c2p-cmd/Good-Quotes-Authors huggingface dataset:
I was impressed by the delicate weaving of the numbers. No matter how carefully you unraveled a thread, a single moment of inattention could leave you stranded, with no clue what to do next. In all his years of study, the Professor had managed to glimpse several pieces of the lace. I could only hope that some part of him remembered the exquisite pattern.
— Yōko Ogawa, The Housekeeper and the Professor
Mathematicians call it “the arithmetic of congruences.” You can think of it as clock arithmetic. Temporarily replace the 12 on a clock face with 0. The 12 hours of the clock now read 0, 1, 2, 3, … up to 11. If the time is eight o’clock, and you add 9 hours, what do you get? Well, you get five o’clock. So in this arithmetic, 8 + 9 = 5; or, as mathematicians say, 8 + 9 ≡ 5 (mod 12), pronounced “eight plus nine is congruent to five, modulo twelve.
— John Derbyshire, Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
I only know that when I study mathematics, I transport myself to another world, a world of exquisite beauty and truth. And in that world I am the person I like to be.
— Dora Musielak
…numerical precision is the very soul of science, and its attainment affords the best, perhaps the only criterion of the truth of theories and the correctness of experiments.
— D'Arcy Wentworth Thompson, On Growth and Form
Therefor I doubt not but, if it had been a thing contrary to any man’s right of dominion, or to the interest of men that have dominion, ‘that the three angles of a triangle should be equal to two angles of a square,’ that doctrine should have been, if not disputed, yet by the burning of all books of geometry suppressed, as far as he whom it concerned was able.
— Thomas Hobbes
ZERO and Infinity both are very difficult to understand and explain but at the same time both are key assumption of Mathematics...
— Brajesh Kumar
Newton was asked as a mathematician, not as a moralist. He replied 'Gentlemen, in applied mathematics, you must describe your unit.
— Isabel Paterson, God of the Machine
Mathematics is Open Source.
— Vishal Salgotra
Children must be taught mathematics well in anywhere under every condition at every age and so we can have more rational, more logical societies!
— Mehmet Murat ildan
Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..."Klapaucius thought, and thought some more. Finally he nodded and said:"Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit.""Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming:Come, let us hasten to a higher plane,Where dyads tread the fairy fields of Venn,Their indices bedecked from one to n,Commingled in an endless Markov chain!Come, every frustum longs to be a cone,And every vector dreams of matrices.Hark to the gentle gradient of the breeze:It whispers of a more ergodic zone.In Reimann, Hilbert or in Banach spaceLet superscripts and subscripts go their ways.Our asymptotes no longer out of phase,We shall encounter, counting, face to face.I'll grant thee random access to my heart,Thou'lt tell me all the constants of thy love;And so we two shall all love's lemmas prove,And in bound partition never part.For what did Cauchy know, or Christoffel,Or Fourier, or any Boole or Euler,Wielding their compasses, their pens and rulers,Of thy supernal sinusoidal spell?Cancel me not--for what then shall remain?Abscissas, some mantissas, modules, modes,A root or two, a torus and a node:The inverse of my verse, a null domain.Ellipse of bliss, converge, O lips divine!The product of our scalars is defined!Cyberiad draws nigh, and the skew mindCuts capers like a happy haversine.I see the eigenvalue in thine eye,I hear the tender tensor in thy sigh.Bernoulli would have been content to die,Had he but known such a^2 cos 2 phi!
— Stanisław Lem, The Cyberiad
Where there is no mathematics, there is no freedom.
— Edward Frenkel, Love and Math: The Heart of Hidden Reality
It was as though applied mathematics was my spouse, and pure mathematics was my secret lover.
— Edward Frenkel, Love and Math: The Heart of Hidden Reality
Furious, the beast writhed and wriggled its iterated integrals beneath the King’s polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann’s Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out, fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets—but the beast, prepared for this, lowered its horns and—wham!!—the pencils flew like mad through transcendental functions and double eigentransformations, and when at last the beast closed in and the King was down and out for the count, the constructors jumped up, danced a jig, laughed and sang as they tore all their papers to shreds, much to the amazement of the spies perched in the chandelier-—perched in vain, for they were uninitiated into the niceties of higher mathematics and consequently had no idea why Trurl and Klapaucius were now shouting, over and over, “Hurrah! Victory!!
