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).
Artificial Intelligence »Artificial Intelligence
Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
No: computers are limited by Gödel's theorems »No: computers are limited by Gödel's theorems
Mathematical insight is non-algorithmic
Alogrithms are fixed interpretations »Alogrithms are fixed interpretations
The absurdity of algorithmic insight »The absurdity of algorithmic insight
Mathematical insight is not the important issue »Mathematical insight is not the important issue
Mathematical truth may evolve  »Mathematical truth may evolve
Penrose's intuition is irrelevant »Penrose's intuition is irrelevant
Roger Penrose »Roger Penrose
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