis.
2. Make 211 no out in the fourth innings of the last test match at the Oval.
3. Find an argument for the nonexistence of God which shall convince the general public.
4. Be the first man at the top of Mt. Everest.
5. Be proclaimed the first president of the U.S.S.R., of Great Britian, and Germany.
6. Murder Mussolini. 3. Find an argument for the nonexistence of God which shall convince the general public.
4. Be the first man at the top of Mt. Everest.
5. Be proclaimed the first president of the U.S.S.R., of Great Britian, and Germany.
6. Murder Mussolini.
G.H. Hardy, from The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel
882
 
He [Ramanujan] would probably have been a greater mathematician if he had been caught and tamed a little in his youth; he would have discovered more that was new, and that, no doubt, of greater importance. On the other hand he would have been less of a Ramanujan, and more of a European professor, and the loss might have been greater than the gain. He [Ramanujan] would probably have been a greater mathematician if he had been caught and tamed a little in his youth; he would have discovered more that was new, and that, no doubt, of greater importance. On the other hand he would have been less of a Ramanujan, and more of a European professor, and the loss might have been greater than the gain.
G.H. Hardy, from The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel
883
 
The positive integers stand there, a continual and inevitable challenge to the curiosity of every healthy mind.
G.H. Hardy, quoted in Elementary Number Theory by David M. Burton.
905
 
I believe that mathematical reality lies outside of us and that our function is to discover, or observe it, and that the theorems which we prove, and which we describe gradiloquently as our "creations" are simply notes on our observations.
G. H. Hardy,
156
 
The elementary theory of numbers should be one of the very best subjects for early mathematical instruction. It demands very little previous knowledge; its subject matter is tangible and familiar; the processes of reasoning which it employs are simple, general and few; and it is unique among the mathematical sciences in its appeal to natural human curiosity. A month's intelligent instruction in the theory of numbers ought to be twice as instructive, twice as useful, and at least ten times as entertaining as the same amount of ``calculus for engineers.''
G. H. Hardy, quoted in Excursions in Calculus, by Robert Young.
157
 
I have [very rarely] encountered a pupil who could face the simplest problem involving the ideas of infinity, limit, or continuity with a vestige of the confidence with which he could deal with questions of a different character and of far greater intrinsic difficulty.
G.H. Hardy, from The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel
879
 
A continuous curve can fill a portion of space: this is one of the most remarkable facts of set theory, whose discovery we owe to G. Peano.
Hausdorff, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1125
 
If you do not make mistakes then you are not trying.
Coleman Hawkins, quoted in " Practice almost makes perfect" by Jean Mastrangeli, PRIMUS, vol. XI, no. 4, Dec. 2001, pp. 337-47.
915
 
Easy reading is damned hard writing.
Nathaniel Hawthorne, quoted in A Primer of Mathematical Writing by Steven G. Krantz.
740
 
Life is never so bad at its worst that it is impossible to live; it is never so good at it's best that it is easy to live.
Gabriel Heatter,
932
 
The Nothing Nots.
M. Heidegger, quoted in Sweet Reason, by J. Henle and T. Tymoczko.
159
 
Where books are burned, in the end people will be burned.
Heinrich Heine, from the U.S. Holocaust Memorial Museum
969
 
Whenever they burn books they will also, in the end, burn human beings.
Heinrich Heine,
998
 
…the definition of irrational numbers, on which geometric representations have often had a confusing influence…. I take in my definition a purely formal point of view, calling some given symbols numbers, so that the existence of these numbers is beyond doubt.
Heine, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1112
 
I am free because I know that I alone am morally responsible for everything I do.
Robert Heinlein,
844
 
In the natural sciences, then, the object of research is no longer nature as such, but a nature confronted by human questions, and in this sense, here too, man encounters himself.
Werner Heisenberg, Quoted in Radical Constructivism: A Way of Knowing and Learning by Ernst von Glasersfeld.
773
 
In my paper the fact the XY was not equal to YX was very disagreeable to me. I felt this was the only point of difficulty in the whole scheme...and I was not able to solve it.
W. Heisenberg, from Contemporary Abstract Algebra, by J. Gallian.
160
 
At first, I was deeply alarmed. I had the feeling that, through the surface of atomic phenomena, I was looking at the strangely beautiful interior and felt almost giddy at the thought that I now had to probe this wealth of mathematical structures spread out before me.
Werner Heisenberg, quoted in Insights of Genius: Imagery and Creativity in Science and Art, by Arthur I. Miller.
563
 
In this way quantum theory reminds us, as Bohr has put it, of the old wisdom that when searching for harmony in life one must never forget that in the drama of existence we are ourselves both players and spectators. It is understandable that in our scientific relation to nature our own activity becomes very important when we have to deal with parts of nature into which we can penetrate only by using the most elaborate tools.
Werner Heisenberg, from Physics and Philosophy.
1060
 