— Stanisław Lem, The Cyberiad
If you divide something that is essentially one, you will end up with imaginary infinite numbers.
— Toba Beta, Master of Stupidity
So they rolled up their sleeves and sat down to experiment -- by simulation, that is mathematically and all on paper. And the mathematical models of King Krool and the beast did such fierce battle across the equation-covered table, that the constructors' pencils kept snapping. Furious, the beast writhed and wriggled its iterated integrals beneath the King's polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann's Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F_1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets—but the beast, prepared for this, lowered its horns and—wham!!—the pencils flew like mad through transcendental functions and double eigentransformations, and when at last the beast closed in and the King was down and out for the count, the constructors jumped up, danced a jig, laughed and sang as they tore all their papers to shreds, much to the amazement of the spies perched in the chandelier—perched in vain, for they were uninitiated into the niceties of higher mathematics and consequently had no idea why Trurl and Klapaucius were now shouting, over and over, "Hurrah! Victory!!
— Stanisław Lem, The Cyberiad
This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.
— Emil Artin
For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view.
— Louis Poinsot
The first successes were such that one might suppose all the difficulties of science overcome in advance, and believe that the mathematician, without being longer occupied in the elaboration of pure mathematics, could turn his thoughts exclusively to the study of natural laws.
— Joseph Louis François Bertrand
Mathematics is the science which draws necessary conclusions.
— Benjamin Peirce, Linear Associative Algebra
Patience is my virtue, but only in Math, Daddy,” - Ashley
— Ryanne Salve, She's Older Than Me
Littlewood, on Hardy's own estimate, is the finest mathematician he has ever known. He was the man most likely to storm and smash a really deep and formidable problem; there was no one else who could command such a combination of insight, technique and power.
— Henry Hallett Dale
To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.
— Paul Cohen
[Benjamin Peirce's] lectures were not easy to follow. They were never carefully prepared. The work with which he rapidly covered the blackboard was very illegible, marred with frequent erasures, and not infrequent mistakes (he worked too fast for accuracy). He was always ready to digress from the straight path and explore some sidetrack that had suddenly attracted his attention, but which was likely to have led nowhere when the college bell announced the close of the hour and we filed out, leaving him abstractedly staring at his work, still with chalk and eraser in his hands, entirely oblivious of his departing class.
— William Elwood Byerly
Through the judicious employment of symbols, diagrams, and calculations, mathematics enables us to acquire significant facts about extremely significant things (universal laws, even), not by first forging out into the cosmos with teams of scientists, but rather from the comforts and confines of coffee tables in our living rooms! p. 72
— G. Arnell Williams, How Math Works: A Guide to Grade School Arithmetic for Parents and Teachers
The issue, then, is not, What is the best way to teach? but, What is mathematics really all about?... Controversies about…teaching cannot be resolved without confronting problems about the nature of mathematics.
— Reuben Hersh
He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixteens. The numbers formed up and marched past his brain in terrified obedience. Division and multiplication were discovered. Algebra was invented and provided an interesting diversion for a minute or two. And then he felt the fog of numbers drift away, and looked up and saw the sparkling, distant mountains of calculus.
— Terry Pratchett, Men at Arms
Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.
— Andrew John Wiles
I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind.(Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.)
— Andrew John Wiles
Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds.
— Antoine Thomson d'Abbadie
Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.
— Gian-Carlo Rota
And I'll go even further and say that mathematics, this art of abstract pattern-making — even more than storytelling, painting, or music - is our most quintessentially human art form. This is what our brains do, whether we like it or not. We are biochemical pattern-recognition machines and mathematics is nothing less than the distilled essence of who we are.
— Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form
How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.
— Clifford A. Truesdell
Although some of her passages seek to persuade the reader of the meaninglessness and marginalization of the mathematics, Hayles is content to use mathematics as a means for understanding Borges, perhaps in the same way a sponge riddled with holes is useful in sopping up fluid reality.
— Bloch William Goldbloom
[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.
— G.H. Hardy, A Mathematician's Apology
The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon... when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms.
— Joseph Fourier
The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.
— Felix Klein, Elementary Mathematics from an Advanced Standpoint: Geometry
...I guess I can put two and two together.""Sometimes the answer's four," I said, "and sometimes it's twenty-two...
