Mathematical insight is not the important issue
Even if there's no algorithm for mathematical insight, the lack of one isn't crucial as insight isn't important to mathematics. Problems like Gödel’s theorem and the halting problem can be solved reliably by probalistic algorithms.
Whether or not they are solved by insight or not doesn't matter. Mathematics is grounded in its reliability, not in any particular kind of insight.

Daniel Dennett (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 »Mathematical insight is non-algorithmic
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Mathematical insight is not the important issue
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Daniel Dennett »Daniel Dennett
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