Mathematical insight is non-algorithmic
Many problems of mathematics—eg Gödel's incompleteness problem, the halting problem, etc—can be understood by conscious humans but can't be solved algorithmically. This shows mathematical insight is based on conscious non-algorithmic processes.
Roger Penrose (1990).
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Artificial Intelligence »Artificial Intelligence
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Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
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No: computers are limited by Gödel's theorems »No: computers are limited by Gödel's theorems
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Mathematical insight is non-algorithmic
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Alogrithms are fixed interpretations »Alogrithms are fixed interpretations
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The absurdity of algorithmic insight »The absurdity of algorithmic insight
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Mathematical insight is not the important issue »Mathematical insight is not the important issue
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Mathematical truth may evolve  »Mathematical truth may evolve
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Penrose's intuition is irrelevant »Penrose's intuition is irrelevant
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Roger Penrose »Roger Penrose
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