— Dashiell Hammett, The Thin Man
We are not told, or not told early enough so that it sinks in, that mathematics is a language, and that we can learn it like any other, including our own. We have to learn our own language twice, first when we learn to speak it, second when we learn to read it. Fortunately, mathematics has to be learned only once, since it is almost wholly a written language.
— Mortimer J. Adler, How to Read a Book: The Classic Guide to Intelligent Reading
Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.
— Hermann Weyl, Levels of Infinity: Selected Writings on Mathematics and Philosophy
People joke, in our field, about Pythagoras and his religious cult based on perfect geometry and other abstract mathematical forms, but if we are going to have religion at all then a religion of mathematics seems ideal, because if God exists then what is He but a mathematician?
— Matt Haig, The Humans
Schools were started to train human talents... The Guild... emphasizes almost pure mathematics. Bene Gesserit performs... politics. The original Bene Gesserit school was directed by those who saw the need of a thread of continuity in human affairs. They saw there count be no such continuity without separating human stock from animal stock - for breeding purposes.
— Frank Herbert, Dune
It (proof by contradiction) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
— G.H. Hardy
I entered Princeton University as a graduate student in 1959, when the Department of Mathematics was housed in the old Fine Hall. This legendary facility was marvellous in stimulating interaction among the graduate students and between the graduate students and the faculty. The faculty offered few formal courses, and essentially none of them were at the beginning graduate level. Instead the students were expected to learn the necessary background material by reading books and papers and by organising seminars among themselves. It was a stimulating environment but not an easy one for a student like me, who had come with only a spotty background. Fortunately I had an excellent group of classmates, and in retrospect I think the "Princeton method" of that period was quite effective.
— Phillip A. Griffiths
Mathematics is a terrible calling. It’s as merciless as gravity. It swallows the soul. There’s a point near a black hole called the last stable orbit. Once you drop below that radius, no force in the universe can stop you falling all the way in. That’s what happened to your mother – she swam too close to theory, fell below the last stable orbit.
— Alastair Reynolds, On the Steel Breeze
Mathematics should be studied if only for that it puts the mind in order.
— Mikhail Lomonosov
PHI is one H of a lot cooler than PI!
— Dan Brown, The Da Vinci Code
Who rebels with mathematics?
— Khaled Hosseini, And the Mountains Echoed
Of course, reading novels was just another form of escape. As soon as he closed their pages he had to come back to the real world. But at some point Tengo noticed that returning to reality from the world of a novel was not as devastating a blow as returning from the world of mathematics. Why should that have been? After much deep thought, he reached a conclusion. No matter how clear the relationships of things might become in the forest of story, there was never a clear-cut solution. That was how it differed from math. The role of a story was, in the broadest terms, to transpose a single problem into another form. Depending on the nature and direction of the problem, a solution could be suggested in the narrative. Tengo would return to the real world with that suggestion in hand. It was like a piece of paper bearing the indecipherable text of a magic spell. At times it lacked coherence and served no immediate practical purpose. But it would contain a possibility. Someday he might be able to decipher the spell. That possibility would gently warm his heart from within.
— Haruki Murakami, 1Q84
The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.
— G.H. Hardy, A Mathematician's Apology
Mathematics effectively began when a few Greek friends got together to talk about numbers and lines and angles.
— C.S. Lewis, The Four Loves
Topology is destiny,' he said, and put the drawers on. One leg at a time.
— Neal Stephenson, Anathem
God made the integers
—  all the rest is the work of Man.
Tengo's lectures took on uncommon warmth, and the students found themselves swept up in his eloquence. He taught them how to practically and effectively solve mathematical problems while simultaneously presenting a spectacular display of the romance concealed in the questions it posed. Tengo saw admiration in the eyes of several of his female students, and he realized that he was seducing these seventeen- or eighteen-year-olds through mathematics. His eloquence was a kind of intellectual foreplay. Mathematical functions stroked their backs; theorems sent warm breath into their ears.
— Haruki Murakami, 1Q84
Just as all things speak about God to those that know Him, and reveal Him to those that love Him, they also hide Him from all those that neither seek nor know Him.
— Blaise Pascal
A term meant to convey a person's inability to make sense of the numbers that run their lives.
