On the Navier–Stokes Millennium Prize Problem

They are highly capable, no doubt about that, but:

1) We don't really know how they arrived to this result except that they had a lead and that they threw millions of compute at the problem. The article is written in a way that makes you believe that it was just an agent loop with little human intervention, but without any evidence.

2) If the threats are to be believed, it is concerning how far they are willing to go to show how capable the model is. One would think their products and credibility would be enough to speak for themselves.

Yes, I read the original statement. Buckmaster explicitly stated:

> I have not seen OpenAI’s proof. I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything.

People saying that he accuses OpenAI stole his proof are putting words into his mouth and I consider that very disrespectful to him. It's basically using Buckmaster as a tool to express their dissatisfaction over OpenAI.

I suspect this controversy will blow the case for ZDR wide open. Whatever the facts (possibly unknowable), it's going to become a very public lesson that data sovereignty was never about "having nothing to hide".

If this is what they do to academic pure mathematicians, where the stakes are so low (financially)—just imagine the sort of front-running that could be happening in other places.

So the timeline is:

Aug 28: OpenAI starts training a new model.

Sep 1: OpenAI sees a rumor on Twitter that two Millenium Prize problems were solved and starts their own effort to attack all the prize problems using the new (4 day old!) model.

Sep 3: The new model makes some progress toward Navier-Stokes. Based on this progress, OpenAI focuses on Navier-Stokes over the other Millenium Prize problems, using several approaches in parallel.

Sep 5: Navier-Stokes is solved. Assuming Astra API prices, $15m in output tokens were used by the whole effort.

In this account of the story, no specific information about Tristan and Levent's work is used to inform OpenAI's approach. The focus on Navier-Stokes and the choice of approaches to pursue came from OpenAI's own progress, not specific knowledge of Tristan's concurrent work.

There is a caveat that they "can't rule out" the possibility that Tristan's Codex data could have been part of the training set of the new model, though it is described as "unlikely" and the proofs are substantially different.

This timeline is insane. Navier-Stokes was solved start-to-finish in 5 days? A model in training for at most eight days dramatically outperforms Astra and Fable, and not just in mathematics?