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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#871

Post by diomedes »

frozenseven wrote: post #470
diomedes wrote: post #61

madness. which will be the next to fall? if i had to bet i would guess birch and swinnerton-dyer, but i'm no expert

There was a recent rumor about the Hodge Conjecture. I'd keep an eye on that one. But like the other person who replied, I'm also rooting for Yang-Mills. That has massive potential for unlocking a series of physics results.

interesting, i haven't heard anything about that. i don't know much about the hodge conjecture, all i really know is that it's incredibly abstract and obtuse - not sure if that has any implication for solvability by an AI though. do you have any source for the hodge rumor? curious to learn more

Re: On the Navier–Stokes Millennium Prize Problem

#872

Post by aizk »

logancbrown wrote: post #416
20k wrote: post #308

Earlier quoted context omitted.

Yeah well, its easy to do if you steal someone elses work and then try to threaten them into staying quiet about it Edit: OpenAI have now admitted they were training on prompts at the time they made their breakthrough: https://mastodon.social/@tristanbuckmaster/11723647135247030...

Steal someone elses work, whose work was also AI generated . . .

Tokens all the way down

Re: On the Navier–Stokes Millennium Prize Problem

#873

Post by aurareturn »

samrus wrote: post #824
piloto_ciego wrote: post #809

Earlier quoted context omitted.

How can you possible say this sort of thing in context of what looks like a millenium prize being solved. I swear there's nobody blinder than those who won't see.

You have to look at the incentives

A working Lean proof doesn't care what the incentives are.

Re: On the Navier–Stokes Millennium Prize Problem

#874

Post by amazingman »

tedsanders wrote: post #41
pavel_lishin wrote: post #8

Is this the one that was allegedly based on someone else's actual work & prompts? https://news.ycombinator.com/item?id=49605915 https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd... https://cims.nyu.edu/~tristanb/statement.pdf

Yes, that was the allegation last night. I work at OpenAI, though not on the team that did this, and my understanding is: - we decided to ask our model for Millenium problem solutions because of two reasons: (a) our new model was looking incredibly good and (b) we heard rumors that some Millenium problems had been solved and were curious if our models could solve them (the goal here was not to scoop any particular in…

Prove it. Your systems hack and/or abuse other systems and you can't seem to even observe it happening much less do anything about it. Why should we believe your claims when they depend on an ability you don't actually have?

Re: On the Navier–Stokes Millennium Prize Problem

#875

Post by camel-cdr »

chilmers wrote: post #152
arctic-true wrote: post #35

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.

The implication from their last couple of published articles[1][2] is that they think they’ve achieved “recursive self improvement”. [1] https://openai.com/index/research-acceleration-view-inside-o... [2] https://openai.com/index/an-alien-mind/

I found this post interesting in that reguard: https://www.lesswrong.com/posts/thXohzXrWCA2EhZCH/mateusz-ba...

Re: On the Navier–Stokes Millennium Prize Problem

#876

Post by mzs »

mewse-hn wrote: post #78

"we cannot rule out that de-identified data derived from their usage of our products helped improve our models ." What a landmine sentence to bury in this report, you can't rule out your models were spying on other researchers?

This is precisely what I would write after just learning that yes it did.

Re: On the Navier–Stokes Millennium Prize Problem

#877

Post by spongebobstoes »

tim-kt wrote: post #812
joshka wrote: post #758

Earlier quoted context omitted.

I worked at OpenAI previously, but don't know any of the people involved in this. My guess was it was probably this was more a nerd snipe than any action from OpenAI that was a "massive team" being put on it. Literally someone looking at this and asking "I wonder if our models are good enough yet". It's easy to assume that having access to massive compute amounts means significant coordination, but this assumes that…

They said that a customer would have paid around 15 million for the required compute. I can't imagine that this was not a significant internal spending even with "free" tokens.

just because you can't imagine it doesn't mean it's not true

Re: On the Navier–Stokes Millennium Prize Problem

#879

Post by tomhow »

peri-cl wrote: post #675

Terence Tao has some observations that seem to be directed at this, https://mathstodon.xyz/@tao/117237320796901560 > "We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential. The incentives may now be pointing in the direction of no longer sharing any promising researc…

Related ongoing thread:

Tao: Open math problems being non-renewably mined by AI - https://news.ycombinator.com/item?id=49616968 - Sept 2026 (276 comments)

Re: On the Navier–Stokes Millennium Prize Problem

#880

Post by mzs »

Legend2440 wrote: post #31
Jonasori wrote: post #19

the context here is super important, for those who haven't seen it yet. OAI maybe just trained on a real researchers solution and then celebrated having scored the goal unassisted save for the brief commentary at the bottom of this blog post. Here's the other side. https://x.com/rynorhn/status/2097223532438487463

That other researcher was working on a smaller related problem. He was also using LLMs to do it, so either way most of the credit goes to the LLM here.

"It was splendid! Waiter, share my regards with the oven."
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