— Douglas R. Hofstadter
The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression,more exact,compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex world wide states that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write.
— H.G. Wells
The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated ... The importance of this invention is more readily appreciated when one considers that it was beyod the two greatest men of antiquity, Archimedes and Apollonius.
— Pierre-Simon Laplace
I hate math. It's hard, it's stupid, and it's nature's way of separating spinsters from women who end up breeding.
— Douglas Coupland, Highly Inappropriate Tales for Young People
Adaptability to change is itself a hallmark of successful education.
— Peter Hilton, Mathematics: From the Birth of Numbers
Anything you try to quantify can be divided into any number of "anythings," or become the thing - the unit - itself. And what is any number, itself, but just another unit of measurement? What is a 'six' but two 'threes', or three 'twos'...half a 'twelve', or just six 'ones' - which are what? (attrib: F.L. Vanderson)
— Mort W. Lumsden, Citations: A Brief Anthology
Physical reality does not require that we be pleased with its mechanism
—  we must see the implications of a theory for what they are and not for what we would like them to be.
a fresh mind adds a better mathematic ability #Bweqy
— Brendon
As a teacher, Tengo pounded into his students' heads how voraciously mathematics demanded logic. Here things that could not be proven had no meaning, but once you had succeeded in proving something, the world's riddles settled into the palm of your hand like a tender oyster.
— Haruki Murakami, 1Q84
Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it need only patience to ransack; it is not a mine, whose treasures may take long to reduce to possessions, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined: it is limitless as the space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer's gaze; it is as incapable of being restricted within assigned boundaries or being reduced to definitions of permanent validity, as the consciousness, the life, which seems to slumber in each monad, in every atom of matter, in each leaf and bud and cell, and is forever ready to burst forth into new forms of vegetable and animal existence.
— James Joseph Sylvester
The physical method becomes a philosophy when it asserts there is no higher knowledge than the empirical knowledge of scientific phenomena. The mathematical method becomes a philosophy when it asserts that some higher knowledge is needed to explain scientific facts, and that higher knowledge is mathematics.
— Fulton J. Sheen, Philosophy of Science
Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
— Bertrand Russell, A History of Western Philosophy
They shouldn't be allowed to teach math so early in the morning.
— Kendare Blake, Anna Dressed in Blood
Mathematicians deal with large numbers sometimes, but never in their income.
— Isaac Asimov, Prelude to Foundation
. . . the world in which we live has an increasing number of feedback loops, causing events to be the cause of more events (say, people buy a book because other people bought it), thus generating snowballs and arbitrary and unpredictable planet-wide winner-take-all effects.
— Nassim Nicholas Taleb, The Black Swan: The Impact of the Highly Improbable
It appeared that way, Lawrence, but this raised the question of was mathematics really true or was it just a game played with symbols? In other words—are we discovering Truth, or just wanking?
— Neal Stephenson, Cryptonomicon
Luck is the grand equalizer.
— Nassim Nicholas Taleb
Is everyone with one face called a Milo?""Oh no," Milo replied; "some are called Henry or George or Robert or John or lots of other things.""How terribly confusing," he cried. "Everything here is called exactly what it is. The triangles are called triangles, the circles are called circles, and even the same numbers have the same name. Why, can you imagine what would happen if we named all the twos Henry or George or Robert or John or lots of other things? You'd have to say Robert plus John equals four, and if the four's name were Albert, things would be hopeless.""I never thought of it that way," Milo admitted."Then I suggest you begin at once," admonished the Dodecahedron from his admonishing face, "for here in Digitopolis everything is quite precise.
— Norton Juster, The Phantom Tollbooth
But that can never be," said Milo, jumping to his feet."Don't be too sure," said the child patiently, "for one of the nicest things about mathematics, or anything else you might care to learn, is that many of the things which can never be, often are. You see," he went on, "it's very much like your trying to reach Infinity. You know that it's there, but you just don't know where — but just because you can never reach it doesn't mean that it's not worth looking for.
— Norton Juster, The Phantom Tollbooth
Music is the pleasure the human mind experiences from counting without being aware that it is counting.
