Theorem Quotes & Sayings

Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel. — Johannes Kepler

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them. — George Polya

Evans-Pritchard's confession reveals the way the power advantage of the subject whose definition of a situation prevails in the larger social context (in this case the majority of the Azande) shapes the environment and behavioral constraints that impact the subject who, although does not define the situation the same way, has to behave according to the former subject's definition in order to obtain the needed resources (in this case Evans-Pritchard, who is interested in gaining knowledge of the social organization of the Azande). For Evans-Pritchard, while living among the Azande, the actual world is as if there were magical forces around, true oracles and evil witches, as his whole daily life is structured around those nonexistent entities. — Istvan Aranyosi

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

Those who have more power are liable to sin more; no theorem in geometry is more certain than this. — Lord Acton

A human being without the proper empathy or feeling is the same as an android built so as to lack it, either by design or mistake. We mean, basically, someone who does not care about the fate which his fellow living creatures fall victim to; he stands detached, a spectator, acting out by his indifference John Donne's theorem that 'No man is an island,' but giving that theorem a twist: that which is a mental and a moral island is not a man. — Philip K. Dick

if a theorem is geometrically obvious why prove it? This was exactly the attitude taken in the eighteenth century. The result, in the nineteenth century, was chaos and confusion: for intuition, unsupported by logic, habitually assumes that everything is much nicer behaved than it really is. Good — Ian Stewart

Science is the one culture that's truly global - protons, proteins and Pythagoras's Theorem are the same from China to Peru. It should transcend all barriers of nationality. It should straddle all faiths, too. — Martin Rees

Note for a Textbook

The question is never answered, never resolved,
The circle of love and anger never squared,
The stubborn instinct not translated yet
In decimals, accurate and predictable
In union dues or payroll cuts or blood...

Always a symbol lost in the lovely theorem,
A fraction that will not fit in the sum of the system,
A jutting thrust in the graph of the commissar's forecast,
A troublesome blank in gauleiter's careful accounting,
An awkward hitch in the plans of the second vice-president.

The answers worked on the slate are never the same,
And the answers proved in the back of the book are wrong. — Charles Bruce

If a customer asks you to build a system that handles netsplits while staying consistent and available, you know that you need to either calmly explain the CAP theorem or run away (possibly by jumping through a window, for a maximal effect). — Fred Hebert

There is no answer to the Pythagorean theorem. Well, there is an answer, but by the time you figure it out, I got 40 points, 10 rebounds and then we're planning for the parade. — Shaquille O'Neal

Any effect, constant, theorem or equation named after Professor X was first discovered by Professor Y , for some value of Y not equal to X. — John C. Baez

In science, progress is possible. In fact, if one believes in Bayes' theorem, scientific progress is inevitable as predictions are made and as beliefs are tested and refined. — Nate Silver

I took a break from acting for four years to get a degree in mathematics at UCLA, and during that time I had the rare opportunity to actually do research as an undergraduate. And myself and two other people co-authored a new theorem: Percolation and Gibbs States Multiplicity for Ferromagnetic Ashkin-Teller Models on Two Dimensions, or Z2. — Danica McKellar

A Fairy must make her own way in the world, for the world will never make way for her. That, incidentally, is the First Theorem of Questing Physicks, which you'll learn all about when you're older and don't care anymore. — Catherynne M Valente

I think it is said that Gauss had ten different proofs for the law of quadratic reciprocity. Any good theorem should have several proofs, the more the better. For two reasons: usually, different proofs have different strengths and weaknesses, and they generalise in different directions - they are not just repetitions of each other. — Michael Atiyah

I know well that many of my readers do not think as I do. This also is most natural and confirms the theorem. For although my opinion turn out erroneous, there will always remain the fact that many of those dissentient readers have never given five minutes' thought to this complex matter. How are they going to think as I do? But by believing that they have a right to an opinion on the matter without previous effort to work one out for themselves, they prove patently that they belong to that absurd type of human being which I have called the "rebel mass." It is precisely what I mean by having one's soul obliterated, hermetically closed. Here it would be the special case of intellectual hermetism. The individual finds himself already with a stock of ideas. He decides to content himself with them and to consider himself intellectually complete. — Ortega Y Gasset

The primes are the raw material out of which we have to build arithmetic, and Euclid's theorem assures us that we have plenty of material for the task. — G.H. Hardy

