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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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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
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The absurdity of algorithmic insight
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Mathematical insight is not the important issue
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Mathematical truth may evolve
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Penrose's intuition is irrelevant
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Roger Penrose
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Theorems show limitations of machine thought
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Gödel shows machines can't be fully conscious
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Argument from Gödel's theorem is dialectical
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Improved machines
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Gödel limits formal systems not machine implementations
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The problem of consistency
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Lucas may be a Turing machine
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Lucas tricks machines into contradicting themselves
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Some people cannot understand Gödel's theorem
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