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- Page 124
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
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
Mathematics effectively began when a few Greek friends got together to talk about numbers and lines and angles.
C.S. Lewis
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
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
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
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
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
Adaptability to change is itself a hallmark of successful education.
Peter Hilton
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
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
[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
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 return to the general analysis of the Rosicrucian outlook. Magic was a dominating factor, working as a mathematics-mechanics in the lower world, as celestial mathematics in the celestial world, and as angelic conjuration in the supercelestial world. One cannot leave out the angels in this world view, however much it may have been advancing towards the scientific revolution. The religious outlook is bound up with the idea that penetration has been made into higher angelic spheres in which all religions were seen as one; and it is the angels who are believed to illuminate man's intellectual activities.In the earlier Renaissance, the magi had been careful to use only the forms of magic operating in the elemental or celestial spheres, using talismans and various rituals to draw down favourable influences from the stars. The magic of a bold operator like Dee, aims beyond the stars, aims at doing the supercelestial mathematical magic, the angel-conjuring magic. Dee firmly believed that he had gained contact with good angels from whom he learned advancement in knowledge. This sense of close contact with angels or spiritual beings is the hallmark of the Rosicrucian. It is this which infuses his technology, however practical and successful and entirely rational in its new understanding of mathematical techniques, with an unearthly air, and makes him suspect as possibly in contact, not with angels, but with devils.
Frances A. Yates
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
…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
In adolescence, I hated life and was continually on the verge of suicide, from which, however, I was restrained by the desire to know more mathematics.
Bertrand Russell
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations’, are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards.
G H Hardy
Only dead mathematics can be taught where competition prevails: living mathematics must always be a communal possession.
Mary Everest Boole
Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence.
Keith J. Devlin
the theorem of incompleteness . . . [shows] there is nothing on this level of existence that can fully explain this level of existence.
Pat Cadigan
Mathematics takes us still further from what is human into the region of absolute necessity, to which not only the actual world, but ever possible world, must conform.
Bertrand Russell
What did we know? This was early days. We had no idea what was out there. How dangerous it might be. It was just a school maths problem. They never asked that in the exams, did they? Like, “If John walks at three miles an hour from London to Brighton, and he's attacked by rabid grown-ups four times, and they bite his right leg off, how long will it take him to bleed to death?
Charlie Higson
The best mathematics is serious as well as beautiful—‘important’ if you like, but the word is very ambiguous, and ‘serious’ expresses what I mean much better
G H Hardy
The ‘seriousness’ of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is ‘significant’ if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas. Thus a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself and even in other sciences.
G H Hardy
The geometer offers to the physicist a whole set of maps from which to choose. One map, perhaps, will fit the facts better than others, and then the geometry which provides that particular map will be the geometry most important for applied mathematics.
G H Hardy
The play is independent of the pages on which it is printed, and ‘pure geometries’ are independent of lecture rooms, or of any other detail of the physical world.
G H Hardy
It seems that mathematical ideas are arranged somehow in strata, the ideas in each stratum being linked by a complex of relations both among themselves and with those above and below. The lower the stratum, the deeper (and in general more difficult) the idea. Thus the idea of an ‘irrational’ is deeper than that of an integer; and Pythagoras’s theorem is, for that reason, deeper than Euclid’s.
G H Hardy
In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras, and will not end with Einstein, but is the oldest and the youngest of all.
G H Hardy
Numbers written on restaurant bills within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe. This single fact took the scientific world by storm. It completely revolutionized it. So many mathematical conferences got held in such good restaurants that many of the finest minds of a generation died of obesity and heart failure and the science of maths was put back by years.
Douglas Adams
Essentially, all models are wrong, but some are useful
George E.P. Box
...317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is, because mathematical reality is built that way.
G H Hardy
So the mathematician and the artist are companioned in the same dark, and do obeisance to the same gods.
Howard Jacobson
The important thing to remember about mathematics is not to be frightened
Richard Dawkins
I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and Abyss. I saw - as one might see the transit of Venus or even the Lord Mayor's Show - a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go.
Winston S. Churchill
I could never have gone far in any science because on the path of every science the lion Mathematics lies in wait for you.
C.S. Lewis
Follow your heart, not the crowd ...
