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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 jdm2212 »

angry_octet wrote: post #843
hellohello2 wrote: post #812

Earlier quoted context omitted.

Hm. Looks like its possible everyone behaved terribly here unfortunately. :/ I remained impressed by ChatGPT however!

Everyone?? No, most definitely OpenAI. But they have learnt their lesson, next time they won't reach out to who they stole it from, they will publish first.

Seems like OpenAI did a boring normal corporate thing (find out your competitor made a breakthrough, try to replicate it) and then when the other mathematicians found out OpenAI had beat them to Navier-Stokes, they decided to lie about what happened because they were upset they didn't get to make the big breakthrough themselves.

Re: On the Navier–Stokes Millennium Prize Problem

#853

Post by medler »

piloto_ciego wrote: post #816
noir_lord wrote: post #782

Earlier quoted context omitted.

Recursive self improvement of their upcoming IPO value maybe. They are fluffy PR pieces otherwise.

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

Re: On the Navier–Stokes Millennium Prize Problem

#854

Post by hansvm »

hollowcelery wrote: post #836
hansvm wrote: post #738

Earlier quoted context omitted.

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…

But the researchers also did their research using essentially the same models, so that isn’t a counterpoint to AI models being at the far frontier…

> not a counterpoint

>> isn't a counterpoint

Where do we disagree?

Re: On the Navier–Stokes Millennium Prize Problem

#855

Post by eulgro »

hansvm wrote: post #738
intenex wrote: post #440

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

#856

Post by dekhn »

octoberfranklin wrote: post #848
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

#857

Post by dekhn »

medler wrote: post #853
piloto_ciego wrote: post #816

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

#858

Post by lixtra »

redox99 wrote: post #594
adverbly wrote: post #503

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

#859

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

#860

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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