I understand that now. Was not my original takeaway. Apologies for the confusion.
I think the halting problem is more profound: it shows that there are fundamental problems with mathematics, which computation resolves (to the degree to which they can be resolved).
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Do you mean that mathematics itself has inherent flaws or is it just that our understanding of it is fundamentally rudimentary?
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IMHO Gödel has shown that the nonconstructive parts of math are flawed.
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