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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#81

Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.

Astra was trained more than two weeks ago.

Re: On the Navier–Stokes Millennium Prize Problem

#82

Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.

Pre-IPO marketing?

Re: On the Navier–Stokes Millennium Prize Problem

#83
post #66

It's great that important discoveries like this can now routinely be accompanies by formalized proofs. The fact that it's being released alongside a Lean proof from Day 1, rather than the Lean proof being released months or years later, is super helpful for verifying that it's correct.

I feel sorry for whoever has to read and understand the solution. It looks like the typical convoluted unreadable mess I see the models generate for software. It might be technically correct, but gaining insight from it is just intellectual hell.

Re: On the Navier–Stokes Millennium Prize Problem

#85
This is utterly shocking. Even the AI optimists did not expect this to happen in 2026. Wow.

Millennium Prize Problems were used as examples of something the current approach to AI just wasn't capable of, discussions that would result in "we'll need a totally new architecture".

Re: On the Navier–Stokes Millennium Prize Problem

#86
post #53

> We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. WOW?

This is going to be dramatic in so many different ways. - First off, to reiterate, WOW. - Second of all, when does this end? Are we at the dawn of the singularity now? - People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? - Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can butt…

> People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them?

The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit.

"People" are just misinformed and keep spreading misinformation.

Re: On the Navier–Stokes Millennium Prize Problem

#87

Earlier quoted context omitted.

Can you point me to any nasty things being posted? I'll ask them to delete.

Haven't seen a single post doing this on X or anywhere really from OAI employees. Only seen knives pointed at Sebastian on social media so this is extreme and shameful gaslighting.

I do see people claiming he's abusive/unscrupulous which are pretty extreme allegations.

https://news.ycombinator.com/item?id=49605915#49610498

https://x.com/dheeraj_nagaraj/status/2097266146445774924?s=6...

(I can't reply to the below comment, but I was aware this was about Sebastien, I was trying to be charitable by including stuff said about both people)

Re: On the Navier–Stokes Millennium Prize Problem

#88
post #58

It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774

Buckmaster: > "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer." OpenAI (i.e. this OP): > "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helpe…

I feel like it's far more likely that ordinary corporate espionage or leak led to this rather than OpenAI sifting through piles of user data to find this approach. Buckmaster's collaborator works at Anthropic, and could have been targeted. That would also explain why they aren't forthcoming with the source of the prompt.

Re: On the Navier–Stokes Millennium Prize Problem

#89
post #37

Earlier quoted context omitted.

What else can they declare really? Yeah the model has training data from previous attempts. Alpöge and Buckmaster also similarly benefited from attempts before theirs.

They could have thought about the problem for like 2 minutes and not done this! I think that literally any academic mathematician could have explained to them, had they asked, why it is considered extraordinarily rude to react to rumors of research progress by desperately rushing to get there first.

right, surely they could've waited or even reached out? It reads as desperation to get there for marketing purposes
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