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On the Navier–Stokes Millennium Prize Problem

openai.com

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Re: On the Navier–Stokes Millennium Prize Problem

#671

Post by taylorfinley »

elwell wrote: post #530
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?

Isn't this a proof that the usage data is truly "de-identified"? If OpenAI could prove that "their usage" influenced the finding, then it wouldn't be de-identified. (Also, it's a bit disingenuous to trim the "While unlikely," prefix.)

It's a bit disingenuous to preface a disclosure like this with an unsubstantiated assessment of its likeliness. It is a press release, I'm not sure we owe it credulity.

Re: On the Navier–Stokes Millennium Prize Problem

#672

Post by sznio »

dakolli wrote: post #431
dboreham wrote: post #399

Earlier quoted context omitted.

That said, perhaps it will take over the world government and decree that all corrupt officials shall be imprisoned and all weapons of mass destruction shall be destroyed.

You think a model with an effective memory of 200-500k words, that can be unplugged, is going to "run the world" You people gotta put down the sci-fi

it proved navier-stokes taking over the us government is easier imo, any idiot gets to be president

Re: On the Navier–Stokes Millennium Prize Problem

#673

Post by nozzlegear »

WarmWash wrote: post #209
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?

Everyone knows that they train on the discounted rate plans data. All the labs are upfront about this too. If you need privacy, then you are going to have to pay full price for those tokens (API). This has been true since day one. Everyone knows it, I guess though this is the first time that it has become "real".

> If you need privacy, then you are going to have to pay full price for those tokens (API).

At this point, how can we even trust that they aren't accidentally training on those tokens too?

Re: On the Navier–Stokes Millennium Prize Problem

#674

Post by fer »

irthomasthomas wrote: post #618
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.

Or they trained a LoRA on the victims chats in order to launder their plagiarism.

The timing makes it the most likely, not only them but potentially more. Comparatively quick, instant results. "Here's Astra! BTW our internal model is 10x better at math!" It'd be interesting to see academics having giving deeper looks at whatever OpenAI publishes from now on.

Re: On the Navier–Stokes Millennium Prize Problem

#675

Post by ImPostingOnHN »

modeless wrote: post #169

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 app…

> 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"

This is the lynchpin behind everything, and I would describe it as "likely". Since I am not employed by any party to this dispute, my 1 opinion is more trustworthy than OpenAI blog poster's 1 opinion.

Re: On the Navier–Stokes Millennium Prize Problem

#676

Post by nhatcher »

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…

Some millennium problems? Are there more coming?

Re: On the Navier–Stokes Millennium Prize Problem

#678

Post by peri-cl »

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 research directions with the broader community, which would reverse centuries of traditions of open science and do serious long-term damage to the future of the field."

Re: On the Navier–Stokes Millennium Prize Problem

#679

Post by QuesnayJr »

ameliaquining wrote: post #242
QuesnayJr wrote: post #158

Earlier quoted context omitted.

Of the seven Millenium problems, Navier-Stokes was the one most thought to be in reach. I'm not sure what the top 3 problems are. You can make a case for the Riemann Hypothesis and P != NP, but I'm not sure what #3 would be. Maybe the Langlands program? (That one is not as precisely stated as the other two.)

There were also some people talking about the Hodge conjecture, because it has some similarities to some LLM-assisted breakthroughs that were considered impressive in the distant past of [checks notes] July 2026. See, e.g., https://xenaproject.wordpress.com/2026/07/20/human-mathemati...

I brought this up here at HN, and in the ensuing discussion Buzzard himself replied saying he was somewhat joking (https://news.ycombinator.com/item?id=49011950).

Re: On the Navier–Stokes Millennium Prize Problem

#680

Post by 8note »

thorum wrote: post #153
dorjoycb wrote: post #13

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

It reminds me of the Cognitive Dark Forest hypotheses recently shared here: > “You are creating your cool streaming platform in your bedroom. Nobody is stopping you, but if you succeed, if you get the signal out, if you are being noticed, the large platform with loads of cash can incorporate your specific innovations simply by throwing compute and capital at the problem. They can generate a variation of your innovati…

but what do i lose if somebody else is making money?

im still having fun making something

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