Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don't happen to have all the data. In mathematics we have all the data and yet we don't understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.
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Mathematical reasoning may be regarded...
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. -
Mathematics, rightly viewed, posses not only truth, but supreme beauty a beauty cold and austere, like that of sculpture.
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In studying mathematics or simply using a mathematical principle, if we get the wrong answer in sort of algebraic equation, we do not suddenly feel that there is an anti-mathematical principle that is luring us into the wrong answers.
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Mathematics may be compared to a mill of exquisite workmanship, which grinds your stuff to any degree of fineness; but, nevertheless, what you get out depends on what you put in; and as the grandest mill in the world will not extract wheat flour from peas cods, so pages of formulae will not get a definite result out of loose data.
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So-called professional mathematicians have, in their reliance on the relative incapacity of the rest of mankind, acquired for themselves a reputation for profundity very similar to the reputation for sanctity possessed by theologians.
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What would life be without arithmetic, but a scene of horrors?
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How happy the lot of the mathematician! He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve. No cashier writes a letter to the press complaining about the incomprehensibility of Modern Mathematics and comparing it unfavorably with the good old days when mathematicians were content to paper irregularly shaped rooms and fill bathtubs without closing the waste pipe.
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I know that two and two make four -- and should be glad to prove it too if I could -- though I must say if by any sort of process I could convert 2 and 2 into five it would give me much greater pleasure.
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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.
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Mathematicians are like Frenchman: whatever you say to them they translate Into their own language, and forthwith it is something entirely different.
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