Extensive discussion on OpenAI's blog post on Navier-Stokes: https://news.ycombinator.com/item?id=49613262 .

Quanta Magazine article that also discusses some of the controversy: https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-...

> Navier-Stokes is one of six “Millennium Problems” on a list compiled by the Clay Mathematics Institute in 2000.

Seven, not six. One is solved already, but is still a millennium problem.

> OpenAI, meanwhile, says its experience with Navier-Stokes could open the door to solving puzzles with more practical relevance. “We are now able to spend millions of dollars on a problem that we really care about and that really matters: developing new materials, finding cures to diseases,” Bubeck said. “All of those things that we have been talking about for a long time—now they seem to be at our fingertips.”

Eh? There's no connection at all between the Navier-Stokes work and those things.

Moving forward, I can't imagine other mathematicians wanting to have this kind of experience. So there has to be a shift away from these services.

OpenAI apparently used Buckmaster and Alpöge‘s work w/ Codex to bootstrap “their” dis-proof. https://cims.nyu.edu/~tristanb/statement.pdf

The core section:

> However, communications quickly became contentious. According to Buckmaster, OpenAI offered to give him sole authorship on the Navier-Stokes solution—but only if Alpöge’s name was removed from the work and if the write-up would acknowledge the problem had been resolved by an internal OpenAI model. Buckmaster refused, in part because he was troubled by the question of what OpenAI's system had actually seen. For example, Buckmaster said the company did not initially give him a clear answer about whether its agents had access to the pair's logs on Codex (which is an OpenAI product).

> OpenAI executives have denied that any employee or AI agent saw the pair’s work before the researchers released it publicly on 7 September. But there still remains a separate question: Could the pair's work have reached OpenAI's models through its training data?

> OpenAI’s blog announcing the Navier-Stokes solution does not dismiss the possibility: “While unlikely, we cannot rule out that de-identified data derived from [Buckmaster and Alpöge’s] usage of our products helped improve our models .”

My impression: the re-aristocratization of scientific research seems inevitable.

Does it matter who gets the credit at this point? Both used AI to do 99%+ of the work. So... do machines have ego?

Regardless of what you think of the priority dispute issue discussed on sibling threads, I’m highly skeptical of the closing quote that this Navier Stokes result means that the same approach of casually spending a few million on agentic computation is going to solve end to end materials design or drug development.

Those problems can’t be formally verified with an automated theorem prover. We have a lot of physics based simulation tools, but they tend to focus on small subsets of the full design problem and they make limiting approximations because otherwise they’d be too computationally expensive, or we just don’t have the right data to parameterize them beyond describing qualitative behavior. Agents are helping accelerate research in these fields but I think it’s mostly a different class of problem that’s a lot harder to specify and verify

Hmm, is the formal verification through? Lean just asserts no errors in the proof, but like can prerequisites not be fullfilled?

I think it was a pretty questionable thing to do by trying to front-run these researchers even if they didn’t make use of their techniques. The fact that they may have inadvertently “borrowed” their work via training data makes it much worse.

OpenAI’s behavior here — even if you only consider there side of the story — was (at best) in bad taste.

Who should get credit? All the humans who ever worked to create the training data for the LLM.

The AI company for making the search program.