The Theorem reste upon the validity of my longstanding argument that the world contains precisely two kinds of people:
Dumpers and Dumpees.
Everyone is predisposed to being either one or the other, but of course not all people are COMPLETE
Dumpers and Dumpees.
Hence the bell curve:
The majority of people fall somewhere close to the vertical dividing line with the occasional statisticaly outliner (e.g., me) representing a tiny percentage of overall individuals. The numerical expression of the graph can be something like 5 being extreme Dumper, and 0 being me. Ergo, if the Great One was a 4 and I am a 0, total size of the Dumper/Dumpee differetial = -4 (Assuming negative numbers if the guy is more of a Dumpee; positive if the girl is.) — John Green

Well, three reasons. First, because I've been thinking about our Theorem and I have a question. How does it work if you're gay?"
"Huh?"
"Well it's all graph-going up means boy dumps girls and graph going-down means girl dumps boy, right? But what if they're both boys?"
"It doesn't matter. You just assign a position to each person. Instead of being 'b' and 'g', it could just as easily be 'b1' and 'g', it could just as easily be 'bi' and 'b2.'
That's how algebra works. — John Green

When I give this talk to a physics audience, I remove the quotes from my 'Theorem'. — Brian Greene

Under Bayes' theorem, no theory is perfect. Rather, it is a work in progress, always subject to further refinement and testing. — Nate Silver

You wouldn't think there was a need for a Coase Theorem, really. — Ronald Coase

Human rights are an aspect of natural law, a consequence of the way the universe works, as solid and as real as photons or the concept of pi. The idea of self- ownership is the equivalent of Pythagoras' theorem, of evolution by natural selection, of general relativity, and of quantum theory. Before humankind discovered any of these, it suffered, to varying degrees, in misery and ignorance. — L. Neil Smith

His sense of humor was permanently replaced by the Pythagorean Theorem. — Dima Zales

Oh, Anyone can make a quilt,' she said modestly. 'It's just scraps, from the clothes you've sewn.'
'Yes, but the talent is in joining the pieces, the way you have.'
'Look,' Om pointed, 'look at that - the poplin from our very first job.'
'You remember,' said Dina, pleased. 'And how fast you finished those first dresses. I thought I had two geniuses.'
'Hungry stomachs were driving our fingers,' chuckled Ishvar.
'Then came that yellow calico with orange strips. And what a hard time this young fellow gave me. Fighting and arguing about everything.'
'Me?Argue?Never.'
...
He steeped back, pleased with himself, as though he had elucidated an intricate theorem. 'So that's the rule to remember, the whole quilt is much more important than the square'. — Rohinton Mistry

Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure. — David Hilbert

Dullards would have you believe that once you have eliminated the impossible, whatever remains, however improbable, must be the truth ... but to a mathematical mind, the impossible is simply a theorem yet to be solved. We must not eliminate the impossible, we must conquer it, suborn it to our purpose. — Kim Newman

But my shift to the serious study of economics gradually weakened my belief in Major Douglas's A+B theorem, which was replaced in my thought by the expression MV = PT. — James Meade

If you hold there is a 100 percent probability that God exists, or a 0 percent probability, then under Bayes's theorem, no amount of evidence could persuade you otherwise. — Nate Silver

Immortality is often ridiculous or cruel: few of us would have chosen to be Og or Ananias or Gallio. Even in mathematics, history sometimes plays strange tricks; Rolle figures in the textbooks of elementary calculus as if he had been a mathematician like Newton; Farey is immortal because he failed to understand a theorem which Haros had proved perfectly fourteen years before; the names of five worthy Norwegians still stand in Abel's Life, just for one act of conscientious imbecility, dutifully performed at the expense of their country's greatest man. But on the whole the history of science is fair, and this is particularly true in mathematics. No other subject has such clear-cut or unanimously accepted standards, and the men who are remembered are almost always the men who merit it. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments. — G.H. Hardy

To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples ... — John B. Conway

Colin,
I hate to fulfill the Theorem, but I don't think we should be involved romantically.
The problem is that I secretly in love with Hassan.
I can't help myself. I hold your bony shoulder blades in my hands and think of his fleshy back.
I kiss your stomach and I think of his awe-inspiring gut. I like you,
Colin, I really do. But-I'm sorry. It's just not going to work.
I hope we can still be friends.
Sincerely,
Lindsey Lee Wells
P.S. Just kidding. — John Green

