Millmans Theorem Quotes

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

In a world in which the price of calculation continues to decrease rapidly, but the price of theorem proving continues to hold steady or increase, elementary economics indicates that we ought to spend a larger and larger fraction of our time on calculation. ~ John Tukey

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

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

Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they? ~ Alfred Renyi

Stephen Hawking has proven a general theorem stating that all solutions of Einstein's equations that allow faster-than-light travel must involve negative matter or energy. ~ Michio Kaku

Imagine you're sitting having dinner in a restaurant. At some point during the meal, your companion leans over and whispers that they've spotted Lady Gaga eating at the table opposite. Before having a look for yourself, you'll no doubt have some sense of how much you believe your friends theory. You'll take into account all of your prior knowledge: perhaps the quality of the establishment, the distance you are from Gaga's home in Malibu, your friend's eyesight. That sort of thing. If pushed, it's a belief that you could put a number on. A probability of sorts. As you turn to look at the woman, you'll automatically use each piece of evidence in front of you to update your belief in your friend's hypothesis Perhaps the platinum-blonde hair is consistent with what you would expect from Gaga, so your belief goes up. But the fact that she's sitting on her own with no bodyguards isn't, so your belief goes down. The point is, each new observations adds to your overall assessment. This is all Bayes' theorem does: offers a systematic way to update your belief in a hypothesis on the basis of the evidence. It accepts that you can't ever be completely certain about the theory you are considering, but allows you to make a best guess from the information available. So, once you realize the woman at the table opposite is wearing a dress made of meat -- a fashion choice that you're unlikely to chance up on in the non-Gaga population -- that might be enough to tip your belief over the thresho ~ Hannah Fry

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

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

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

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful. ~ George Boole

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

There is a theorem that colloquially translates, You cannot comb the hair on a bowling ball ... Clearly, none of these mathematicians had Afros, because to comb an Afro is to pick it straight away from the scalp. If bowling balls had Afros, then yes, they could be combed without violation of mathematical theorems. ~ Neil DeGrasse Tyson

Gradually, at various points in our childhoods, we discover different forms of conviction. There's the rock-hard certainty of personal experience ("I put my finger in the fire and it hurt,"), which is probably the earliest kind we learn. Then there's the logically convincing, which we probably come to first through maths, in the context of Pythagoras's theorem or something similar, and which, if we first encounter it at exactly the right moment, bursts on our minds like sunrise with the whole universe playing a great chord of C Major. ~ Philip Pullman

And now of a sudden my illusion vanished. What was my body to me? A kind of flunkey in my service. Let my anger wax hot, my love grow exalted, my hatred collect in me, and the boasted solidarity between me and my body was gone.

Your son is in a burning house. Nobody can hold you back. You may burn up, but what do you think of that? You are ready to bequeath the rags of your body to any man who will take them. You discover that what you set so much store by is trash. You would sell your hand, if need be, to give a hand to a friend. It is in your act that you exist, not in your body. Your act is yourself, and there is no other you. Your body belongs to you: it is not you. Are you about to strike an enemy? No threat of bodily harm can hold you back. You? It is the death of your enemy that is you. You? It is the rescue of your child that is you. In that moment you exchange yourself against something else; and you have no feeling tat you lost by the exchange. Your members? Tools. A tool snaps in your hand: how important is that tool? You exchange yourself against the death of your enemy, the rescue of your child, the recovery of your patient, the perfection of your theorem...Your true significance becomes dazzlingly evident. Your true name is duty, hatred, love, child, theorem. There is no other you than this. ~ Antoine De Saint Exupery

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

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

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

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

The overall structure of the calculus is simple. The subject is defined by a fantastic leading idea, one basic axiom, a calm and profound intellectual invention, a deep property, two crucial definitions, one ancillary definition, one major theorem, and the fundamental theorem of the calculus.
The fantastic leading idea: the real world may be understood in terms of the real numbers.
The basic axiom: brings the real numbers into existence.
The calm and profound invention: the mathematical function.
The deep property: continuity.
The crucial definitions: instantaneous speed and the area underneath a curve.
The ancillary definition: a limit
The major theorem: the mean value theorem.
The fundamental theorem of the calculus is the fundamental theorem of the calculus.
These are the massive load-bearing walls and buttresses of the subject. ~ David Berlinski

The theorem can be likened to a pearl, and the method of proof to an oyster. The pearl is prized for its luster and simplicity; the oyster is a complex living beast whose innards give rise to this mysteriously simple gem. ~ Douglas R. Hofstadter

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

Kurt Gödel's achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible far in space and time. ... The subject of logic has certainly completely changed its nature and possibilities with Gödel's achievement." - John von Neumann ~ John Von Neumann

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

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

About Thomas Hobbes: He was 40 years old before he looked on geometry; which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and "twas the 47 El. libri I" [Pythagoras' Theorem]. He read the proposition "By God", sayd he, "this is impossible:" So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that truth. This made him in love with geometry. ~ John Aubrey

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

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

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

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

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

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

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

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

Mean-Value Theorem for Integrals, 123 but for Hal's synoptic purposes here it's enough to say that megatonnage is distributed among Combatants according to an integrally regressed ratio of (a) ~ David Foster Wallace

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

In that moment, the future - uncontainable by any Theorem mathematical or otherwise - stretched out before Colin: infinite and unknowable and beautiful. ~ John Green

Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics. ~ Lord Kelvin

I swear the older I get, the more I value bad examples over good ones. It's a good thing too, because most people are egotistical, neurotic, self-absorbed peons, insistent on wearing near-sighted glasses in a far-sighted world. And it's this exact sort of myopic ignorance that has led to my groundbreaking new theory. I call it Mim's Theorem of Monkey See Monkey Don't, and what it boils down to is this: it is my belief that there are some people whose sole purpose of existence is to show the rest of how not to act. ~ David Arnold

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

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