We have to remember that what we observe is not nature in itself but nature exposed to our method of questioning.
Werner Heisenberg, from Physics and Philosophy.
1059
 
Orr would be crazy to fly more missions and sane if he didn't,but if he was sane he had to fly them. If he flew them he was crazy and didn't have to; but if he didn't want to he was sane and had to.
Joseph Heller, from Words I Wish I Wrote by Robert Fulgham
950
 
All good books are alike in that they are truer than if they had really happened and after you are finished reading one you will feel that all that happened to you and afterwards it all belongs to you; the good and the bad, the ecstasy, the remorse, and sorrow, the people and the places and how the weather was.
Ernest Hemingway,
999
 
With the aid of hyperspace philosophy, Theosophy, fantasies like Abbott’s Flatland, and the science fiction of Wells and others, the fourth dimension had become almost a household word by 1910. Non-Euclidean geometry never achieved such a widespread popularity, in part because it did not lend itself to such a variety of interpretations. Ranging from an ideal Platonic or Kantian reality -- or even Heaven -- to the answer to all of the problems puzzling contemporary science, the fourth dimension could be all things to all people.
Linda Dalrymple Henderson, from The Fourth Dimension and non-Euclidean Geometry in Modern Art.
663
 
When understood in their original context, however, “the fourth dimension” and no-Euclidean geometry are far from being the “scourge of every history of modern painting,” as they have been termed. Instead, these concepts open the door to our understanding more fully the goals of many seminal artists of the early twentieth century.
Linda Dalrymple Henderson, from The Fourth Dimension and non-Euclidean Geometry in Modern Art.
662
 
In most sciences one generation tears down what another has built and what one has established another undoes. In mathematics alone each generation adds a new story to the old structure.
Herman Henkel, from A Mathematical Journey, by S. Gudder.
161
 
The struggle to become a better teacher begins all over again with the advent of each new class.
Martin Henley,
162
 
The function of education has never been to free the mind and the spirit of man, but to bind them; and to the end that the mind and spirit of his children should never escape, Homo Sapiens has employed praise, ridicule, admonition, accusation, mutilation, and even torture to chain them to the culture pattern.
Jules Henry, quoted in Teaching Is..., by Merrill Harmin and Tom Gregory.
163
 
The paradox of the human condition is expressed more in education than elsewhere in human culture, because learning to learn has been and continues to be Homo Sapiens' most formidable evolutionary task... It must also be clear that we will never quite learn how to learn, for since Homo Sapiens is self-changing, and since the more culture changes the faster it changes, man's methods and rate of learning will never quite keep pace with his need to learn.
Jules Henry, quoted in Teaching Is..., by Merrill Harmin and Tom Gregory.
164
 
If you do not expect the unexpected, you will not find it; for it is hard to be sought out, and difficult.
Heraclitus, quoted in Mathematics and the Imagination by Edward Kasner and James Newman.
689
 
I find mathematics an infinitely complex and mysterious world; exploring it is an addiction from which I hope never to be cured.
Reuben Hersh, from The Mathematical Experience
861
 
Very often in mathematics the crucial problem is to recognize and discover what are the relevant concepts; once this is accomplished the job may be more than half done.
I. N. Herstein, from Contemporary Abstract Algebra, by J. Gallian.
165
 
The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver.
I. N. Herstein, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.
166
 
One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than we originally put into them.
Heinrich Hertz,
167
 
... I do not consider myself less ignorant than most people. I have been and still am a seeker, but I have ceased to question stars and books; I have begun to listen to the teachings my blood whispers to me. My story is not a pleasant one; it is neither sweet nor harmonious, as invented stories are; it has the taste of nonsense and chaos, of madness and dreams - like the lives of all men who stop deceiving themselves.
Hermann Hesse, from the Prologue of Demain
1062
 
What Weyl and Brouwer are doing is none other than a revival of Kronecker"s idea. They try to save mathematics by tossing overboard all that provokes concern... They crumble and chop science. If we accepted the reform they propose, then we would run the risk of losing the greatest part of our precious treasure.
David Hilbert, quoted in In Search of Infinity by N.Ya. Vilenkin (translated by Abe Shenitzer).
728
 
No one will expel us from the paradise that Cantor has created.
David Hilbert, quoted in Patterns in Mathematics, by McCowen and Sequeira.
169
 
[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.
David Hilbert, quoted in The History of Mathematics, by D. Burton.
170
 
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
David Hilbert, quoted in Excursions in Calculus, by Robert Young.
171
 
The infinite! No other question has ever moved so profoundly the spirit of man.
David Hilbert,
172
 
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
David Hilbert, quoted in Excursions in Calculus, by R.M. Young.
173
 
