Pythagorean Theorem Quotes

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

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

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

That is why one day I said my game will be like the Pythagorean Theorem - hard to figure out. A lot of people really don't know the Pythagorean Theory. They don't make them like me anymore. They don't want to make them like that anymore. ~ Shaquille O'Neal

I am the number one Ninja and I have killed all the Shoguns in front of me. ~ Shaquille O'Neal

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

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

Scramble Books were written prior to the personal computer. For the most part they were used to supplement text books as a teaching and testing tool. I wrote a scramble book to help students understand the "Pythagorean theorem or Law of Pythagoras." What made these books different from text books was that the answers to questions would lead you to different pages, which in turn would confirm that either your answer was right or it would direct you to another page explaining how to arrive at the correct answer. ~ Hank Bracker

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

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

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

Thus the thought, for example, which we expressed in the Pythagorean theorem is timelessly true, true independently of whether anyone takes it to be true. It needs no bearer. It is not true for the first time when it is discovered, but is like a planet which, already before anyone has seen it, has been in interaction with other planets. ~ Gottlob Frege

Number is the ruler of forms and ideas, and the cause of gods and demons. ~ Pythagoras

Therefore Godel's theorem had an electrifying effect upon logicians, mathematicians, and philosophers interested in the foundations of mathematics, for it showed that no fixed system, no matter how complicated could represent the complexity of the whole numbers: 0,1,2,3,..... ~ Douglas R. Hofstadter

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

There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann. ~ George Polya

To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well. ~ Albert Camus

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

There are lots of things I don't understand - say, the latest debates over whether neutrinos have mass or the way that Fermat's last theorem was (apparently) proven recently. But from 50 years in this game, I have learned two things: (1) I can ask friends who work in these areas to explain it to me at a level that I can understand, and they can do so, without particular difficulty; (2) if I'm interested, I can proceed to learn more so that I will come to understand it. Now Derrida, Lacan, Lyotard, Kristeva, etc. -- even Foucault, whom I knew and liked, and who was somewhat different from the rest -- write things that I also don't understand, but (1) and (2) don't hold: no one who says they do understand can explain it to me and I haven't a clue as to how to proceed to overcome my failures. That leaves one of two possibilities: (a) some new advance in intellectual life has been made, perhaps some sudden genetic mutation, which has created a form of "theory" that is beyond quantum theory, topology, etc., in depth and profundity; or (b) ... I won't spell it out. ~ Noam Chomsky

Today I discovered a little theorem which gave me some intense moments of pleasure. It is beautiful and fell into my hand like a jewel from the sky. ~ Freeman Dyson

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

It is a common misconception, in the spirit of the sentiments expressed in Q16, that Godel's theorem shows that there are many different kinds of arithmetic, each of which is equally valid. The particular arithmetic that we may happen to choose to work with would, accordingly, be defined merely by some arbitrarily chosen formal system. Godel's theorem shows that none of these formal systems, if consistent, can be complete; so-it is argued-we can keep adjoining new axioms, according to our whim, and obtain all kinds of alternative consistent systems within which we may choose to work. The comparison is sometimes made with the situation that occurred with Euclidean geometry. For some 21 centuries it was believed that Euclidean geometry was the only geometry possible. But when, in the eighteenth century, mathematicians such as Gauss, Lobachevsky, and Bolyai showed that indeed there are alternatives that are equally possible, the matter of geometry was seemingly removed from the absolute to the arbitrary. Likewise, it is often argued, Godel showed that arithmetic, also, is a matter of arbitrary choice, any one set of consistent axioms being as good as any other. ~ Roger Penrose

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

Why fit in someones equation when you can create your own theorem. ~ Nivesh Raj

Mythic Background

Describing his approach to science, Einstein said something that sounds distinctly prescientific, and hearkens back to those ancient Greeks he admired:

What really interests me is whether God had any choice in the creation of the world.

Einstein's suggestion that God-or a world-making Artisan-might not have choices would have scandalized Newton or Maxwell. It fits very well, however, with the Pythagorean search for universal harmony, or with Plato's concept of a changeless Ideal.

If the Artisan had no choice: Why not? What might constrain a world-making Artisan?

One possibility arises if the Artisan is at heart an artist. Then the constraint is desire for beauty. I'd like to (and do) infer that Einstein thought along the line of our Question-Does the world embody beautiful ideas?-and put his faith in the answer "yes!"

Beauty is a vague concept. But so, to begin with, were concepts like "force" and "energy." Through dialogue with Nature, scientists learned to refine the meaning of "force" and "energy," to bring their use into line with important aspects of reality.

