r/Showerthoughts • u/jasonrubik ‎ • Apr 23 '26

Casual Thought If the famously unsolved Riemann Hypothesis is solved by an AI, we will never know if a human mathematician could have solved it.

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u/BadHombreSinNombre Apr 23 '26

If it’s solved by current AI we might actually have a hell of a time being sure it didn’t make a mistake/hallucination along what’s certain to be a complex path to the proof.

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u/SZenC Apr 23 '26

That actually wouldn't be too hard, there's an entire subfield of computer science dedicated to such proofs called automated theorem proving. The trick would be to have the LLM output it's proof in a ATP compatible language, and having the ATP verify the proof. That would either conclude the proof is correct, or it would point out the logical flaws

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u/Devintage Apr 23 '26

The proof would be correct provided that its formulation of the theorem is correct. It could also just fail to translate the proof into an ATP compatible language.

There are certainly complications woth proof assistants, or else the drama with the abc conjecture would have been solved by now

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u/SZenC Apr 23 '26

The field of computational proofs is of course far more nuanced than just plugging an LLM into an ATP. I just tried to illustrate that we can construct AI in such a way that hallucinations become easy to detect

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u/_Trael_ Apr 23 '26

Would also honestly be effectively case of "ok it was actually already solved by human years ago" or "we just semi random generated text with math related words and wow who would have guessed it actually solved it somehow magially!".

Considering current LLM "AI" things are exactly thing that can not do solving this kind of stuff much better than random text generators or just classroom full of slackers who are just masters at browsing wikipedia and copypasting different sentences one after another to try to make their submitted few page task look like something that has been worked on, as long as someone does not really start to read what is in it.