Ian Tucker
If it gathers dust, give it away ...
Ian Tucker
Give as you wish to live, it all come's back to you. And that's without exception ...
Ian Tucker
Your mind will enchain you. Your heart will set you free
Rasheed Ogunlaru
The great error consists in supposing that poetry is an unnatural form of language. We should all like to speak poetry at the moment when we truly live, and if we do not speak it, it is because we have an impediment in our speech. It is not song that is the narrow or artificial thing, it is conversation that is a broken and stammering attempt at song. When we see men in a spiritual extravaganza, like Cyrano de Bergerac, speaking in rhyme, it is not our language disguised or distorted, but our language rounded and made whole.
G.K. Chesterton
I've made peace with myself.Good for you. That's the hardest war of all to win.Didn't say I won. Just stopped fighting.
Joe Abercrombie
Every public speaker likes his hearer to imagine his oratory as an unpremeditated gift of nature, and not the result of prolonged and patient study [Lionel Logue said]
Mark Logue
See and live life for the wonderful gift that it is ...acknowledging everyone's beauty, flaws, frailty, strength, gifts and possibilities. Honour and cherish it and above be loving and compassionate. Here is the birthplace of inner and worldly peace.
Rasheed Ogunlaru
We are most of us two people, your Highness. There is something lacking in the man who is one thing only, and so, as he believes, at peace with the world and with himself.
Robert Aickman
I tended to do anything as long as it felt like an adventure, and to stop when it felt like work. Which meant that life did not feel like work.
Neil Gaiman
So long as I am acting from duty and conviction, I am indifferent to taunts and jeers. I think they will probably do me more good than harm.
Winston S. Churchill
He very soon acquired the reputation of being the best public speaker of his time. He had taken pains to master the art, approaching it with scientific precision. On the morning of a day on which he was giving a speech, he once told Wilkie Collins, he would take a long walk during which he would establish the various headings to be dealt with. Then, in his mind’s eye, he would arrange them as on a cart wheel, with himself as the hub and each heading a spoke. As he dealt with a subject, the relevant imaginary spoke would drop out. When there were no more spokes, the speech was at an end. Close observers of Dickens noticed that while he was speaking he would make a quick action of the finger at the end of each topic, as if he were knocking the spoke away.
Simon Callow
Today, with tears in my eyes, I telephoned the mother of one of our children (aged thirteen) who had spoken for the first time since the age of three...
Michael Braccia
Um, people.”It wasn’t hard to get their attention. They gathered around. Even the littlest ones toned down their giggling, at least a bit.“First of all, thanks to Albert and his helpers for this meal. Let’s give it up for the true Mac Daddy.”A round of hearty applause and some laughter, and Albert waved sheepishly. He frowned a little too, obviously conflicted about the use of the “Mac” prefix in a way that was not approved in the McDonald’s manual.“And we have to mention Lana and Dahra, because without them, there would be a lot fewer of us here.”Now the applause was almost reverential.“Our first Thanksgiving in the FAYZ,” Sam said when the applause died down.“Hope it’s our last,” someone shouted.“Yeah. You got that right,” Sam agreed. “But we’re here. We’re here in this place we never wanted to be. And we’re scared. And I’m not going to lie and tell you that from here on, it will all be easy. It won’t be. It will be hard. And we’ll be scared some more, I guess. And sad. And lonely. Some terrible things have happened. Some terrible things…” For a moment, he lost his way. But then he stood up straighter again. “But, still, we are grateful, and we give thanks to God, if you believe in Him, or to fate, or to just ourselves, all of us here.”“To you, Sam,” someone shouted.“No, no, no.” He waved that off. “No. We give thanks to the nineteen kids who are buried right there.” He pointed at the six rows of three, plus the one who started a seventh row. Neat hand-painted wooden tombstones bore the names of Bette and too many others.“And we give thanks to the heroes who are standing around here right now eating turkey. Too many names to mention, and they’d all just be embarrassed, anyway, but we all know them.”There was a wave of loud, sustained applause, and many faces turned toward Edilio and Dekka, Taylor and Brianna, and some toward Quinn.“We all hope this will end. We all hope we’ll soon be back in the world with people we love. But right now, we’re here. We’re in the FAYZ. And what we’re going to do is work together, and look out for each other, and help each other.” People nodded, some high-fived.“Most of us are from Perdido Beach. Some are from Coates. Some of us are…well, a little strange.” A few titters. “And some of us are not. But we’re all here now, we’re all in it together. We’re going to survive. If this is our world now…I mean, it is our world now. It is our world. So, let’s make it a good one.”He stepped down in silence.Then someone started clapping rhythmically and saying, “Sam, Sam, Sam.” Others joined in, and soon every person in the plaza, even some of the prees, was chanting his name.
