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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Mathematical insight is not the important issue
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Daniel Dennett »Daniel Dennett
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