The three discrete invariances - reflection invariance, charge conjugation invariance, and time reversal invariance - are connected by an important theorem called the CPT theorem. — Chen-Ning Yang

Combinatorial analysis, in the trivial sense of manipulating binomial and multinomial coefficients, and formally expanding powers of infinite series by applications ad libitum and ad nauseamque of the multinomial theorem, represented the best that academic mathematics could do in the Germany of the late 18th century. — Richard Askey

Ellison's Theorem: the further right your position, the less telling your satire. A corollary of which is that you can't lampoon anywhere near where you stand, because you'd annihilate your own troops. — Harlan Ellison

The great poem and the deep theorem are new to every reader, and yet are his own experiences, because he himself recreates them. — Jacob Bronowski

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

A felicitous but unproved conjecture may be of much more consequence for mathematics than the proof of many a respectable theorem. — Atle Selberg

If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it. — George Polya

Words are the children of reason and, therefore, can't explain it. They really can't translate feeling because they're not part of it. That's why it bugs me when people try to analyze jazz as an intellectual theorem. It's not. It's feeling. — Bill Evans

We are on the verge: Today our program proved Fermat's next-to-last theorem. — Alan Perlis

Finally, the dishonesty in the movement of the publication of a Greek philosophy, becomes very glaring, when we refer to the fact, purposely that by calling the theorem of the Square on the Hypotenuse, the Pythagorean theorem, it has concealed the truth for centuries from the world, who ought to know that the Egyptians taught Pythagoras and the Greeks, what mathematics they knew. — George G. M. James

How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasturenothing but years of effort can extract it. You can't hurry the process. Or pass from arithmetic to algebra; you can't shoulder your way past quadratic equations or ripple through the binomial theorem. Instead, the other way; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on the horizon. — Stephen Leacock

Carnot's theorem: The most efficient heat engine is one that operates reversibly. — Don S. Lemons

Schelling's God is the totality of Nature struggling towards consciousness, and Man is as far as the struggle has got, with the animals not too far behind, vegetables somewhat lagging, and rocks nowhere as yet. Do we believe this? Does it matter? Think of it as a poem or a painting. Art doesn't have to be true like a theorem. It can be true in other ways. This truth says there is a meaning to it all, and Man is where the meaning begins to show. — Tom Stoppard

Statistical inference is really just the marriage of two concepts that we've already discussed: data and probability (with a little help from the central limit theorem). — Charles Wheelan

Any good theorem should have several proofs, the more the better — Michael Atiyah

I think I have met nearly all the Laureates in Economics. Among the few I haven't met, I suppose I'd most like to meet Ronald Coase because of his legendary power to persuade his colleagues of the validity of the Coase Theorem. — Eric Maskin

A theorem is a proposition which is a strict logical consequence of certain definitions and other propositions — Anatol Rapoport

...internalized the Negro theorem of needing to be twice as good to get half as far. — Margot Lee Shetterly

[...] provability is a weaker notion than truth — Douglas R. Hofstadter

The Open Source theorem says that if you give away source code, innovation will occur. Certainly, Unix was done this way ... However, the corollary states that the innovation will occur elsewhere. No matter how many people you hire. So the only way to get close to the state of the art is to give the people who are going to be doing the innovative things the means to do it. That's why we had built-in source code with Unix. Open source is tapping the energy that's out there. — Bill Joy

A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution. — Richard Arnold Epstein

Do people believe in human rights because such rights actually exist, like mathematical truths, sitting on a cosmic shelf next to the Pythagorean theorem just waiting to be discovered by Platonic reasoners? Or do people feel revulsion and sympathy when they read accounts of torture, and then invent a story about universal rights to help justify their feelings? — Jonathan Haidt

Context enables us to determine which of several meanings is in play in a particular text. The verb in "I see" means something quite different if uttered by a formerly blind man healed with spittle and dust, by a student who has just received an extended explanation of a difficult mathematical theorem, or by a skeptical wife whose husband offers a lame explanation for the lipstick on his collar. In the first context, see refers to physical sight, while in the latter two it refers to understanding, and in the last it could hardly be said without a heap of sarcasm. — Peter J. Leithart

I realized that anything to do with Fermat's Last Theorem generates too much interest. — Andrew Wiles

All I remember about the examination is that there was a question on Sturm's theorem about equations, which I could not do then and cannot do now. — Louis J. Mordell

