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AlphaProof's Greatest Hits

(rishimehta.xyz)
248 points rishicomplex | 2 comments | 17 Nov 24 17:20 UTC | HN request time: 1.131s | source
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wslh ◴[17 Nov 24 18:35 UTC] No.42165921[source]▶
If you were to bet on solving problems like "P versus NP" using these technologies combined with human augmentation (or vice versa), what would be the provable time horizon for achieving such a solution? I think we should assume that the solution is also expressible in the current language of math/logic.
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zarzavat ◴[17 Nov 24 18:59 UTC] No.42166122[source]▶
Probably a bad example, P vs NP is the most likely of the millennium problems to be unsolvable, so the answer may be "never".

I'll bet the most technical open problems will be the ones to fall first. What AIs lack in creativity they make up for in ability to absorb a large quantity of technical concepts.

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wslh ◴[17 Nov 24 19:13 UTC] No.42166245[source]▶
Thank you for the response. I have a follow-up question: Could these AIs contribute to advancements in resolving the P vs NP problem? I recall that the solution to Fermat’s Last Theorem relied on significant progress in elliptic curves. Could we now say that these AI systems might play a similar role in advancing our understanding of P vs NP?
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1. ccppurcell ◴[17 Nov 24 22:08 UTC] No.42167783[source]▶
Just my guess as a mathematician. But if LLMs are good for anything it will be for finding surprising connections and applying our existing tools in ways beyond human search. There's a huge space of tools and problems, and human intuition and brute force searching can only go so far. I can imagine that LLMs might start to find combinatorial proofs of topological theorems, maybe even novel theorems. Or vice versa. But I find it difficult to imagine them inventing new tools and objects that are really useful.
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2. nemonemo ◴[17 Nov 24 22:47 UTC] No.42168066[source]▶
Do you have a past example where this already-proven theorem/new tools/objects would have been only possible by human but not AI? Any such example would make your arguments much more approachable by non-mathematicians.