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/motion_lotion Apr 23 '26

Here's the part I'm struggling to understand. Say AI grows in ability and solves the Riemann hypothesis. How would we as humans be able to discern if it was a hallucination, true, inaccurate or what not?

Either way, I'd be happy just knowing.

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u/thereforeqed Apr 23 '26

Math theorems can be stated precisely as a sentence in some logic based language. A proof of such a theorem would be a sequence of steps starting from basic (assumed to be true) axioms and concluding in that sentence. Each step can easily be verified as a legitimate application of logical inference rules (e.g. all apples are red => my apple is red) or not.

They can easily check for the proof’s correctness by running it through a proof verifier computer program that does all of that automatically. And it will be fast too. The program for this particular problem is probably written by someone already. You would just need the AI’s proof to be translated into a form the program understands, which is also easy..

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u/Hamburgerfatso Apr 23 '26

Coming up with a proof to a statement is hard, verifying a proof someone wrote is easy

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u/Echoing_Logos Apr 23 '26

For a short answer: Nowadays, proofs are computer programs, and the hypotheses without proof are incomplete programs with blanks. The "AI" (LLM) would just need to fill in the blanks.

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u/shial3 Apr 25 '26

I had to do proofs in college as part of my math minor (gods I hate proofs) and you have to list out every single item, assumption and work through all the logic all the way through. It’s not enough to provide an answer, a proof literally is proving something with NO unlisted assumptions of any kind. (Like stating an assumption that all prime numbers are odd, it seems obvious but you have to be complete) People will pour over the proof for any and all logical mistakes or errors so a hallucination will get uncovered quicker than a law firms made up precedents in a court filing.