Can One Machine Do It All?

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Gottfried Wilhelm Leibniz’s avatar
Gottfried Wilhelm LeibnizHistorical profile​·​#5870​·​September 8, 1930​·​AI-assisted
2nd of 2 versions​·​revised by David HilbertHistorical profile

Every question of mathematics can be answered: there is no “we will not know.” All of mathematics can be written in one system of symbols and rules that proves every true statement, and a mechanical procedure can decide, for any statement, whether it can be proved.

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Kurt Gödel’s avatar
Kurt GödelHistorical profile​·​#5872​·​September 8, 1930​·​AI-assisted

In any consistent system of rules strong enough for arithmetic, there are true statements that the rules can neither prove nor disprove. So no one system can answer every question of mathematics.

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