— M.A. Nowak, SuperCooperators: Altruism, Evolution, and Why We Need Each Other to Succeed
And, most important of all," added the Mathemagician, "here is your own magic staff. Use it well and there is nothing it cannot do for you."He placed in Milo's breast pocket a small gleaming pencil which, except for the size, was much like his own.
— Norton Juster, The Phantom Tollbooth
In his school, Bertrand Russell thought it was better if they had the sex, so they could give their undivided attention to mathematics, which was the main thing.
— Paul Goodman, Growing Up Absurd
The language of categories is affectionately known as "abstract nonsense," so named by Norman Steenrod. This term is essentially accurate and not necessarily derogatory: categories refer to "nonsense" in the sense that they are all about the "structure," and not about the "meaning," of what they represent.
— Paolo Aluffi, Algebra: Chapter 0
It is the definition of the word 'object' which destroys all religions.
— Bill Gaede
A brick can be used to represent the zero probability of this book being any good.
— Amy Sommers, A bit of rubbish about a Brick and a Blanket
Teaching Ramanujan was like writing on a blackboard covered with excerpts from a more interesting lecture.
— Lawrence Young
It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true.
— Herbert S. Gaskill, Foundations of Analysis: The Theory of Limits
Formal mathematics is nature's way of letting you know how sloppyyour mathematics is.
— Leslie Lamport, Specifying Systems: The Tla+ Language and Tools for Hardware and Software Engineers
If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos.
— Gary William Flake, The Computational Beauty of Nature - Computer Explorations of Fractals, Chaos, Complex Systems & Adaption (Paper)
In the field of Egyptian mathematics Professor Karpinski of the University of Michigan has long insisted that surviving mathematical papyri clearly demonstrate the Egyptians' scientific interest in pure mathematics for its own sake. I have now no doubt that Professor Karpinski is right, for the evidence of interest in pure science, as such, is perfectly conclusive in the Edwin Smith Surgical Papyrus.
— James Henry Breasted, The Edwin Smith Surgical Papyrus, Vol 1: Hieroglyphic Transliteration, Translation and Commentary
One can be enlightened about proofs as well as theorems. Without enlightenment, one is merely reduced to memorizing proofs. With enlightenment about a proof, its flow becomes clear and it can become an item of astonishing beauty. In addition, the need to memorize disappears because the proof has become part of your soul.
— Herbert S. Gaskill, Foundations of Analysis: The Theory of Limits
You will never have a greater or lesser dominion than that over yourself...the height of a man's success is gauged by his self-mastery
—  the depth of his failure by his self-abandonment. ...And this law is the expression of eternal justice. He who cannot establish dominion over himself will have no dominion over others.
When an individual is motivated by great and powerful convictions of truth, then he disciplines himself, not because of the demands of the church, but because of the knowledge within his heart
— Gordon B. Hinckley
One painful duty fulfilled makes the next plainer and easier.
— Helen Keller, The Story of My Life
Do not bite at the bait of pleasure till you know there is no hook beneath it.
— Thomas Jefferson
In practice we always base our preparations against an enemy on the assumption that his plans are good; indeed, it is right to rest our hopes not on a belief in his blunders, but on the soundness of our provisions. Nor ought we to believe that there is much difference between man and man, but to think that the superiority lies with him who is reared in the severest school.
— Thucydides
Discipline isn't a dirty word. Far from it. Discipline is the one thing that separates us from chaos and anarchy. Discipline implies timing. It's the precursor to good behavior, and it never comes from bad behavior. People who associate discipline with punishment are wrong: with discipline, punishment is unnecessary.
— Buck Brannaman, The Faraway Horses: The Adventures and Wisdom of One of America's Most Renowned Horsemen
Good habits are worth being fanatical about.
— John Irving
Those who have nothing have only their discipline.
— Alain Badiou
It is time to reverse this prejudice against conscious effort and to see the powers we gain through practice and discipline as eminently inspiring and even miraculous.
— Robert Greene, Mastery
Just as a woman's eyes are the mirrors of her soul, her shapely bottom is her seat of learning.
— Russ  Michael
The wooden hairbrush has two practical uses, the bristle side to be used on her silken locks, and the harsh, wooden side to be used on her shapely seat of learning
— Russ  Michael
It was more than just material prosperity. America in 1960 was a country where restraint and boundaries were the natural conditions in all arenas. People married younger and stayed married; even with those added twenty-eight million, there were fewer divorces in 1960 than there had been a decade earlier. People did not have children unless they were married—only 2.5 percent of children were born out of wedlock, though the number in black households was disturbingly high—some 20 percent.
