“In plausible reasoning the principal thing is to distinguish… a more reasonable guess from a less reasonable guess.”

Induction and Analogy in Mathematics (1954)

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George Pólya35

Hungarian mathematician 1887–1985

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“The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference.”

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“Everyone knows that mathematics offers an excellent opportunity to learn demonstrative reasoning, but I contend also that there is no other subject in the usual curricula of the schools that affords a comparable opportunity to learn plausible reasoning. …let us learn proving, but also let us learn guessing.”

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