"Fifty years ago Kurt Gödel... proved that the world of pure mathematics is inexhaustible. No finite set of axioms and rules of inference can ever encompass the whole of mathematics. Given any finite set of axioms, we can find meaningful mathematical questions which the axioms leave unanswered. This discovery... came at first as an unwelcome shock to many mathematicians. It destroyed... the hope that they could solve the problem of deciding by a systematic procedure the truth or falsehood of any mathematical statement. ...Gödel's theorem, in denying ...the possibility of a universal algorithm to settle all questions, gave... instead, a guarantee that mathematics can never die. ...there will always be, thanks to Gödel, fresh questions to ask and fresh ideas to discover."
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Academics from the United StatesLogicians from AustriaAcademics from AustriaLogicians from the United StatesMathematicians from Austria
Original Language: English
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Sources
Freeman Dyson, Infinite in All Directions (1988)
https://en.wikiquote.org/wiki/Kurt_G%C3%B6del
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Kurt Gödel
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