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Alan Turing and the Limits of Computation

Turing wore many hats during his lifetime. But his fundamental contribution to the development of computing as a mathematical discipline is possibly where his significant scientific impact persists to date. ....

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Turing Uncomputability

As Leibniz suggested, we appear to live in the best of all possible worlds, where the computable functions make life predictable enough to be survivable, while the uncomputable functions make life (and mathematical truth) unpredictable enough to remain interesting, no matter how far computers continue to advance ....

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