Theorems Quotes - Page 7

• The fundamental laws of the universe which correspond to the two fundamental theorems of the mechanical theory of heat.
  1. The energy of the universe is constant.
  2. The entropy of the universe tends to a maximum.

  Rudolf Clausius

  Science, Law, Two

  Rudolf Clausius (1867). “The Mechanical Theory of Heat: With Its Applications to the Steam-engine and to the Physical Properties of Bodies”, p.365

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• I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn.

  Archimedes

  Education, Math, Littles

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• Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It's just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas.

  William Thurston

  Math, Thinking, Errors

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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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• Too much knowledge could be a bad thing. I was lead to the Szemerédi theorem by proving a result, about squares, that Euler had already proven, and I relied on an "obvious" fact, about arithmetical progressions, that was unproved at the time. But that lead me to try and prove that formerly unproved statement- about arithmetical progressions-and that ultimately lead to the Szemerédi Theorem.

  Endre Szemeredi

  Science, Squares, Trying

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

  Alan Perlis

  Today, Lasts, Next

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• 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

  Spring, Blue, Wind

  Carl Sandburg (2003). “The Complete Poems of Carl Sandburg”, p.318, Houghton Mifflin Harcourt

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• Mathematics does not grow through a monotonous increase of the number of indubitably established theorems but through the incessant improvement of guesses by speculation and criticism, by the logic of proofs and refutations.

  Imre Lakatos

  Numbers, Criticism, Doe

  Imre Lakatos (1976). “Proofs and Refutations: The Logic of Mathematical Discovery”, p.5, Cambridge University Press

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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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• 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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• 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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• 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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• 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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• [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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