Gödel’s discovery brought back a sense of wonder to mathematics and to the rest of human knowledge. His incompleteness theorem underlies the fact that human investigation can never exhaust all that can be known. Every discovery builds a path to a new discovery.
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David Hilbert wanted all mathematics to be proved by logical steps. Kurt Gödel showed that no axiomatic system could be complete and consistent at the same time.
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The limits of science can be as instructive as the discoveries. If science someday proved that computer systems could never reproduce some aspect of mind, we'd have learned something important about the nature of mind.
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Kurt Gödel (1906–1978) proved that there are truths in mathematical logic that lie outside mathematical logic, which means that the mind cannot be understood simply as a computer.
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