So too, by studying the Artisan's handiwork, we evolve refined concepts of "symmetry," and ultimately of "beauty"-concepts that reflect important aspects of reality, while remaining true to the spirit of their use in common language. ~ Frank Wilczek

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

Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can't be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere – no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what's also amazing is that we own all of them. No one can patent a mathematical formula, it's ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It's too precious to be given away to the "initiated few." It belongs to all of us. ~ Edward Frenkel

In this world, headwinds are far more prevalent than winds from astern (that is, if you never violate the Pythagorean maxim). ~ Herman Melville

This excerpt is presented as reproduced by Copernicus in the preface to De Revolutionibus: "Some think that the earth remains at rest. But Philolaus the Pythagorean believes that, like the sun and moon, it revolves around the fire in an oblique circle. Heraclides of Pontus and Ecphantus the Pythagorean make the earth move, not in a progressive motion, but like a wheel in rotation from west to east around its own center." ~ Plutarch

Pythagorean thought was dominated by mathematics, but it was also profoundly mystical. ~ Vanna Bonta

For as in this world, head winds are far more prevalent than winds from astern (that is, if you never violate the Pythagorean maxim), so for the most part the Commodore on the quarter-deck gets his atmosphere at second hand from the sailors on the forecastle. He thinks he breathes it first; but not so. In much the same way do the commonalty lead their leaders in many other things, at the same time that the leaders little suspect it. ~ Herman Melville

During the first century A.D., Alexandria was a veritable hotbed of mystical activity, a crucible in which Judaic, Mithraic, Zoroastrian, Pythagorean, Hermetic, and neo-Platonic doctrines suffused the air and combined with innumerable others. ~ Michael Baigent

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

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

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

The most famous Diophantine equation in history is the one known as Fermat's last Theorem, the celebrated statement by Pierre de Fermat (1601-55) that there are no whole number solutions to the equation x^n + y^n = z^n, where n is any number greater than 2. When n = 2, there are many solutions (in fact an infinite number). For instance, 3^2 + 4^2 = 5^2 (9 + 16 = 25); or 12^2 +5^2 = 13^2 (144 + 25 = 169). Miraculously, when we go from n = 2 to n = 3, there are no whole numbers x,y,z that satisfy x^3 + y^3 = z^3, and the same is true for any other value of n that is greater than 2. Appropriately, it was in the margin of the second book of Diophantus's Arithmetica, which Fermat was eagerly reading, that he wrote his extraordinary claim-one that took no fewer than 356 years to prove. ~ Mario Livio

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

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

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

That great portion of what is generally received as Christian truth is, in its rudiments or in its separate parts, to be found in heathen philosophies and religions. For instance, the doctrine of a Trinity is found both in the East and in the West; so is the ceremony of washing; so is the rite of sacrifice. The doctrine of the Divine Word is Platonic; the doctrine of the Incarnation is Indian; of a divine kingdom is Judaic; of Angels and demons is Magian; the connection of sin with the body is Gnostic; celibacy is known to Bonze and Talapoin; a sacerdotal order is Egyptian; the idea of a new birth is Chinese and Eleusinian; belief in sacramental virtue is Pythagorean; and honours to the dead are a polytheism. Such is the general nature of the fact before us; Mr. Milman argues from it, - 'These things are in heathenism, therefore they are not Christian:' we, on the contrary, prefer to say, 'these things are in Christianity, therefore they are not heathen.' That is, we prefer to say, and we think that Scripture bears us out in saying, that from the beginning the Moral Governor of the world has scattered the seeds of truth far and wide over its extent; that these have variously taken root, and grown up as in the wilderness, wild plants indeed but living; and hence that, as the inferior animals have tokens of an immaterial principle in them, yet have not souls, so the philosophies and religions of men have their life in certain true ideas, though they are not directly divine. Wha ~ John Henry Newman

It is impossible to decide whether a particular detail of the Pythagorean universe was the work of the master, or filled in by a pupil a remark which equally applies to Leonardo or Michelangelo . But there can be no doubt that the basic features were conceived by a single mind; that Pythagoras of Samos was both the founder of a new religious philosophy, and the founder of Science, as the word is understood today. ~ Arthur Koestler

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

The essence of Hilbert's program was to find a decision process that would operate on symbols in a purely mechanical fashion, without requiring any understanding of their meaning. Since mathematics was reduced to a collection of marks on paper, the decision process should concern itself only with the marks and not with the fallible human intuitions out of which the marks were reduced. In spite of the prolonged efforts of Hilbert and his disciples, the Entscheidungsproblem was never solved. Success was achieved only in highly restricted domains of mathematics, excluding all the deeper and more interesting concepts. Hilbert never gave up hope, but as the years went by his program became an exercise in formal logic having little connection with real mathematics. Finally, when Hilbert was seventy years old, Kurt Godel proved by a brilliant analysis that the Entscheindungsproblem as Hilbert formulated it cannot be solved.

Godel proved that in any formulation of mathematics, including the rules of ordinary arithmetic, a formal process for separating statements into true and false cannot exist. He proved the stronger result which is now known as Godel's theorem, that in any formalization of mathematics including the rules of ordinary arithmetic there are meaningful arithmetical statements that cannot be proved true or false. Godel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not ~ Freeman Dyson

The first [method] I might speak about is simplification. Suppose that you are given a problem to solve, I don't care what kind of problem-a machine to design, or a physical theory to develop, or a mathematical theorem to prove or something of that kind-probably a very powerful approach to this is to attempt to eliminate everything from the problem except the essentials; that is, cut is down to size. Almost every problem that you come across is befuddled with all kinds of extraneous data of one sort or another; and if you can bring this problem down into the main issues, you can see more clearly what you are trying to do an perhaps find a solution. Now in so doing you may have stripped away the problem you're after. You may have simplified it to the point that it doesn't even resemble the problem that you started with; but very often if you can solve this simple problem, you can add refinements to the solution of this until you get back to the solution of the one you started with. ~ Claude Shannon

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

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