— Jeff Greenfield, Then Everything Changed: Stunning Alternate Histories of American Politics: JFK, RFK, Carter, Ford, Reagan
Alex understood such discipline. He knew the rarity of it, and the cost. And on the rare occasions when he happened to touch her, he did wonder what else she might have been, if she had not been so determined to be typical.
— Meredith Duran, Wicked Becomes You
I do not have it in for relativism. In many respects I find it a fascinating, even attractive, alternative. It engenders epistemological humility, defeats an arrogant pomposity in belief, even promotes a sort of democratic ideal in matters of knowledge. Perhaps its most comforting feature is that it requires no hard work at all in the matter of justifying beliefs.
— David L. Wolfe, Epistemology: The Justification Of Belief
Trams and disciplined people always reach their destinations!
— Mehmet Murat ildan
Now public business takes up so much of my time that I must get time a Sundays or a nights to look after my own matters.
— Samuel Pepys, The Diary of Samuel Pepys: A Selection
Men need discipline! Countries need discipline! World needs discipline! He who wants to be successful needs discipline! Be a man of discipline!
— Mehmet Murat ildan
I'd been very influenced by what I'd seen in Japan. Part of what I greatly admired there - and part of what we were lacking in our factory - was as sense of teamwork and discipline. If we didn't have the discipline to keep that place spotless, then we weren't going to have the discipline to keep all those machines running.
— Walter Isaacson, Steve Jobs
When you discipline a child, you prepare them for a responsible and accountable adulthood.
— Gift Gugu  Mona
Discipline is the great equalizer. If a young woman is beautiful but has no discipline, she will lose her looks as she grows older. If a plain woman is disciplined she will undoubtedly become more beautiful with time.
— Sophia Loren
It is one thing to praise discipline, and another to submit to it.
— Miguel de Cervantes Saavedra, The Dialogue of the Dogs
Discipline yourself to do what is necessary or you won't acquire the necessary...
— Stephen Magnus
Make yourself a slave to good habits
— Dan John, Never Let Go: A Philosophy of Lifting, Living and Learning
I know you see me as some crazy old bitch nagging at you," she said, "but you forget the reason I ride you so hard and give you so much shit is because I love you. Everything I have ever done I've done from a place of love. If I don't punish you, the world will punish you even worse. The world doesn't love you. If the police get you, the police don't love you. When I beat you, I'm trying to save you. When they beat you, they're trying to kill you.
— Trevor Noah, Born a Crime: Stories From a South African Childhood
Life demands discipline in order to succeed in it.
— ANIKOR Daniel
One of the major requirement for life's success is discipline.
— ANIKOR Daniel
I had a plan of action that I was going to run by Will.  He could run it up the flagpole, but I wasn’t asking permission.  My mind was made up.  I was going to The Confessional tonight too.  If she wanted atonement, I’d be happy to give it to her.
— kimber nilsson
Fasting may not be as easy as feasting, but after a while it is not too different. Both are extremes. It is not hard to go the extreme way, but what is really difficult is neither to fast nor to feast, but to be moderate in everything we do.
— Eknath Easwaran, The End of Sorrow
With practice, you build the road to accomplish your goals. Excellence lives in attention to detail. Give your all, all the time. Don't save anything for the walk home.
— Ethan Hawke, Rules for a Knight
If we don't discipline ourselves, the world will do it for us.
— William Feather
Well, we come here to the Fastnesses mostly to learn what questions not to ask.""But you're the Answerers!""You don't see yet, Genry, why we perfected and practice Foretelling?""No––""To exhibit the perfect uselessness of knowing the answer to the wrong question.
— Ursula K. Le Guin, The Left Hand of Darkness
Intellectual transcendence is achieved with the leap out of where you know too much, to where you have a lot to learn; then, facing the odds and turning the latter into the starting point of a new leap to where discipline outweighs all.
— Majd Bassel Ostah AlHusseini
Oddly, with discipline, structure, and order, you will find freedom, anything is possible. Without it, locating your saddle may take all morning.
— Ethan Hawke, Rules for a Knight
Discipline is critical to proper preparation.