The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic. — Ronald Fisher

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means ... — Henri Poincare

REJECTION MINIMIZATION THEOREM (RMT):
Think about it: boys basically, want to kiss girls. Guys want to make out. Always. Hassan aside, there's a rarely a time when a boy is thinking, Eh, I think I'd rather not kiss a girl today. — John Green

Our offense is like the pythagorean theorem: There is no answer! — Shaquille O'Neal

We live in a society where we're not taught how to deal with our weaknesses and frailties as human beings. We're not taught how to speak to our difficulties and challenges. We're taught the Pythagorean theorem and chemistry and biology and history. We're not taught anger management. We're not taught dissolution of fear and how to process shame and guilt. I've never in my life ever used the Pythagorean theorem! — Iyanla Vanzant

What philosophy worthy of the name has truly been able to avoid the link between poem and theorem? — Michel Serres

Occasionally, I get a letter from someone who is in "contact" with extraterrestrials. I am invited to "ask them anything." And so over the years I've prepared a little list of questions. The extraterrestrials are very advanced, remember. So I ask things like, "Please provide a short proof of Fermat's Last Theorem." Or the Goldbach Conjecture. And then I have to explain what these are, because extraterrestrials will not call it Fermat's Last Theorem. So I write out the simple equation with the exponents. I never get an answer. On the other hand, if I ask something like "Should we be good?" I almost always get an answer. — Carl Sagan

I smiled. Mom laughed, shaking her head. "That's the punchline? Why is that even funny?" "It's the Pythagorean theorem," said Lauren. "It's a math formula for . . . something." "Right triangles," I said, and looked pointedly at Margaret. "I told you I'd already done geometry. — Dan Wells

the clerk in the ministry to correct this, he pulled out his original typescript. "See for yourself, madam. Quod erat demonstrandum it is Missing," he said, as if he'd proved Pythagoras's theorem, the sun's central position in the solar system, the roundness of the — Abraham Verghese

I loved doing problems in school. I'd take them home and make up new ones of my own. But the best problem I ever found, I found in my local public library. I was just browsing through the section of math books and I found this one book, which was all about one particular problem - Fermat's Last Theorem. — Andrew Wiles

Fourier's theorem has all the simplicity and yet more power than other familiar explanations in science. Stated simply, any complex pattern, whether in time or space, can be described as a series of overlapping sine waves of multiple frequencies and various amplitudes. — Bruce Hood

Across the board at the office there was a belief, an unproved theorem, about Coinman's blind faith in Ratiram; that if one thought Coinman could willingly sip a cup of Botulinum if Ratiram wished so, it still underestimated the reverence that dwelt in Coinman's heart for Ratiram. — Pawan Mishra

But he could no longer disbelieve in the reality of love, since God Himself had loved his individual soul with divine love from all eternity. Gradually, as his soul was enriched with spiritual knowledge, he saw the whole world forming one vast symmetrical expression of God's power and love. Life became a divine gift for every moment and sensation of which, were it even the sight of a single leaf hanging on the twig of a tree, his soul should praise and thank the Giver. The world for all its solid substance and complexity no longer existed for his soul save as a theorem of divine power and love and universality. — James Joyce

My favourite fellow of the Royal Society is the Reverend Thomas Bayes, an obscure 18th-century Kent clergyman and a brilliant mathematician who devised a complex equation known as the Bayes theorem, which can be used to work out probability distributions. It had no practical application in his lifetime, but today, thanks to computers, is routinely used in the modelling of climate change, astrophysics and stock-market analysis. — Bill Bryson

But you can't prove God exists. And isn't that what all science is ultimately about? Proving theories about the universe?"
"Provability is not truth, Caro. Godel's incompleteness theorem tells us that, if we didn't already know it intuitively, which we do. — Anna Jarzab

the theorem of incompleteness . . . [shows] there is nothing on this level of existence that can fully explain this level of existence. — Pat Cadigan

Uh-oh," Moni sang, and nodded her head in Chantal's direction. "I think someone's a wee bit upset with us." She turned and walked a few steps backward.
"Careful," I said. "We're not out of range."
"Have no fear, Super Brain is here." Moni whipped out her calculator, holding it up like a shield.
"What are you going to do, daze her with denominators?"
"Maybe. But first I'm going to pummel her with my Pythagorean theorem. — Charity Tahmaseb

