Math Quotes - Page 37

Grid View List View
Quote of the DayPicture QuotesTop 100 Inspirational QuotesTop 100 Love QuotesTop 100 Happiness Quotes
Carl SaganMarcus AureliusEpictetusZig ZiglarMother TeresaMarcus Tullius CiceroJordan PetersonKobe BryantNapoleon BonaparteJohann Wolfgang Von Goethe
DatingOceanI Miss YouInspirationalSuccessKingsBrainyWeddingPatienceUplifting

... being perpetually charmed by his familiar siren, that is, by his geometry, he neglected to eat and drink and took no care of his person; that he was often carried by force to the baths, and when there he would trace geometrical figures in the ashes of the fire, and with his finger draws lines upon his body when it was anointed with oil, being in a state of great ecstasy and divinely possessed by his science.

I'd say it's that most people think that very wealthy people take huge risks and that's why they have huge rewards. But the very best on earth are completely obsessed with not losing money. That sounds overly simplistic, but they know that if you lost 50 percent, it takes 100 percent to get even. Most people don't make that math in their head, so it takes years and years. They are obsessed with not losing money.

The historical resonances are sharp. [Louis] Brandeis is nominated on Jan. 28, 1916. Confirmed on June 1. Waits 125 days between nomination and confirmation, which remains an unbroken record, although Merrick Garland will surpass it in July, if my math is right. Anti-Semitism was definitely not the central reason for the opposition, which tended to focus more on his anti-corporate radicalism, but it was a theme.

I don't want to exaggerate; having as many African American men as we've had in the criminal-justice system, and the amount of time it takes for the damage done by that to wash through our society and our communities, the disadvantages born out of kids being undiagnosed with mental-health problems early, or not getting the kind of exposure to reading and math when they're 4 or 5 or 6 years old, that carries a cost.

A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is like a monkey who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise.

...I think there's only one [thing] that anybody teaches, and this is character. And I think that whether you are teaching history, math, or biology, or music, what you are really doing is, you are helping to shape the character of that person who is your student... Music is such a wonderful teaching tool, because while you are developing musical skills, that student can learn a lot about discipline [and] cooperation.

If I'd loved my chemistry teacher and my maths teacher, goodness knows what direction my life might have gone in. I remember there was a primary school teacher who really woke me up to the joys of school for about one year when I was ten. He made me interested in things I would otherwise not have been interested in - because he was a brilliant teacher. He was instrumental in making me think learning was quite exciting.

I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would be claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming . . . and a little mad.

Q: What’s hard for you? A: Mostly I straddle reality and the imagination. My reality needs imagination like a bulb needs a socket. My imagination needs reality like a blind man needs a cane. Math is hard. Reading a map. Following orders. Carpentry. Electronics. Plumbing. Remembering things correctly. Straight lines. Sheet rock. Finding a safety pin. Patience with others. Ordering in Chinese. Stereo instructions in German.

The key to good worldbuilding is leaving out most of what you create. You, as the author, had damn well better know the where all that dragon food comes from, but that doesn't mean that I, as a reader, want to read a five thousand word essay about you explaining it to me. I don't need to see the math, but I can tell by the details you provide whether or not you've thought these things through to their logical conclusions.

...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.

Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks... Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.

There was quite a lot of competitiveness about it, with everybody wanting to beat not only cancer itself, but also the other people in the room. Like, I realize that this is irrational, but when they tell you that you have, say, a 20 percent chance of living five years, the math kicks in and you figure that’s one in five . . . so you look around and think, as any healthy person would: I gotta outlast four of these bastards.

"It's very good jam," said the Queen. "Well, I don't want any to-day, at any rate." "You couldn't have it if you did want it," the Queen said. "The rule is jam tomorrow and jam yesterday but never jam to-day." "It must come sometimes to "jam to-day,""Alice objected. "No it can't," said the Queen. "It's jam every other day; to-day isn't any other day, you know." "I don't understand you," said Alice. "It's dreadfully confusing."

The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions.

In whatever you choose to do, do it because it's hard, not because it's easy. Math and physics and astrophysics are hard. For every hard thing you accomplish, fewer other people are out there doing the same thing as you. That's what doing something hard means. And in the limit of this, everyone beats a path to your door because you're the only one around who understands the impossible concept or who solves the unsolvable problem.

When you could discern a real threat from everything else, it was called caution. When you couldn't, it was called paranoia. ... You cannot separate paranoia from knowledge. The more you know, the more possibilities you see. The more possibilities you see, the more possibilities someone else sees. The more "someones" there are, the more "they" there are. It's a matter of simple math before you realize that They might not like you.