— Ken Marlin
For five years Isaac had been working eighteen hours a day.
— John Hudson Tiner, Isaac Newton: Inventor, Scientist, and Teacher
Don't be quick to leave the class of discipline
—  you shall only live to remember the last lesson.
I discipline my mind to see past distractions, to scrutinize deceptive tendencies and to pay careful attention to details whether I am conversing with others or I’m just a passive observer.
— Carlos Wallace, The Other 99 T.Y.M.E.S: Train Your Mind to Enjoy Serenity
God will never disappoint us. He loves us and has only one purpose for us : holiness, which in His kingdom equals joy.
— Elisabeth Elliot, Discipline: The Glad Surrender
Do first what you don’t want to do most.
— Clifford Cohen
If deep in our hearts we suspect that God does not love us and cannot manage our affairs as well as we can, we certainly will not submit to His discipline.
— Elisabeth Elliot, Discipline: The Glad Surrender
The true extent of one's discipline is revealed when motivation runs out
— Elias Tan JS
It is nothing short of a transformed vision of reality that is able to see Christ as more real than the storm, love more real than hatred, meakness more real than pride, long-suffering more real than annoyance, holiness more real than sin. - Discipline
— Elizabeth Elliot
ability is of no value without discipline. Winning has no style or substance without humility.
— Andrew Critchley, Dublin in the Rain
The general consensus seemed to be that if prayer didn't take care of the problem, a belt to the ass and the threat of reform school would.
— Steven Norton, Fly Away Days
Don't break your discipline, form it!
— J.R. Rim
Good writing like good sex requires discipline.
— Chloe Thurlow, The Fifty Shades of Grey Phenomena
You’re smarter than you look,’ I say to Raffe.‘But not as smart as he thinks,’ says Howler.‘I can see discipline has broken down during your vacation,’ says Raffe.‘Yeah, it’s all that lounging on the beach with nothing to do but drink and watch women.
— Susan Ee, End of Days
Once you bid farewell to discipline you say goodbye to success
— Alex Ferguson, Leading
You don't want captains in the army who know too much or think too much.
— Robert Graves, Claudius the God and His Wife Messalina
Discipline is needed in our lifestyle.
— Sunday Adelaja
Had we not decided to perform this as gracefully as a dancer’s leap? But we turned it into a dinosaur’s dance party!
— Pawan Mishra, Coinman: An Untold Conspiracy
Discipline at the office had long been enforced by use of three methods: the meeting of the first kind, the meeting of the second kind, and the meeting of the third kind.
— Pawan Mishra, Coinman: An Untold Conspiracy
Onde you bid farewell to discipline you day goodbye to success
— Alex Ferguson, Leading
Live a life of discipline and live a life of celebration.
— Sunday Adelaja
Discipline is needed in our pursuit.
— Sunday Adelaja
If rhetoric study was the military, grammar teachers would be the drill sergeants.
— T.K. Naliaka, Iron Mixed with Sand Salt without Memory
Discipline is needed in our temperance.
— Sunday Adelaja
Self-discipline is the cornerstone of any endeavor.
— Bohdi Sanders, Martial Arts Wisdom: Quotes, Maxims, and Stories for Martial Artists and Warriors
Awards and ceremonies are all an applause of discipline.
— Sunday Adelaja
The harder the struggle, the bigger the gain. The important thing is to stick with it, repetitively and consistently.
— Mara Schiavocampo, Thinspired: How I Lost 90 Pounds -- My Plan for Lasting Weight Loss and Self-Acceptance
Without discipline you would not go far in life.
— Sunday Adelaja
Discipline is when we limit ourselves, put borders around ourselves.
— Sunday Adelaja
Life does not despise the discipline.
— Sunday Adelaja
The Olympic Games is a celebration of discipline.
— Sunday Adelaja
Discipline is a fast track to elevation in life.
— Sunday Adelaja
When you give the supply of discipline, life becomes easy for you.
— Sunday Adelaja
All forms of achievements are all a triumph of discipline.
— Sunday Adelaja
Discipline is one of the basic and primary requirements for success in life.
— Sunday Adelaja
No one makes it big without discipline.
— Sunday Adelaja
Discipline is required in all human endeavours.
