The nature of mathematical demonstration is totally different from all other, and the difference consists in this—that, instead of showing the contra… - William Rowan Hamilton

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The nature of mathematical demonstration is totally different from all other, and the difference consists in this—that, instead of showing the contrary of the proposition asserted to be only improbable, it proves it at once to be absurd and impossible. This is done by showing that the contrary of the proposition which is asserted is in direct contradiction to some extremely evident fact, of the truth of which our eyes and hands convince us.