I've written about 2,000 short stories; I've only published 300 and I feel I'm still learning. Any man who keeps working is not a failure. He may not be a great writer, but if he applies the old fashioned virtues of hard, constant labor, he'll eventually make some kind of career for himself as a writer. Ray Bradbury, 1967 interview (Doing the Math - that means for every story he sold, he wrote six "un-publishable" ones. Keep typing!)

What is the fundamental hypothesis of science, the fundamental philosophy? We stated it in the first chapter: the sole test of the validity of any idea is experiment. ... If we are told that the same experiment will always produce the same result, that is all very well, but if when we try it, it does not, then it does not. We just have to take what we see, and then formulate all the rest of our ideas in terms of our actual experience.

It's amazing to me that not only can we put a probe around Saturn and get images of its moons, but our math and physics are so freaking accurate we can say, "Hey, you know what? On this date at this time if we turn Cassini that way we'll see a moon over 2 million kilometers away pass in front of another one nearly 3 million kilometers away." Every morning, I have a 50/50 chance of finding my keys. That kinda puts things in perspective.

When I got to college, I planned to be a math major, and, in addition to signing up for some math courses, I decided to take some philosophy. Quite by chance, I took a philosophy of science course in which the entire semester was devoted to reading Locke's Essay. I was hooked. For the next few semesters, I took nothing but philosophy and math courses, and it wasn't long before I realised that it was the philosophy that really moved me.

When will it begin, anyway?" Sirus held his gaze for a moment, his eyes full of concern- a concern that Joss didn't understand. "Probably sooner than you're ready for." "When's that?" "Well." Sirus sighed, as if doing the math in his head."It'll take us about three minutes to gather this stuff and get to the cabin, and another two or three for Abraham to realize you're here. So I'd say you have about seven more minutes of freedom left.

Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It's just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas.

I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the "Law of Frequency of Error." The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement, amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of Unreason.

Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this . . . . The imagination in a mathematician who creates makes no less difference than in a poet who invents. . . . Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer.

Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.

There is a distinction between what may be called a problem and what may be considered an exercise. The latter serves to drill a student in some technique or procedure, and requires little if any, original thought... No exercise, then, can always be done with reasonbable dispatch and with a miniumum of creative thinking. In contrast to an exercise, a problem, if it is a good one for its level, should require though on the part of the student.

Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice. Trying to swim, you imitate what other people do with their hands and feet to keep their heads above water, and, finally, you learn to swim by practicing swimming. Trying to solve problems, you have to observe and to imitate what other people do when solving problems, and, finally, you learn to do problems by doing them.

When you're the guy behind the camera, you're aware of the reasons for the compromises or the changes that get made. As an actor, you go and do your thing, and someone else down the line then does all the math and goes, "We can't include that thing where he's pretending to be dumb and needling those people, because it takes a minute and a half, and it ruins the next scene. It doesn't make sense." If you're directing, you're the one doing that.

The mathematical question is "Why?" It's always why. And the only way we know how to answer such questions is to come up, from scratch, with these narrative arguments that explain it. So what I want to do with this book is open up this world of mathematical reality, the creatures that we build there, the questions that we ask there, the ways in which we poke and prod (known as problems), and how we can possibly craft these elegant reason-poems.

Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed. They are no exceptions to the rule that God always geometrizes. Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems, and the morphologist is, ipso facto, a student of physical science.

Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties, and we may confidently look forward to a time when they shall form but one body with one soul.

One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics.

As far as I know, Clifford Pickover is the first mathematician to write a book about areas where math and theology overlap. Are there mathematical proofs of God? Who are the great mathematicians who believed in a deity? Does numerology lead anywhere when applied to sacred literature? Pickover covers these and many other off-trail topics with his usual verve, humor, and clarity. And along the way the reader will learn a great deal of serious mathematics.

The real truth - like anything, you have an idea about something you might write and it changes. People reflect on it or you get other ideas and maybe your original idea is radically different than how it ends up being. It's not a theorem. You don't sit down and prove something. You start with an initial idea and it grows and grows. The math of the narrative changes. In some ways your original document and what the film ends up being are quite different.

We sat looking out at the ocean. There was just so much of it, and it never failed to take my breath away. Looking at the ocean gave me the same sensation I'd get staring at a sky full of stars- that I was small. Like the way a math problem reveals its undeniable truth, I knew when I stared into this sort of endlessness that my life didn't count for much of anything. And knowing that, that I was nothing but a speck, I felt pretty lucky for all that I had.

