Theorems Quotes - Page 4

• 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

  Beautiful, Analysis, May

  Lord Kelvin, LL.D., D.C.L., F.R.S. and Peter Guthrie Tait, M.A. (1912). “Elements of Natural Philosophy”

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• 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

  Space, Simplicity, Patterns

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• All theorems have three names: a French name, a German name, and a Russian name, each nationality having claimed to discover it first. Once in a while there's an English name, too, but it's always Newton.

  Arthur Mattuck

  Names, Three, Firsts

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• The theory that gravitational attraction is inversely proportional to the square of the distance leads by remorseless logic to the conclusion that the path of a planet should be an ellipse .... It is this logical thinking that is the real meat of the physical sciences. The social scientist keeps the skin and throws away the meat.... His theorems no more follow from his postulates than the hunches of a horse player follow logically from the latest racing news. The result is guesswork clad in long flowing robes of gobbledygook.

  Anthony Standen

  Horse, Real, Distance

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• One would normally define a "religion" as a system of ideas that contain statements that cannot be logically or observationally demonstrated... Gödels theorem not only demonstrates that meathematics is a religion, but shows that mathematics is the only religion that proves itself to be one!

  John D. Barrow

  Ideas, Mathematics, Prove It

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• The Limbaugh Theorem is the way Obama gets away with no accountability for anything he's done is he never was perceived as governing. He was always as an outsider campaigning all the time against powerful forces trying to stop whatever it was he wanted to do.

  Rush Limbaugh

  Powerful, Accountability, Trying

  Source: www.rushlimbaugh.com

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• One way of looking at Impossibility Theorem is that we proposed some criteria for what a good system should be: what is it you want from a voting system, and impose some conditions. And then ask: can you have a voting system that guarantees that?

  Kenneth Arrow

  Guarantees That, Voting, Want

  Source: electology.org

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• In my [Impossibility] theorem I'm assuming that the information is a ranking. Each voter can say of any two candidates, I prefer this one to this one. So then we have essentially a ranking. It's a list saying this is my first choice. This is my second choice. Each voter, in principle, could be asked to give that entire piece of information. In the ordinary Plurality Voting, say as used in electing Congressmen, we generally only ask for the first choice. But, in principle, we could ask for more choices.

  Kenneth Arrow

  Two, Giving, Voting

  Source: electology.org

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• There's only one problem that bothers me. And that's something my theorem [ of Impossibility] really doesn't cover. In my theorem I was assuming people vote sincerely. The trouble with methods where you have three or four classes, I think if people vote sincerely they may well be very satisfactory. The problem is the incentive to misrepresent your vote may be high.

  Kenneth Arrow

  Thinking, Class, People

  Source: electology.org

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• Never call yourself a philosopher, nor talk a great deal among the unlearned about theorems, but act conformably to them. Thus, at an entertainment, don't talk how persons ought to eat, but
  eat as you ought. For remember that in this manner Socrates also universally avoided all ostentation.

  Epictetus

  Entertainment, Philosopher, Remember

  Epictetus (2012). “The Handbook of Epictetus”, p.17, Simon and Schuster

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• 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

  Mistake, Fall, Mean

  "The Shifting Realities of Philip K. Dick". Book by Lawrence Sutin, 1995.

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• It is not so much whether a theorem is useful that matters, but how elegant it is.

  Stanislaw Ulam

  Matter, Elegant

  "Adventures of a Mathematician". Book by Stanislaw Ulam, 3rd edition. Chapter 15: "Random Reflections on Mathematics and Science", p. 274, 1991.

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• There's no answer for my offense, just like the polythagorean theorem.

  Shaquille O'Neal

  Stupid, Nba, Answers

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• 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

  Thinking, Should Have, Law

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• 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.

  IU?. I. Manin

  Goal, Definitions, Steps

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• Did chemistry theorems exist? No: therefore you had to go further, not be satisfied with the quia, go back to the origins, to mathematics and physics. The origins of chemistry were ignoble, or at least equivocal: the dens of the alchemists, their abominable hodgepodge of ideas and language, their confessed interest in gold, their Levantine swindles typical of charlatans and magicians; instead, at the origin of physics lay the strenuous clarity of the West-Archimedes and Euclid.

  Primo Levi

  Ideas, Alchemist, Gold

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• Without computers we will be stuck only proving theorems that have short proofs.

  Kenneth Appel

  Science, Computer, Mathematics

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• 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

  Confused, Science, Trying

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• We decided that 'trivial' means 'proved'. So we joked with the mathematicians: We have a new theorem- that mathematicians can prove only trivial theorems, because every theorem that's proved is trivial.

  Richard P. Feynman

  Mean, Science, Mathematics

  Richard P Feynman (2014). “Surely You're Joking Mr Feynman: Adventures of a Curious Character as Told to Ralph Leighton”, p.84, Random House

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• I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths.

  Gottlob Frege

  Roots, Tree, Technique

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• 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

  World, Economics, Increase

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• ... 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

  Squares, Two Sides, Brain

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• The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.

  Kurt Gödel

  Development, Well Known, Mathematics

  Kurt Gödel, S. Feferman (1986). “Kurt Gödel: Collected Works: Volume I: Publications 1929-1936”, p.145, Oxford University Press

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• 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

  Examination, Remember, Equations

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• 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

  Independent, Thinking, Civilization

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