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The ideas of a time are like the clothes of a season: they are as arbitrary, as much imposed by some superior will which is seldom explicit. They are utilitarian and political, the instruments of smooth-running government.
Wyndham Lewis
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Mathematics is the body of knowledge centered on concepts such as quantity, structure, space, and change, and the academic discipline which studies them. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.


  • If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics.
  • <math>10^{50}</math> is a long way from infinity.
    • Daniel Shanks, Solved and Unsolved Problems in Number Theory, 3rd edition, chapter IV, page 217.
    • Computer calculation even up to a big number can't really say much about asymptotic behaviour.
  • Numbers exist only in our minds. There is no physical entity that is number 1. If there were, 1 would be in a place of honor in some great museum of science, and past it would file a steady stream of mathematicians gazing at 1 in wonder and awe.
    • Linear Algebra by Fraleigh/Beauregard
  • Great fleas have little fleas upon their backs to bite 'em,
    And little fleas have lesser fleas, and so ad infinitum,
    And the great fleas themselves, in turn, have greater fleas to go on,
    While these again have greater still, and greater still, and so on.
  • So, nat'ralists observe, a flea
    Hath smaller fleas that on him prey,
    And these have smaller still to bite 'em
    And so proceed ad infinitum.
  • A man with all the algebra in the world is often only an ass when he knows nothing else. Perhaps in ten years society may derive advantage from the curves which these visionary algebraists will have laboriously squared. I congratulate posterity beforehand. But to tell you the truth I see nothing but a scientific extravagance in all these calculations. That which is neither useful nor agreeable is worthless. And as for useful things, they have all been discovered; and to those which are agreeable, I hope that good taste will not admit algebra among them.
  • As to your Newton, I confess I do not understand his void and his gravity; I admit he has demonstrated the movement of the heavenly bodies with more exactitude than his forerunners; but you will admit it is an absurdity to to maintain the existence of Nothing.
    • Frederick the Great, Letters of Voltaire and Frederick the Great (New York: Brentano's, 1927), transl. Richard Aldington, letter 221 from Frederick to Voltaire, 25 November 1777.
  • Euler calculated the force of the wheels necessary to raise the water in a reservoir … My mill was carried out geometrically and could not raise a drop of water fifty yards from the reservoir. Vanity of vanities! Vanity of geometry!
    • Frederick the Great, Letters of Voltaire and Frederick the Great (New York: Brentano's, 1927), transl. Richard Aldington, letter 221 from Frederick to Voltaire, 25 November 1777.
  • Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.
    • W.S. Anglin, in Mathematics and History, elucidating the symmetry between the creative and logical aspects of mathematics.
  • Mathematics, rightly viewed, possesses not only truth, but supreme beauty —a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
  • ... from the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.
  • ... mathematics has the dubious honor of being the least popular subject in the curriculum ... Future teachers pass through the elementary schools learning to detest mathematics ... They return to the elementary school to teach a new generation to detest it.


  • Mathematics is man's attempt on understanding nature.
  • A mathematician is a blind man in a dark room looking for a black cat which isn't there.
  • Mathematics seems to endow one with something like a new sense.
  • Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable sub-human who has learned to wear shoes, bathe, and not make messes in the house.
  • As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
  • Do not worry about your problems with mathematics, I assure you mine are far greater.
  • God does not care about our mathematical difficulties. He integrates empirically.
  • I don't believe in mathematics.
  • Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.
  • As long as algebra is taught in school, there will be prayer in school.
  • He who can properly define and divide is to be considered a god.
  • The knowledge of which geometry aims is the knowledge of the eternal.
  • Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state.
  • I admit that mathematical science is a good thing. But excessive devotion to it is a bad thing.
  • I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.
  • I have no faith in political arithmetic.
  • If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.
  • In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy.
  • In mathematics you don't understand things. You just get used to them.
  • It is easy to lie with statistics. It is hard to tell the truth without it.
  • Life is good for only two things, discovering mathematics and teaching mathematics.
  • Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.
  • Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another.
  • [Mathematics] is an independent world created out of pure intelligence.
  • Mathematics is not yet capable of coping with the naïveté of the mathematician himself.
  • Mathematics is the only instructional material that can be presented in an entirely undogmatic way.
  • Mathematics is the science of what is clear by itself.
  • Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. (referring to the axiomatic method, where certain properties of an (otherwise unknown) structure are assumed and consequences thereof are then logically derived)
  • Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.
  • How dare we speak of the laws of chance? Is not chance the antithesis of all law?
  • Measure what is measurable, and make measurable what is not so.
  • No human investigation can be called real science if it cannot be demonstrated mathematically.
  • Now I feel as if I should succeed in doing something in mathematics, although I cannot see why it is so very important...The knowledge doesn't make life any sweeter or happier, does it?
  • One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.
  • Sex is the mathematics urge sublimated.
  • The art of doing mathematics consists in finding that special case which contains all the germs of generality.
  • The infinite! No other question has ever moved so profoundly the spirit of man.
  • Mathematics is a game played according to certain simple rules with meaningless marks on paper.
  • The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and not being.
  • The mathematician has reached the highest rung on the ladder of human thought.
  • The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.
  • The simplest schoolboy is now familiar with facts for which Archimedes would have sacrificed his life.
  • There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.
  • There is something I don't understand about algebra: It has been around for thousands of years, yet no one has ever found out what the value of "x" really is.

Falsely attributed

  • The good Christian should beware of mathematicians, and all those who make empty prophesies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell. -- St. Augustine This is a very bad mistranslation of De genesim ad litteram libri XII, book 2, 17.37. 'Mathematici' in Latin means astrologers, not mathematicians, and the book makes repeated attacks on astrology. The text really reads: For which reason both astrologers and those impiously making divinings, as the truth says emphatically, must be avoided by the good Christian, lest after making a pact of agreement they entangle their soul in a hidden partnership with demons.

See also

External links

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