Math Quotes - Page 25

• I concluded that I might take as a general rule the principle that all things which we very clearly and obviously conceive are true: only observing, however, that there is some difficulty in rightly determining the objects which we distinctly conceive.

  Rene Descartes

  Principles, Might, Difficulty

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• When writing about transcendental issues, be transcendentally clear.

  Rene Descartes

  Writing, Issues, Transcendental

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• Gauss replied, when asked how soon he expected to reach certain mathematical conclusions, that he had them long ago, all he was worrying about was how to reach them!

  Rene Dubos

  Long Ago, Worry, Certain

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• What is this frog and mouse battle among the mathematicians?

  Albert Einstein

  Battle, Frogs, Mice

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• Make your mistakes work for you by learning from them.

  Donald Trump

  Mistake, Teaching

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• Figures don't lie, but liars figure.

  Mark Twain

  Liars, Lying, Teaching

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• The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.

  John von Neumann

  Teaching, Thinking, Achievement

  John Von Neumann, F. Bródy, Tibor Vámos (1995). “The Neumann Compendium”, p.620, World Scientific

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• Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the universal organ for world understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation.

  Hermann Weyl

  Teaching, Creative, Understanding

  Hermann Weyl (1968). “Gesammelte Abhandlungen”

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• A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press.

  Gottlob Frege

  Giving, Foundation, Letters

  Note in the appendix of "Grundlagen der Arithmetik" (Vol. 2), after Frege had received a letter of Bertrand Russell in which Russell had explained his discovery of, what is now known as, Russell's paradox, 1903.

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• The mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe.

  Karl Pearson

  May, Results, Description

  Karl Pearson (1900). “The grammar of science”, p.505, Рипол Классик

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• The world of ideas is not revealed to us in one stroke; we must both permanently and unceasingly recreate it in our consciousness.

  Rene Thom

  Ideas, World, Consciousness

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• ... if one were to refuse to have direct, geometric, intuitive insights, if one were reduced to pure logic, which does not permit a choice among every thing that is exact, one would hardly think of many questions, and certain notions ... would escape us completely.

  Henri Lebesgue

  Thinking, Choices, Doe

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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

  Thinking, Errors, Ideas

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• The years of searching in the dark for a truth that one feels but cannot express, the intense desire and the alternations of confidence and misgiving until one breaks through to clarity and understanding, are known only to him who has experienced them himself.

  Albert Einstein

  Dark, Years, Break Through

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• The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.

  David Hilbert

  Figures, Diagrams, Formulas

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• ... commutative algebra is a lot like topology, only backwards.

  John C. Baez

  Topology, Algebra, Backwards

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• Geometry is the art of correct reasoning from incorrectly drawn figures.

  Henri Poincare

  Art, Figures, Geometry

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• Mathematical objects are determined by - and understood by - the network of relationships they enjoy with all the other objects of their species.

  Barry Mazur

  Determined, Enjoy, Understood

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• A great deal more is known than has been proved.

  Richard P. Feynman

  Deals, Has Beens, Known

  "The Music of the Primes : Searching to Solve the Greatest Mystery of Mathematics". Book by Marcus du Sautoy, 2003.

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• There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.

  Alfred North Whitehead

  Errors, Facts, Common

  Alfred North Whitehead (1958). “An Introduction to Mathematics”, p.16, New York : Oxford University Press, 1958 [c1948]

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• The electron is a theory we use; it is so useful in understanding the way nature works that we can almost call it real.

  Richard P. Feynman

  Real, Understanding, Use

  "Surely You're Joking, Mr. Feynman!". Book by Richard P. Feynman, p. 70, 1985.

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• Although this may seem a paradox, all exact science is based on the idea of approximation. If a man tells you he knows a thing exactly, then you can be safe in inferring that you are speaking to an inexact man.

  Bertrand Russell

  Men, Ideas, May

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• I don't know if the police of naming statements would agree with this.

  Roman Abramovich

  Police, Agree, Knows

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• Quadratic reciprocity is the song of love in the land of prime numbers.

  Kato

  Song, Land, Numbers

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• The prime ideal is a princess of the world of ideals. Her father is the prince 'Point' in the world of geometry. Her mother is the princess 'Prime Numbers' in the world of numbers. She inherits the purity from her parents.

  Kato

  Mother, Father, Princess

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