In mathematics, as in any scientific research, we find two tendencies present. On the one hand, the tendency toward abstraction seeks to crystallize the logical relations inherent in the maze of material that is being studied, and to correlate the material in a systematic and orderly manner. On the other hand the tendency toward intuitive understanding fosters a more immediate group of the subjects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations.
David Hilbert, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.
168
 
Before beginning [to try to prove Fermat"s Last Theorem] I should have to put in three years of intensive study, and I haven"t that much time to squander on a probable failure.
David Hilbert, quoted in "Fermat"s Last Stand," by Simon Singh and Kenneth A. Ribet, in Scientific American, November 1997.
599
 
With his theorem, which states that a continuous function of a real variable actually attains its least upper and greatest lower bounds, i.e., necessarily possesses a maximum and a minimum, Weierstrass created a tool which today is indispensable to all mathematicians for more refined analytical or arithmetical investigations.
Hilbert, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1114
 
Mathematics is an organism for whose vital strength the indissoluble union of the parts is a necessary condition.
David Hilber, quoted in Mathematical Thought from Ancient to Modern Times by Morris Kline.
1093
 
For it is true, generally speaking, that mathematics is not a popular subject, even though its importance may be generally conceded. The reason for this is to be found in the common superstition that mathematics is but a continuation, a further development, of the fine art of arithmetic, juggling with numbers.
David Hilbert, from Geometry and the Imagination
815
 
This conviction... is a powerful incentive. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no "we shall not know."
David Hilbert, quoted in Bridges to Infinity by Michael Guillen.
535
 
We have already seen that the infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to. Can though about things be so much different from things? Can thinking processes be so unlike the actual process of things? In short, can thought be so far removed from reality? Rather is it not clear that, when we think that we have encountered the infinite in some real sense, we have merely been seduced into thinking so by the fact that we often encounter extremely large and extremely small dimensions in reality?
David Hilbert, quoted in Understanding the Infinite by Shaughan Lavine.
547
 
The conception of the inconceivable [imaginary], this measurement of what not only does not, but cannot exist, is one of the finest achievements of the human intellect. No one can deny that such imaginings are indeed imaginary. But they lead to results grander than any which flow from the imagination of the poet. The imaginary calculus is one of the masterkeys to physical science. These realms of the inconceivable afford in many places our only mode of passage to the domains of positive knowledge. Light itself lay in darkness until this imaginary calculus threw light upon light. And in all modern researches into electricity, magnetism, and heat, and other subtile physical inquiries, these are the most powerful instruments.
Thomas Hill, quoted in Memorabilia Mathematica, by Robert E. Moritz.
175
 
The discoveries of Newton have done more for England and for the race, than has been done by whole dynasties of British monarchs.
Thomas Hill, quoted in The History of Mathematics, by D. Burton.
174
 
A pamphlet is never read more than once, but a song is learned by heart and repeated over and over again.
Joe Hill,
1233
 
The U.S. Bureau of Labor Statistics predicted that OR [Operations Research] will be the third fastest- growing career area for U.S. college graduates from 1990 to 2005. It is also predicted that 100,000 people will be employed as operations research analysts in the United States by the year 2005.
F. Hillier and G. Lieberman, from Introduction to Operations Research.
176
 
Just as any sensitive human being can be brought to appreciate beauty in art, music or literature, so that person can be educated to recognize the beauty in a piece of mathematics. The rarity of that recognition is not due to the "fact" that most people are not mathematically gifted but to the crassly utilitarian manner of teaching mathematics and of deciding syllabi and curricula, in which tedious, routine calculations, learned as a skill, are emphasized at the expense of genuinely mathematical ideas, and in which students spend almost all their time answering someone else"s questions rather than asking their own.
Peter Hilton, from "Review: The Pleasures of Counting", American Mathematical Monthly, vol. 105, no. 5, May 1998.
700
 
No wonder that Churchill described this effort [the British codebreakers working at Bletchley Park] as "Britian"s secret weapon," a weapon far more effective than the buzz bombs and the rockets that Werner von Braun designed for a German victory, a weapon absolutely decisive, in the judgement of many, in winning the war for the Allies.
Peter Hilton, from "Cryptanalysis in World War II -- and Mathematics Education," Mathematics Teacher, Oct. 1984.
575
 
I.J. Good, a wartime colleague and friend, has aptly remarked that it is forunate that the authorities did not know during the war that [Alan] Turing was a homosexual; otherwise, the Allies might have lost the war.
Peter Hilton, from "Cryptanalysis in World War II -- and Mathematics Education," Mathematics Teacher, Oct. 1984.
574
 
Tests tyrannize us -- they tyrannize teachers and children. They loom so large that they distort the teaching curriculum and the teacher"s natural style; they occur so frequently, and with such dire consequences, that they appear to the child (and, perhaps, to the teacher) to be the very reason for learning mathematics.
Peter J. Hilton, from "Avoiding Math Avoidance," in Mathematics Tomorrow, by Lynn Arthur Steen.
555
 
