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Suppose some random nutjob thought they had solved this problem. What should they do with it?

Am I naive to think we've reached the point where anyone would be able to get a revolutionary thought out there quite easily? If I were such a brilliant nutjob, I'd post it on some math or computer science forum if I just wanted to be recognised. Even if just a few people see it, such an audience would likely be entrenched with the right communities to signal boost it.

Nah, cranks post inscrutable incorrect proofs (and/or bizarre unified theories) to math forums regularly. They often lack the vocabulary to even format it in a way the community can read and correct.

I recall there was a mathematician that was cataloging all the 'squaring the circle' methods people kept mailing him (it's been proven to be impossible).

If their idea were legitimately revolutionary and they had the vocabulary to express it, they could simply publish.

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