Theorems Quotes - Page 3

• The Open Source theorem says that if you give away source code, innovation will occur. Certainly, Unix was done this way... However, the corollary states that the innovation will occur elsewhere. No matter how many people you hire. So the only way to get close to the state of the art is to give the people who are going to be doing the innovative things the means to do it. That's why we had built-in source code with Unix. Open source is tapping the energy that's out there.

  Bill Joy

  Art, Mean, People

  "Creating One Huge Computer". Interview with Spencer Reiss, www.wired.com. July 15, 1998.

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• In the "commentatio" (note presented to the Russian Academy) in which his theorem on polyhedra (on the number of faces, edges and vertices) was first published Euler gives no proof. In place of a proof, he offers an inductive argument: he verifies the relation in a variety of special cases. There is little doubt that he also discovered the theorem, as many of his other results, inductively.

  George Polya

  Numbers, Discovery, Giving

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• He knew by heart every last minute crack on its surface. He had made maps of the ceiling and gone exploring on them; rivers, islands, and continents. He had made guessing games of it and discovered hidden objects; faces, birds, and fishes. He made mathematical calculations of it and rediscovered his childhood; theorems, angles, and triangles. There was practically nothing else he could do but look at it. He hated the sight of it.

  Josephine Tey

  Heart, Games, Rivers

  Josephine Tey (2013). “The Daughter of Time”, p.11, Simon and Schuster

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• 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

  Mathematics, Blah, Mathematical

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• Bells theorem dealt a shattering blow to Einsteins position by showing that the conception of reality as consisting of separate parts, joined by local connections, is incompatible with quantum theory... Bells theorem demonstrates that the universe is fundamentally interconnected, interdependent, and inseparable.

  Fritjof Capra

  Science, Blow, Reality

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• Bell's theorem...proves that quantum theory requires connections that appear to resemble telepathic communication.

  Gary Zukav

  Communication, Science, Connections

  Gary Zukav (1979). “The dancing Wu Li masters: an overview of the new physics”, Bantam

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

  Lord Acton

  Atheism, Sin, Liable

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• Math does come easily to me, but I was always much more interested in what theorems imply about the world than in proving them.

  Antony Garrett Lisi

  Math, Doe, World

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• 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

  Information, Principles, Needs

  Alfréd Rényi (1984). “A diary on information theory”

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• 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

  Science, Hair, Balls

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• Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the "logic piano" imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.

  Henri Poincare

  Mean, Math, Piano

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• There are very few theorems in advanced analysis which have been demonstrated in a logically tenable manner. Everywhere one finds this miserable way of concluding from the special to the general and it is extremely peculiar that such a procedure has led to so few of the so-called paradoxes.

  Niels Henrik Abel

  Science, Special, Peculiar

  Letter to Professor Christoffer Hansteen (1826) "Oeuvres Complètes de N. H. Abel", mathematician, Nouvelle edition (1881) ed., Peter Ludwig Mejdell Sylow & Sophus Lie, Vol. 2, pp. 263-265, as quoted by Øystein Ore, "Niels Henrik Abel: Mathematician Extraordinary", p. 113, 1957.

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• 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

  Believe, Pythagorean Theorem, Rights

  Jonathan Haidt (2012). “The Righteous Mind: Why Good People Are Divided by Politics and Religion”, p.32, Vintage

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• What philosophy worthy of the name has truly been able to avoid the link between poem and theorem?

  Michel Serres

  Philosophy, Names, Links

  Michel Serres, Bruno Latour (1995). “Conversations on Science, Culture, and Time”, p.34, University of Michigan Press

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• Which is to say that culture is not a reflex of political economy, but
  that society is now a reflex of key shifts in music theory and practice....
  [Sampladelia is] the sound made by those early-twentieth-century discoveries
  in particle physics and relativiity theory, the projection of the minds of
  Einstein, Heisenbery, and Bohr, their fateful explorations of liquid time,
  curving space, uncertainty fields and relativity theorems, into densely
  configured and fully ambivalent android music tracks

  Arthur Kroker

  Discovery, Practice, Space

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• Phyllis explained to him, trying to give of her deeper self, 'Don't you find it so beautiful, math? Like an endless sheet of gold chains, each link locked into the one before it, the theorems and functions, one thing making the next inevitable. It's music, hanging there in the middle of space, meaning nothing but itself, and so moving...'

  John Updike

  Beautiful, Moving, Math

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• 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

  Hurt, Math, Science

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• 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

  Teaching, Writing, Science

  "How to Solve It" by George Polya, 2nd edition, (p. xv), 1957.

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• A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution.

  Richard Arnold Epstein

  Games, Information, States

  "Johannes Gutenberg printed playing cards the same year as his famous Bible (1440). The cards from Gutenberg's press were Tarot cards, from which the modern deck is derived. The Theory of Gambling and Statistical Logic". Book by Richard Arnold Epstein, 1977.

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• 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

  Pythagorean Theorem, Challenges, Guilt

  "Iyanla Vanzant interview for fourth season of ‘Iyanla: Fix My Life’ returning Sept. 6". Interview with Rodney Ho, radiotvtalk.blog.ajc.com. September 6, 2014.

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• I have a basic theorem as to how I do my jokes. Growing up, I knew when to cross the line and when not to cross the line. It's the same with my comedy. I know what my audience will take and how much they won't take. I can't give you a formula for it. It's my own personal formula inside my head. Somebody else's might be different.

  Larry the Cable Guy

  Growing Up, Giving, Different

  Source: smashinginterviews.com

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• Though determinants and matrices received a great deal of attention in the nineteenth century and thousands of papers were written on these subjects, they do not constitute great innovations in mathematics.... Neither determinants nor matrices have influenced deeply the course of mathematics despite their utility as compact expressions and despite the suggestiveness of matrices as concrete groups for the discernment of general theorems of group theory.

  Morris Kline

  Expression, Innovation, Groups

  Morris Kline (1990). “Mathematical Thought From Ancient to Modern Times”, p.795, Oxford University Press

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• The proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself.

  Barry Mazur

  Long, Humanity, Lasts

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• I think that mathematics can benefit by acknowledging that the creation of good models is just as important as proving deep theorems.

  David Mumford

  Thinking, Important, Benefits

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• The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations.

  G. H. Hardy

  Years, Numbers, Branches

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