Particularly perverse and absurd is the multiple-choice format. I have been doing mathematics now as a professional for nearly 40 years and have never met a situation (outside of finite group theory!) in which I was faced with a mathematical problem and knew that the answer was one of five possibliites. Moreover if faced, artifically, by such a situation, may approach would, and should, be quite different from that in which I simply had to solve the problem.
Peter J. Hilton, from "Avoiding Math Avoidance," in Mathematics Tomorrow, by Lynn Arthur Steen.
554
 
Mathematics should be fun.
Peter J. Hilton, from "Avoiding Math Avoidance," in Mathematics Tomorrow, by Lynn Arthur Steen.
556
 
When we say that anything is infinite, we signify only that we are not able to conceive the ends and bounds of the thing named.
Thomas Hobbes, quoted in To Infinity and Beyond by Eli Maor.
645
 
To understand this [Torricelli’s Trumpet, a.k.a. Gabriel"s Horn] for sense, it is not required that a man should be a geometrician or a logician, but that he should be mad.
Thomas Hobbes, 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.
620
 
Numbers as realities misbehave.
Douglas Hofstadter, from Godel, Escher, Bach: An Eternal Golden Braid.
719
 
A new and valid idea is worth more than a regiment and fewer men can furnish the former than can command the later.
Oliver Wendel Holmes, Jr, quoted in A Teacher's Treasury of Quotations,
177
 
The best of a book is not the thought which it contains, but the thought which it suggests; just as the charm of music dwells not in the tones but in the echoes of our hearts.
Oliver Wendell Holmes,
1000
 
Your education begins when what is called your education ends.
Oliver Wendell Holmes, Jr.,
1160
 
What a school thinks about its library is a measure of what it feels about education.
Harold Howe,
1001
 
One machine can do the work of fifty ordinary men. No machine can do the work of one extraordinary man.
Elbert Hubbard,
831
 
You should really think of my pictures [of fractals] as a metaphor for all living things.
John Hubbard, from the videotape "The Beauty and Complexity of the Mandelbrot Set".
481
 
What happens to a dream deferred? Does it dry up- Like a raisin in the sun? Or fester like a sore- And then run? Does it stink like rotten meat? Or crust and sugar over- Like a syrupy sweet? Maybe it just sags- Like a heavy load. Or does it explode?
Langston Hughes, (A Dream Deferred).
178
 
In 1953 I realized that the straight line leads to the downfall of mankind. But the straight line has become an absolute tyranny. The straight line is something cowardly drawn with a rule, without thought or feeling; it is the line which does not exist in nature... Any design undertaken with the straight line will be stillborn. Today we are witnessing the triumph of rationalist knowhow and yet, at the same time, we find ourselves confronted with emptiness. An esthetic void, desert of uniformity, criminal sterility, loss of creative power. Even creativity is prefabricated. We have become impotent. We are no longer able to create. That is our real illiteracy.
Friedensreich Hundertwasser, quoted in The Beauty of Fractals, by H.O. Peitgen and P.H. Richter.
478
 
Research is formalized curiosity.
Zora Neale Hurston,
1023
 
The method of fluxions is probably one the greatest, most subtle, and sublime discoveries of any age; it opens a new world to our view, and extends our knowledge, as it were, to infinity; carrying us beyond the bounds that seemed to have been prescribed to the human mind, at least infinitely beyond those to which the ancient geometry was confined.
Charles Hutton, quoted in Memorabilia Mathematica, by R. Moritz.
179
 
The rung of a ladder was never meant to rest upon, but only to hold a man's foot long enough to enable him to put the other somewhat higher.
Thomas Huxley, quoted Essentials of Mathematics by Margie Hale.
955
 
That men do not learn very much from the lessons of history is the most important of all the lessons that history has to teach.
Aldous Huxley, from "See no evil, hear no evil, speak no evil" in Notices of the American Mathematical Society, vol. 45, no. 9, October 1998.
744
 
The greatest tragedy of science - the slaying of a beautiful hypothesis by an ugly fact.
Thomas Huxley,
180
 
Sooner or later, false thinking brings wrong conduct.
Julian Huxley,
561
 
If we evolved a race of Isaac Newtons, that would not be progress. For the price Newton had to pay for being a supreme intellect was that he was incapable of friendship, love, fatherhood, and many other desirable things. As a man he was a failure; as a monster he was superb.
Aldous Huxley, from Interview with J. W. N. Sullivan, Contemporary Mind, London, 1934
860
 
…you [Leibniz] will not deny that you have discovered a very remarkable property of the circle [pi/4 = 1 - 1/3 + 1/5 - 1/7 + ...], which will forever be famous among geometers.
Huygens, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1102
 

99 quotes found and displayed.