In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance. — Martin Gardner

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

Humanism ... is not a single hypothesis or theorem, and it dwells on no new facts. It is rather a slow shifting in the philosophic perspective, making things appear as from a new centre of interest or point of sight. — William James

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

A mathematician experiments, amasses information, makes a conjecture, finds out that it does not work, gets confused and then tries to recover. A good mathematician eventually does so - and proves a theorem. — Steven G. Krantz

The Mean Value Theorem is the midwife of calculus - not very important or glamorous by itself, but often helping to deliver other theorems that are of major significance. — Edward Mills Purcell

Fain would I turn back the clock and devote to French or some other language the hours I spent upon algebra, geometry, and trigonometry, of which not one principle remains with me. Stay! There is one theorem painfully drummed into my head which seems to have inhabited some corner of my brain since that early time: "The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides!" There it sticks, but what of it, ye gods, what of it? — Jessie Belle Rittenhouse

Murphy's Law, that brash proletarian restatement of Godel's Theorem ... — Thomas Pynchon

What we do may be small, but it has a certain character of permanence; and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men. — G.H. Hardy

Share prices follow the theorem: hope divided by fear minus greed. — Dominic Lawson

The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument. — Yuri Manin

In any event, Socrates' proof of prenatal immortality is that one of Meno's uneducated slave boys actually comes up with the Pythagorean theorem without ever having studied geometry! Therefore, he must be remembering it. You recall that theorem: in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Huh? We can barely remember that from tenth grade, let alone from before we were born. — Thomas Cathcart

By now, he was also a 'Protestant Atheist', which he remained all his life. — John Ellis

And I believe that the Binomial Theorem and a Bach Fugue are, in the long run, more important than all the battles of history. — James Hilton

Carnal embrace is sexual congress, which is the insertion of the male genital organ into the female genital organ for purposes of procreation and pleasure. Fermat's last theorem, by contrast, asserts that when x, y and z are whole numbers each raised to power of n, the sum of the first two can never equal the third when n is greater than 2. — Tom Stoppard

I think mathematics is a vast territory. The outskirts of mathematics are the outskirts of mathematical civilization. There are certain subjects that people learn about and gather together. Then there is a sort of inevitable development in those fields. You get to the point where a certain theorem is bound to be proved, independent of any particular individual, because it is just in the path of development. — William Thurston

The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is feasible. — George Polya

The story does what no theorem can quite do. It may not be "like real life" in the superficial sense: but it sets before us an image of what reality may well be like at some more central region. — C.S. Lewis

You can't live with the idea that someone might leave. So instead of being happy for me, like any normal person, you're pissed off because ooh, oh no, Hassan doesn't like me anymore. You're such a sitzpinkler. You're so goddamned scared of the idea that someone might dump you that your whole fugging life is built around not gettting left behind. Well, it doesn't work, kafir. I just - it's not just dumb, it's ineffective. Because then you're not being a good friend or a good boyfriend or whatever, because you're only thinking they-might-not-like-me-they-might-not-like-me, and guess what? When you act like that, no one likes you. There's your goddamned Theorem. — John Green

The future is the result of actions, and actions are the result of behavior, and behavior is the result of prediction. — David McRaney

Bayes's theorem and that looks like this: People who understand Bayes's theorem can use it to work out complex problems involving probability distributions - or inverse probabilities, as they are sometimes called. — Bill Bryson

MacPherson told me that my theorem can be viewed as blah blah blah Grothendieck blah blah blah, which makes it much more respectable. — Jim Propp

Poetry is a theorem of a yellow-silk handkerchief knotted with riddles, sealed in a balloon tied to the tail of a kite flying in a white wind against a blue sky in spring. — Carl Sandburg

I know this may sound like an excuse," he said. "But tensor functions in higher differential topology, as exemplified by application of the Gauss-Bonnett Theorem to Todd Polynomials, indicate that cohometric axial rotation in nonadiabatic thermal upwelling can, by random inference derived from translational equilibrium aggregates, array in obverse transitional order the thermodynamic characteristics of a transactional plasma undergoing negative entropy conversions."
"Why don't you just shut up," said Hardesty. — Mark Helprin

In mathematics, in place of characters, you have variables or unknowns. If I'm trying to plot a theorem, I try to imagine these variables interacting with each other. The boundary of their interaction is the theorem. — Manil Suri