Three new discoveries in mathematics, computer science, and physics

> "We are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory." I'm still not fond of the bicycle manufacturer announcing its achievements in bicycle racing, even if it selects the 5 top cyclists to support the orchestration of the announcement. From past incidences it's already known that their model is very likely trained on input gathered from scientists which use OpenAI as a tool for their research. Suddenly the research community is in a race with the provider of its tool, and can hope for the grace of being selected to judge the output and have an honorable mention in the press-release. The situation would be different if they would collaborate with scientists during the research, and let them publish the results with reference to OpenAI being a supporter/sponsor. But this approach of "thanks to your continuous input we now have a bicycle which even our employees can use to beat you, we invite you to be mentioned in our press-release" doesn't sit well with me...

I think OpenAI deserve credit for adjusting their approach after the last math drop. I think Terrance Tao shares some credit here for galvanizing the response. Including the relevant mathematicians and scientists before dumping this onto the public is sure to go a long way to relaxing fears in those communities. I'm not sure how they will deal with accusations of favoritism but at least they are demonstrating a willingness to participate in a process. I hope the community can express some positivity that will encourage OpenAI and other foundation labs to continue with this collaborative approach.

ETH is false! I really would not have believed it. [0]: > We give a deterministic algorithm for exactly counting the satisfying assignments of an arbitrary k-CNF formula. For every fixed k ⩾ 2, on a formula with n variables and m clauses, our algorithm uses $poly_k (n, m)$ space and runs in time $(n + m)^{O_k(1)} 2^{n/(\log n)^{1/2 + o(1)}}$ The dominant term there is (roughly) $2^{n / (\log n)^{0.5}}$, so still superpolynomial but less than exponential. Fucking wild. [0] https://github.com/openai/math/blob/main/preprints/The-Expon...

ETH is false! This is one of the big long-standing hypotheses that I actually remember from university, and afaik, it was reasonable to assume it would be true; reasonable enough for a lot of papers and results to assume this for bounds or hardness proofs of common problems in parameterized complexity, anyways. Also glad to see that one of the authors of the paper stating it is also in the loop here. 2026 is weird.

Interesting that the physics result is not released yet. From the limited wordings, “unified completion of the Standard Model of particle physics” is probably SU(5), which is experimentally disproved as one describing our universe. So the wording sounds a bit confusing, ie they are not proving or discovering Grand Unified Theory (GUT), and there’s no Higgs. So it is not really the standard model, but models that’s closely related to that. It is still an impressive result. IMO at the level of the recent quasi Riemann hypothesis level result, shy of getting the millennium prize (no mass gap) but is actually a very meaningful result, both of which arguably more impactful that the one they solved a millennium prize problem (Navier–Stokes). More comments in https://blog.kolen.dev/link/openai-shepherds