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OpenAI paper disproves ETH, sparking debate
Ryan Williams says an internal OpenAI model claims to refute ETH, and he, Impagliazzo and Paturi will help organize independent review.
Key points
- OpenAI announced three major scientific discoveries, one each in mathematics (harmonic analysis), computer science (complexity theory), and physics (quantum field theory).
- AndrewCurran_ listed the discoveries as local smoothing and the Kakeya conjecture, the Exponential Time Hypothesis being false, and the existence of quantum chromodynamics and completions of the Standard Model.
- kimmonismus said the key proofs were formally verified in Lean and that independent experts are now examining the work.
- The original author said the release process continues to evolve in response to feedback from the associated academic communities, and described the manuscripts as a form of raw research data.
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Ryan Williams links OpenAI's PDF claiming refutation of ETH: 3SAT on n variables in about exp(n/(log n)^{1/2+o(1)}) time.
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Konsti Wohlwend explains OpenAI didn't prove P=NP but that some NP-complete problems are subexponential, a huge result if it holds.
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Bubeck calls 3SAT solvable in subexponential time the biggest surprise of his 20 years in theory.
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From @danintheory, @BurhanUsman, @TheAaryanKapoor and others. Spam removed, with English and Chinese translations.
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