Navier-Stokes – Tristan Buckmaster [pdf]

This doesn't seem to be clear and is very implausible for a large company. Be as cynical as you want, but a normal researcher will simply not have access rights to this data, which will be siloed away somewhere else.

It might very well be somewhat unfair to catch wind of a promising approach and then try to frontrun them by throwing compute at the problem, but this isn't really the same.

Call this behavior what it is, technofascism. Another comment compared it to the Godfather. To think this is the 21st century and academics are still horrible human beings.

If OpenAI did use the conversations from Buckmaster and Alpoge, then not disclosing it, explicitly, is plagiarism. If they planned to use that plagiarism to pressure the authors to publish, that is even more unethical. What the terms of use say does not make it any more or less ethical.

"Strong agree. I know that there is rivalry between the labs but it's important that we learn to work together given what's coming. " -- Noam Brown, an OpenAI researcher [2]

We all should heed the implied warnings of these top researchers about what's coming. The world is far from ready and everyone who can should pitch in.

[1] https://x.com/_sholtodouglas/status/2097224624274911368 [2] https://x.com/polynoamial/status/2097225279366414541

This sounds like a very big coincidence and it looks really bad for OpenAI but there is an alternative explanation that I can only state as a conjecture.

Suppose that the ability of LLMs to generate mathematical proofs is like a quiver full of arrows: each arrow, one proof. The same quiver is shared between all instances of one model and substantially similar models share substantial subsets of the arrows in the same quiver.

That would allow two independent teams to converge on the same LLM-aided solutions to the same problems. Even more likely so if the quivers were small and finite and their arrows were specific to a distinct class of problems (without being able to suggest a particular class from what we've seen so far).

This would explain the kind of LLM-mediated results we've seen so far that tend to be ... sparse. By which I mean that every time there's a new model release we get some new results and then they seem to dry out, until the next release.

It would also explain how OpenAI was about to prove the same result as Buckmaster and Alpoge, while absolving OpenAI of any misconduct. And this is one reason to prefer this explanation: one should not favour accusations of misconduct as long as there are conceivable alternatives.

But, that's just a conjecture that I can't prove.