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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 eulgro »

hansvm wrote: post #735
intenex wrote: post #439

I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits. This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able…

Not a counterpoint per se, but I burned $50k recently on a much more modest math problem (result already known, just thought I had a sketch of a more interesting proof), and the LLM thought it had proved it within those bounds but had instead subtly fucked up the Lean definition. Take from that what you will. Not to mention, it's still very much up in the air whether the model derived the answer of its own accord or…

How can you afford to burn $50k on an already solved problem?

Re: On the Navier–Stokes Millennium Prize Problem

#852

Post by dekhn »

octoberfranklin wrote: post #844
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

> https://cims.nyu.edu/~tristanb/statement.pdf This really need to be a top-level story on HN.. 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. This whole episode is more horrific than "AI is eat…

We don't have any proof of that at all. Please stop rushing to judge without data.

Re: On the Navier–Stokes Millennium Prize Problem

#853

Post by dekhn »

medler wrote: post #849
piloto_ciego wrote: post #812

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.

Because it seems like most of the work may have been done by human mathematicians and cribbed by OpenAI at the last minute

We don't have enough accurate knowledge to say that, and it doesn't seem to be the case at all.

Re: On the Navier–Stokes Millennium Prize Problem

#854

Post by lixtra »

redox99 wrote: post #593
adverbly wrote: post #502

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

#855

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

#856

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…

[dead]

Re: On the Navier–Stokes Millennium Prize Problem

#857

Post by 6thbit »

nadermx wrote: post #802

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

#858

Post by krackers »

keel-control wrote: post #379
simianwords wrote: post #296

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

#859

Post by [deleted] »

reducesuffering wrote: post #358
kypro wrote: post #320

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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