There are people at the extremes who aren't able to do anything musically, and then others sort of fall in the middle. And the same thing with math, and the same thing with art. You'll find people who are geniuses, or prodigies at the far end of the bell shaped curve, and I think you will find some of the acquired savants in that category who happened to have been endowed with that kind of talent, which explains why not everyone becomes an acquired savant.

And who can doubt that it will lead to the worst disorders when minds created free by God are compelled to submit slavishly to an outside will? When we are told to deny our senses and subject them to the whim of others? When people devoid of whatsoever competence are made judges over experts and are granted authority to treat them as they please? These are the novelties which are apt to bring about the ruin of commonwealths and the subversion of the state.

Nonmathematical people sometimes ask me, “You know math, huh? Tell me something I’ve always wondered, What is infinity divided by infinity?” I can only reply, “The words you just uttered do not make sense. That was not a mathematical sentence. You spoke of ‘infinity’ as if it were a number. It’s not. You may as well ask, 'What is truth divided by beauty?’ I have no clue. I only know how to divide numbers. ‘Infinity,’ ‘truth,’ ‘beauty’—those are not numbers.

Gel'fand amazed me by talking of mathematics as though it were poetry. He once said about a long paper bristling with formulas that it contained the vague beginnings of an idea which could only hint at and which he had never managed to bring out more clearly. I had always thought of mathematics as being much more straightforward: a formula is a formula, and an algebra is an algebra, but Gel'fand found hedgehogs lurking in the rows of his spectral sequences!

Our federal income tax law defines the tax y to be paid in terms of the income x; it does so in a clumsy enough way by pasting several linear functions together, each valid in another interval or bracket of income. An archeologist who, five thousand years from now, shall unearth some of our income tax returns together with relics of engineering works and mathematical books, will probably date them a couple of centuries earlier, certainly before Galileo and Vieta.

I studied physics at Princeton when I was a college student, and my initial intention was to major in it but to also be a writer. What I discovered, because it was a very high-powered physics program with its own fusion reactor, was that to keep up with my fellow students in that program I would need to dedicate myself to math and physics all the time and let writing go. And I couldn't let writing go, so I let physics go and became a science fan and a storyteller.

Superstar lawyers and math whizzes and software entrepreneurs appear at first blush to lie outside ordinary experience. But they don't. They are products of history and community, of opportunity and legacy. Their success is not exceptional or mysterious. It is grounded in a web of advantages and inheritances, some deserved, some not, some earned, some just plain lucky - but all critical to making them who they are. The outlier, in the end, is not an outlier at all.

I didn't think I was good at anything, didn't do well in school. And then in the third grade, I was going to a public school. And the teacher was putting math problems on the board. And I said to myself - it's amazing how you can remember certain incidents at any age that made an impression - I asked myself why is she putting those up when the answers are obvious. And then I saw it wasn't obvious to anybody else in the class. So I said, "Hey, I'm good at something."

I've seen pretty clear, ever since I was a young un, as religion's something else besides notions. It isn't notions sets people doing the right things--it's feelings. It's the same with the notions in religion as it is with math'matics--a man may be able to work problems straight off in's head as he sits by the fire and smokes his pipe; but if he has to make a machine or a building, he must have a will and a resolution, and love something else better than his own ease.

The physicist, in his study of natural phenomena, has two methods of making progress: (1) the method of experiment and observation, and (2) the method of mathematical reasoning. The former is just the collection of selected data; the latter enables one to infer results about experiments that have not been performed. There is no logical reason why the second method should be possible at all, but one has found in practice that it does work and meets with reasonable success.

For me, promotional thing about some new album coming out destroys a lot of the excitement of making records. Records, movies, books - they're not supposed to be like math books. The purpose of them is to kind of take us out of ourselves and give us some sort of alternate experience or respite. To try to maximize the relationship of listening to a record through promotion is like experiencing driving a car by reading about stimulus programs. It kind of defeats the purpose.

These long chains of perfectly simple and easy reasonings by means of which geometers are accustomed to carry out their most difficult demonstrations had led me to fancy that everything that can fall under human knowledge forms a similar sequence; and that so long as we avoid accepting as true what is not so, and always preserve the right order of deduction of one thing from another, there can be nothing too remote to be reached in the end, or to well hidden to be discovered.

To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.

The effort of the economist is to "see," to picture the interplay of economic elements. The more clearly cut these elements appear in his vision, the better; the more elements he can grasp and hold in his mind at once, the better. The economic world is a misty region. The first explorers used unaided vision. Mathematics is the lantern by which what before was dimly visible now looms up in firm, bold outlines. The old phantasmagoria disappear. We see better. We also see further.

Share This Page