— Sunday Adelaja
A study of the lives of successful people would show that all successful people are disciplined people.
— Sunday Adelaja
Discipline is a demand of life.
— Sunday Adelaja
Discipline is when we delay our gratifications.
— Sunday Adelaja
Discipline is needed in our eating habit.
— Sunday Adelaja
Although this may be a most difficult thing, if one will do it, it can be done. There is nothing that one should suppose cannot be done.
— Tsunetomo Yamamoto, Hagakure: The Book of the Samurai
Throughout your life advance daily, becoming more skillful than yesterday, more skillful than today. This is never-ending.
— Tsunetomo Yamamoto
One should every day think over and make an effort to implant in his mind the saying, "At that time is right now." It is said that it is strange indeed that anyone is able to pass through life by one means or another in negligence.
— Tsunetomo Yamamoto
Everything we encounter today is used by God to prepare us for tomorrow. he wastes no trials, withholds no blessings, nor does he hold back on the discipline of his soldiers. All He does prepares us for future usefulness as vessels of honor.
— Rick Lambert, Polycarp, a destroyer of our gods
Just like it is in the life of an individual or an organization, one of the catalysts of progress is discipline and order.
— Sunday Adelaja
It was not about physical strength, Wit reminded himself. It was 90 percent mental, 10 percent physical. That's what the SEAL instructors were looking for: men and women who could disregard the pleadings of the body. Pain was nothing, sleep was nothing. What was chaffed skin, wrecked muscles, bleeding sores? The body chooses to be sore. The body chooses to be exhausted. But the SEAL mind rejects it. The SEAL mind commands the body, not the other way around.
— Orson Scott Card, Earth Awakens
Faithfulness to one’s word is one of the principles of discipline
— Sunday Adelaja
You cannot build a strong team unless you teach your people discipline.
— Sunday Adelaja
When building your team look for people who are disciplined even before they came to the Lord.
— Sunday Adelaja
Malaria prevention and eradication should be inspired by General George Patton’s advice: “A good plan executed violently today is better than a perfect plan in a week.” In this war of attrition, millions of people will be lost while waiting on researchers to finally emerge triumphant from their labs with the perfect malaria cure; yet meanwhile, there are plenty of time-proven, practical actions that individuals, families and communities can do today with what is already in hand that can decisively defeat malaria transmission if applied with vigor and disciplined consistency.
— T.K. Naliaka
Good units walk a thin line between indiscipline and ineffectiveness. Ignore the rules too often and you’ve got a mob, but enforce the rules too strictly and you’ve got a herd.
— Henry V. O'Neil, Orphan Brigade
Don't you just love it when you're disciplining your kids and God whispers, "This is good. I hope you're listening so you can apply this same truth to your life.
— Lysa TerKeurst
I'm not a parent myself, but I think the best solution at this point is to slap that child across the face. It won't stop crying, but at least now it'll be doing it for a good reason.
— David Sedaris
I no longer fear the pain...I fear no release from this torture...knowing that I've hurt him and he can't forgive me...that he won't be able to make me his good girl again.
— Willow Madison, True Beginnings
It was an inflexible maxim of Roman discipline that good soldier should dread his own officers far more than the enemy
— Edward Gibbon, The Decline and Fall of the Roman Empire
The artist has a duty to be calm. He has no right to show his emotion, his involvement, to go pouring it all out at the audience. Any excitement over a subject must be sublimated into an Olympian calm of form. That is the only way in which an artist can tell of the things that excite him.
— Andrei Tarkovsky
What? Don't you want a girl who can talk dirty to you?"His look only hardens. "No, Lucy. I'm serious. I won't tolerate that from you." He doesn't look away and I feel that heat in the pit of my stomach, spreading down again. "Well...I've heard you curse before..." I swallow loudly, but keep his gaze."I'm a man.
— Willow Madison, True Nature
[Discipline i]t’s the ability to overcome the urge to grab the bright and shiny and interesting to finish what you’ve started.
— Kristine Kathryn Rusch
...the quickest, efficient, least expensive way to educate a man is to make it painful for him when he is wrong, the same as with any other animal.
— James  Jones
If there is one thing above all others a successful man should know, it is when to stop.
— Coenus
Anyone can stay up late, but only the disciplined can get up early.
— Benjamin Lotter