Michael Grant
If you're too specific, people will purposely mishear you so they can be outraged about whatever thing that usually outrages them.
Patrick Ness
Really, it is unfair to say that English spelling is not an accurate rendering of speech. It is – it's only that it renders the speech of the 16th century.
Guy Deutscher
Will was not without his intentions to be always generous, but our tongues are little triggers which have usually been pulled before general intentions can be brought to bear.
George Eliot
And the great difference between man and monkey is in the larynx.
H.G.Wells
Such is the state of things in England, and it is well that it should be realised by all of us; but it must not be supposed for a moment that I am afraid of it. I lament it deeply, because I foresee that it may be the ruin of many souls; but I have no fear at all that it really can do aught of serious harm to the Word of God, to Holy Church, to our Almighty King, the Lion of the tribe of Judah, Faithful and True, or to His Vicar on earth. Christianity has been too often in what seemed deadly peril, that we should fear for it any new trial now. So far is certain; on the other hand, what is uncertain, and in these great contests commonly is uncertain, and what is commonly a great surprise, when it is witnessed, is the particular mode by which, in the event, Providence rescues and saves His elect inheritance. Sometimes our enemy is turned into a friend; sometimes he is despoiled of that special virulence of evil which was so threatening; sometimes he falls to pieces of himself; sometimes he does just so much as is beneficial, and then is removed. Commonly the Church has nothing more to do than to go on in her own proper duties, in confidence and peace; to stand still and to see the salvation of God.
John Henry Newman
Always speak the truth - think before you speak - and write it down afterwards.
Lewis Carroll
Mannerism, especially when it takes the form of recurrent word or phrase, is by no means easy to represent; there is but a hair's breadth between the point at which the reader delightfully recognizes is as a revealing habit of speech, and the point at which its iteration begin to weary him.
Mary Lascelles
Today, each of you will make a decision,” Caine said. “To go with Sam, or to stay here. I won’t try to stop anyone, and I won’t hold it against anyone.” He placed his hand over his heart. “For those who choose to stay, let me be very clear: I will be in charge. Not as a mayor, but as a king. My word will be law. My decisions will be final.”That caused some murmuring, most of it unhappy.“But I’ll also do everything I can to leave each of you alone. Quinn, if he chooses to stay, can still fish. Albert, if he chooses to stay, will still run his business. Freaks and normals will be treated equally.”He seemed about to add something else but caught himself after a sidelong look at Toto.The silence lengthened and Sam knew it was time for him to speak. In the past he’d always had Astrid at his side for things like this. He was not much of a speaker. And in any case, he didn’t have much to say.“Anyone who goes with me has a vote in how we do stuff. I guess I’ll be more or less in charge, but we’ll probably choose some other people, create a council like . . . Well, hopefully better than we had before. And, um . . .” He was tempted to laugh at his own pitiful performance. “Look, people, if you want someone, some . . . king, good grief, to tell you what to do, stay here. If you want to make more of your own decisions, well, come with me.”He hadn’t said enough to even cause Toto to comment.“You know which side I’m on, people,” Brianna yelled. “Sam’s been carrying the load since day one.”“It was Caine that saved us,” a voice cried out. “Where was Sam?”The crowd seemed undecided. Caine was beaming confidence, but Sam noticed that his jaw clenched, his smile was forced, and he was worried.
Michael Grant
Two wives despaired of him,’ he said. ‘When he got engaged to Sylvia, she made it a condition that he should take the cure at Zurich. And it worked. He came back in three months a different man. And he hasn't touched a drop since, even though Sylvia walked out on him.’ ‘Why did she do that?’Well, poor Charlie got rather a bore when he stopped drinking. But that’s not really the point of the story.
Evelyn Waugh
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