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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#241

Post by ameliaquining »

QuesnayJr wrote: post #158
jrflo wrote: post #111

Earlier quoted context omitted.

I'm so tired of this "It's just marketing!!" commentary. An AI model just proved one of the top 3 unsolved problems in mathematics, they have a Lean certificate showing it's valid. How much more evidence do you need that these models are actually highly capable?

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...

Re: On the Navier–Stokes Millennium Prize Problem

#242

Post by AlexErrant »

recitedropper wrote: post #10

Sad turn of events for our world. After watching the behavior of the most senior OpenAI researchers on twitter, I feel even less confident in them as a team to be shepherding this much capital and compute. The dark forest awaits..

1. What does the dark forest have to do with this? Because "the most senior OpenAI researchers" are shitposting on social media, we've an answer to the Fermi paradox???

2. The dark forest is fun for scifi stories, but is mathematically bunk anyway https://www.noahpinion.blog/p/the-dark-forest-hypothesis-is-... https://www.reddit.com/r/IsaacArthur/comments/1l06cnk/cool_w... https://www.projectnash.com/aliens-the-fermi-paradox-and-the...

When doomposting please actually say something substantive. Negative news always gets clicks/updoots; fight that human tendency.

Re: On the Navier–Stokes Millennium Prize Problem

#243

Post by pbhjpbhj »

jonas21 wrote: post #225
Turn_Trout wrote: post #191

Earlier quoted context omitted.

OAI could check whether those accounts enabled training data. If "yes", OAI could trace whether that data was used in any related training process. If either of those answers comes out to be "no", then that's sufficient to conclude training data independence. We wouldn't need a full ablated re-training and solution attempt, contra tedsanders in a sibling comment.

> could trace whether that data was used The point of de-identifying data is to ensure you can't trace who it came from. It would be a serious privacy violation if they could.

If the model includes unique data from a person then that person can identify the data - the allegedly plagiarised material - and so re-identify it. There doesn't need to be a privacy breach to close that loop as it requires the person to identify the information is associated with them first.

Re: On the Navier–Stokes Millennium Prize Problem

#244

Post by achierius »

applicative wrote: post #96
int3trap wrote: post #55

Earlier quoted context omitted.

This is the academic equivalent of Trump saying "they stole the election". There's no proof of it but rah rah fuck OpenAI. It's incredibly tiresome and you'd think people could put more effort into it than just following whatever vibes they agree with. Oh well.

No, its a pure outrage. I defended OpenAI til today. I now affirm they must be totally destroyed, burned utterly to the ground.

I mean it's definitely an outrage, but I find it hard to believe that you went from "yay OpenAI" to "literally destroy the company" over... accusations of academic misconduct?

Re: On the Navier–Stokes Millennium Prize Problem

#245

Post by Aboutplants »

rfgplk wrote: post #107

Something I've been going on and on about for months now and no one seems to listen. LLMs today are allowing _anyone_ to access cross-discipline knowledge that was previously entirely inaccessible without a) extremely deep pockets or b) a massively talented and varied team. In fact, contrary to what the masses seem to think LLMs are actually _better_ at hard cutting edge physics/math problems than they are at fronten…

So, physical fields? I’m not catastrophic regarding jobs yet as I have an optimistic view of humanity in general and its ability to meaningfully survive, but the more time I spend thinking about the future of work, the more I’m leaning toward broad general abilities rather than distinct talents. To your point, I no longer need comprehensive knowledge of any particular subject, but what is absolutely valuable is “general” intelligence and adaptability.

I have a young daughter and my goal now is to provide a very broad and varied upbringing, exposing her to as many different perspectives and experiences that will lay the foundation of a broader ability to understand and adapt as the world changes ever faster. You no longer need to be an expert in anything, you need the ability to perform within the landscape that the present opportunities exist.

Re: On the Navier–Stokes Millennium Prize Problem

#246

Post by bananaflag »

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.

Yeah it's Bel

Re: On the Navier–Stokes Millennium Prize Problem

#248

Post by perching_aix »

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".

There's literally an opt out toggle even pesky peons like me can peruse, actually.

Re: On the Navier–Stokes Millennium Prize Problem

#249

Post by shadowgovt »

tedsanders wrote: post #181
lambda wrote: post #130

Earlier quoted context omitted.

Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there ma…

To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effec…

It is, perhaps worth considering that the reputational community might not care about the difficulty for the AI builder to verify pedigree.

If OpenAI's answer to this problem is "We can't know," then the rational conclusion may very well be "If I seek to have my reputation attached to the discovery of the solution, it is not sane to use the AI as an assistive tool, lest it scoop me on my own work using my own work. After all, they don't know it doesn't do that..."

Re: On the Navier–Stokes Millennium Prize Problem

#250

Post by wbl »

cv5005 wrote: post #105

Maybe a naive question, but how does one know that a particular lean proof is actually a proof of what one thinks? Like, ok the logic checks out and it proves something , but there's still the problem of does this logical result actually prove the initial question that was asked?

Very careful human examination. This can be tricky.
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