Mathematics Quotes - Page 25

• Another characteristic of mathematical thought is that it can have no success where it cannot generalize.

  Charles Sanders Peirce

  Success, Science, Thinking

  Charles Sanders Peirce (1933). “Collected Papers of Charles Sanders Peirce: Exact logic (Published papers).. The Simplest mathematics”, Harvard University Press

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• As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

  G. H. Hardy

  History, Achievement, Endure

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.80, Cambridge University Press

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• Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

  Hermann Weyl

  Substance, Mathematical

  "Mind and Nature: Selected Writings on Philosophy, Mathematics, and Physics".

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• Chess problems are the hymn-tunes of mathematics.

  G. H. Hardy

  Science, Hymns, Tunes

  G. H. Hardy (2012). “A Mathematician's Apology”, p.87, Cambridge University Press

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• Distrust even Mathematics; albeit so sublime and highly perfected, we have here a machine of such delicacy it can only work in vacuo, and one grain of sand in the wheels is enough to put everything out of gear. One shudders to think to what disaster such a grain of sand may bring a Mathematical brain. Remember Pascal.

  Anatole France

  Science, Thinking, Sublime

  Anatole France (1920). “The garden of Epicurus”

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• Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

  Lord Kelvin

  Common Sense, Imagine, Harsh

  "Life of Lord Kelvin". Book by Silvanus Phillips Thompson, 1910.

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• Euclid avoids it [the treatment of the infinite]; in modern mathematics it is systematically introduced, for only then is generality obtained.

  Arthur Cayley

  Infinite, Modern, Euclid

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• For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

  Richard Courant

  Philosophy, Science, Sensual

  "What is Mathematics?" by Richard Courant, (p. xix), 1941.

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• Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.

  G. H. Hardy

  Real, Science, Understanding

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.81, Cambridge University Press

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• Having been the discoverer of many splendid things, he is said to have asked his friends and relations that, after his death, they should place on his tomb a cylinder enclosing a sphere, writing on it the proportion of the containing solid to that which is contained.

  Archimedes

  Writing, Science, Spheres

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• I also ask you my friends not to condemn me entirely to the mill of mathematical calculations, and allow me time for philosophical speculations, my only pleasures.

  Johannes Kepler

  Philosophy, Philosophical, Science

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• I also require much time to ponder over the matters themselves, and particularly the principles of mechanics (as the very words: force, time, space, motion indicate) can occupy one severely enough; likewise, in mathematics, the meaning of imaginary quantities, of the infinitesimally small and infinitely large and similar matters.

  Heinrich Hertz

  Science, Space, Principles

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• I confess, that very different from you, I do find sometimes scientific inspiration in mysticism ... but this is counterbalanced by an immediate sense for mathematics.

  Wolfgang Pauli

  Inspiration, Different, Sometimes

  Wolfgang Pauli (2008). “Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u.a. Band IV, Teil III: 1955–1956. Scientific Correspondence with Bohr, Einstein, Heisenberg, a.o. Volume IV, Part III: 1955–1956”, p.148, Springer-Verlag

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• I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world... Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.

  G. H. Hardy

  Differences, Creating, Escaping

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• I never could do anything with figures, never had any talent for mathematics, never accomplished anything in my efforts at that rugged study, and to-day the only mathematics I know is multiplication, and the minute I get away up in that, as soon as I reach nine times seven- [He lapsed into deep thought, trying to figure nine times seven. Mr. McKelway whispered the answer to him.] I've got it now. It's eighty-four. Well, I can get that far all right with a little hesitation. After that I am uncertain, and I can't manage a statistic.

  Mark Twain

  Science, Accomplishment, Effort

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• If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.

  George Polya

  Book, Obvious Things, Giving

  George Pólya (1968). “Mathematical discovery: on understanding, learning, and teaching problem solving”

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• If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

  Henri Poincare

  Science, History, Wish

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• If you want to be a physicist, you must do three things-first, study mathematics, second, study more mathematics, and third, do the same.

  Arnold Sommerfeld

  Science, Three, Want

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• In his wretched life of less than twenty-seven years Abel accomplished so much of the highest order that one of the leading mathematicians of the Nineteenth Century could say without exaggeration, "Abel has left mathematicians enough to keep them busy for five hundred years." Asked how he had done all this in the six or seven years of his working life, Abel replied, "By studying the masters, not the pupils."

  Eric Temple Bell

  Seven Years, Order, Abel

  Eric Temple Bell (1938). “The queen of the sciences”

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• In mathematics there are no true controversies.

  Carl Friedrich Gauss

  Controversy

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• In the last two months I have been very busy with my own mathematical speculations, which have cost me much time, without my having reached my original goal. Again and again I was enticed by the frequently interesting prospects from one direction to the other, sometimes even by will-o'-the-wisps, as is not rare in mathematic speculations.

  Carl Friedrich Gauss

  Two, One Direction, Interesting

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• Integers are the fountainhead of all mathematics.

  Hermann Minkowski

  Fountainhead, Integers

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• It is always noteworthy that all those who seriously study this science [the theory of numbers] conceive a sort of passion for it.

  Carl Friedrich Gauss

  Passion, Numbers, Study

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• This splendid subject [mathematics], queen of all exact sciences, and the ideal and norm of all careful thinking.

  G. Stanley Hall

  Queens, Thinking, Splendid

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• To a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-footed animal is an animal.

  Bertrand Russell

  Animal, Intellectual, Mind

  Bertrand Russell (2009). “The Basic Writings of Bertrand Russell”, p.230, Routledge

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