Theorems Quotes - Page 7

• Theorems are fun especially when you are the prover, but then the pleasure fades. What keeps us going are the unsolved problems.

  Carl Pomerance

  Fun, Math, Science

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• Theorems are not to mathematics what successful courses are to a meal.

  Gian-Carlo Rota

  Successful, Meals, Mathematics

  Mark Kac, Gian-Carlo Rota, Jacob T. Schwartz (2008). “Discrete Thoughts: Essays on Mathematics, Science and Philosophy”, p.155, Springer Science & Business Media

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• The development of mathematics toward 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... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.

  Kurt Gödel

  Simple, Two, Development

  "Kurt Gödel: Collected Works: Volume I: Publications 1929-1936".

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• 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 Wiles

  Beautiful, Simple, Years

  "Andrew Wiles on Solving Fermat". The NOVA Interview, www.pbs.org. November 1, 2000.

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• I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.

  G. H. Hardy

  Lying, Believe, Science

  G. H. Hardy (1992). “A Mathematician's Apology”, p.123, Cambridge University Press

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• I approached the bulk of my schoolwork as a chore rather than an intellectual adventure. The tedium was relieved by a few courses that seem to be qualitatively different. Geometry was the first exciting course I remember. Instead of memorizing facts, we were asked to think in clear, logical steps. Beginning from a few intuitive postulates, far reaching consequences could be derived, and I took immediately to the sport of proving theorems.

  Steven Chu

  Sports, Adventure, Science

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• We may consequently state the fundamental theorem of Natural Selection in the form: The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time.

  Ronald Fisher

  Fundamentals, May, Natural

  "The Genetical Theory of Natural Selection". Book by Ronald Fisher, 1930.

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• Unlike mathematical theorems, scientific results can't be proved. They can only be tested again and again, until only a fool would not believe them. I cannot prove that electrons exist..........if you don't believe in them I have a high voltage cattle prod I'm willing to apply as an argument on their behalf. Electrons speak for themselves.

  Seth Lloyd

  Believe, Fool, Argument

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• 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

  Love, Truth, Years

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• 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

  Real, Ignorance, Self

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• [Barack] Obama still is in campaign mode. The Limbaugh Theorem explains it. We've had eight years of Obama and he still isn't being held accountable for the horrible policies that he has implemented because he continues to portray himself as not attached to them.

  Rush Limbaugh

  Eight, Years, Campaigns

  Source: www.rushlimbaugh.com

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• I just enjoy calculating, and it's an instrument I know how to play. It's almost an athletic performance, in a way. I was just watching the Olympics, and that's how I feel when proving a theorem.

  Freeman Dyson

  Play, Athletic, Olympics

  "Legendary physicist Freeman Dyson talks about math, nuclear rockets, and astounding things about the universe". Interview with Elena Holodny, www.businessinsider.com. September 9, 2016.

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• It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts.

  Adrien-Marie Legendre

  Regret, Numbers, Effort

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• 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

  Expression, Serious, Belief

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