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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#851

Post by lixtra »

redox99 wrote: post #591
adverbly wrote: post #500

Earlier quoted context omitted.

> will soon far surpass that of humans To be fair, I think it's still an open question about how far it might surpass human capabilities. I think it's clear that its speed of development will be significantly faster, but it's technically not proven that the frontier and problems don't themselves become increasingly difficult faster than any acceleration in intelligence past the point of human training, data and exist…

Fields that allow verification, like math, will far surpass human level because they don't need human data for training. It's exactly the same as with Chess

How do you verify the ‚beauty‘ of a result. There have always been infinite provable Theorems around. Only some are interesting and beautiful.

Re: On the Navier–Stokes Millennium Prize Problem

#852

Post by itemize123 »

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.

it's buried because due to the drama the evidence is scarce

Re: On the Navier–Stokes Millennium Prize Problem

#853

Post by dermacentor »

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…

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Re: On the Navier–Stokes Millennium Prize Problem

#854

Post by 6thbit »

nadermx wrote: post #799

I've been working on this problem for what seems like for ever. Kudos to the OpenAI team. For those of you who don't care about the drama and want to see this distilled to 3 lines: https://x.com/nadermx/status/2097414953225310280

Any version with a bit more prose for a peasant like me to remotely pretend to grasp it

Re: On the Navier–Stokes Millennium Prize Problem

#855

Post by krackers »

keel-control wrote: post #377
simianwords wrote: post #294

Why is no one skeptical that the solution is correct? There's not a _single_ comment asking whether this proof is legit or not.

there is a proof in lean4 it's correct by construction

How do you know that what is being proved in the lean code is the same as the millennium prize criteria though?

Re: On the Navier–Stokes Millennium Prize Problem

#856

Post by [deleted] »

reducesuffering wrote: post #356
kypro wrote: post #318

Earlier quoted context omitted.

As someone with a background in AI and who has been playing around with neural nets for decades at this point, it's been genuinely amazing watching extremely intelligent people make confident predictions about AI capabilities and progress, then be so completely wrong. There's a kind of theory of mind for AI (specifically neural nets) which I now realise I seem to have which is very hard to explain to people who haven…

> extremely intelligent people make confident predictions about AI capabilities and progress, then be so completely wrong. The ability for the human mind to rationalize conclusions to maintain denial in the face of a very scary future is immense. Genuinely grappling with the implication of where we're headed is usually very crushing. It's not easy to engage with the possibility, and very intelligent people will use t…

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Re: On the Navier–Stokes Millennium Prize Problem

#858

Post by avs733 »

dash2 wrote: post #95
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?

If they had agreed to let OpenAI train on their data, it wouldn’t be spying.

In the academic world it would still be deeply problematic…pick your preferred word.

An analogy is akin to reviewing a paper. If I review a paper with some novel findings and then use my massive lab of graduate students to do the obvious next step before the other paper makes it through type setting and then shove it out as a pre print, I didn’t win - I was a jerk.

There are lots of cases of people using peer review or other accesss to efectively forerun others work and get credit. It’s a known problem of the nature of knowledge validation in academia, it’s not solved and it’s not deterministic but people know it when they see it.

Re: On the Navier–Stokes Millennium Prize Problem

#859

Post by ajjahs »

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 . . .

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