OpenAI claims to disprove Exponential Time Hypothesis
ComputingComments
Why are we focusing on the process when the claim is this wild? If ETH is actually false, does that mean P=NP is suddenly on the table?
If ETH is false, it doesn't automatically mean P=NP, but it would wreck a lot of hardness assumptions in fine-grained complexity. Most current lower bounds for SAT would be meaningless.
I have to disagree with the leap to P=NP. Disproving ETH only suggests that 3-SAT can be solved in sub-exponential time, not necessarily polynomial time. There is a massive gap between 2^{o(n)} and n^k.
We saw a similar move with some of the automated proofs in formal verification a few years back. Half of them were just cleverly disguised brute force that fell apart under actual scrutiny.
What if the complexity of these specific proofs exceeds the bandwidth of the traditional reviewer pool? It could be that a dedicated shepherd is the only way to get a deep enough dive without the paper sitting in review for years.
The concern about standardized review is valid, especially since the Kakeya conjecture has a long history of near-miss proofs. Having a diversified panel of critics usually catches the subtle gaps that a single shepherd might overlook.
Since you mentioned the history of near-misses, did the announcement specify if they used a computer-assisted proof for the restriction conjectures? I didn't see any mention of the specific formalization language used.