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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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II.6 The Development of the Idea of Proof

Leo Corry

1 Introduction and Preliminary Considerations

In many respects the development of the idea of proof is coextensive with the development of mathematics as a whole. Looking back into the past, one might at first consider mathematics to be a body of scientific knowledge that deals with the properties of numbers, magnitudes, and figures, obtaining its justifications from proofs rather than, say, from experiments or inductive inferences. Such a characterization, however, is not without problems. For one thing, it immediately leaves out important chapters in the history of civilization that are more naturally associated with mathematics than with any other intellectual activity. For example, the ...

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