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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#871

Post by sp527 »

rakejake wrote: post #865
sp527 wrote: post #741

Earlier quoted context omitted.

> Tristan's argument from his essay was that it is hard to brute force with a vanilla prompt (even for seasoned mathematicians) unless you knew very specifically what to mention i.e the search space would have been intractable even for OAI's compute budget. This is a bad argument. This is clearly not how it works. And unless Tristan is some truly alien-like savant (and maybe he is), what's necessary to initiate the A…

Are you saying there is no search space intractable to LLMs? That wouldn't be possible. AIs are statistical pattern-matchers on steroids. The prompt is key to getting anything useful out of them. They are incredibly useful and major game changers but ultimately that does not alter this fact. People (including OAI) have already tried to solve Millenium Problems with it. That OAI woke up last week and suddenly decided…

> Even if OAI had zero data from Buckmaster's sessions, this is in very poor taste and highly unethical. You are front running a researcher just to be able to say you did it first? Tao is right - OAI is treating math results like oil. This is the like Exxon getting a whiff of a massive oil field and racing to the punch by deploying their full crew.

I want to be clear that I agree with this view and with Tao more generally. But we're all just yelling at the wind now.

Re: On the Navier–Stokes Millennium Prize Problem

#872

Post by [deleted] »

Chance-Device wrote: post #643
tedsanders wrote: post #181

Earlier quoted context omitted.

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…

Please answer this question: do you or do you not train your models on anonymized user data, where those users have opted out of such training? The blog post appears to imply the answer to this is yes, as otherwise I assume it would be impossible for this contamination to have happened.

[deleted]

Re: On the Navier–Stokes Millennium Prize Problem

#873

Post by waterTanuki »

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…

> - the proof generated by our model was very different from theirs and also goes far beyond the published literature

I'm hearing two completely conflicting stories. Buckmaster is claiming the approach used by OpenAI is so strikingly similar to the one he used, that mere coincidence is astronomically small. Yet OpenAI is claiming that the methods used are entirely different.

Anyone care to provide primary evidence proving one way or the other?

Re: On the Navier–Stokes Millennium Prize Problem

#874

Post by diomedes »

frozenseven wrote: post #472
diomedes wrote: post #61

madness. which will be the next to fall? if i had to bet i would guess birch and swinnerton-dyer, but i'm no expert

There was a recent rumor about the Hodge Conjecture. I'd keep an eye on that one. But like the other person who replied, I'm also rooting for Yang-Mills. That has massive potential for unlocking a series of physics results.

interesting, i haven't heard anything about that. i don't know much about the hodge conjecture, all i really know is that it's incredibly abstract and obtuse - not sure if that has any implication for solvability by an AI though. do you have any source for the hodge rumor? curious to learn more

Re: On the Navier–Stokes Millennium Prize Problem

#875

Post by aizk »

logancbrown wrote: post #418
20k wrote: post #310

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 . . .

Tokens all the way down

Re: On the Navier–Stokes Millennium Prize Problem

#876

Post by aurareturn »

samrus wrote: post #827
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.

You have to look at the incentives

A working Lean proof doesn't care what the incentives are.

Re: On the Navier–Stokes Millennium Prize Problem

#877

Post by amazingman »

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…

Prove it. Your systems hack and/or abuse other systems and you can't seem to even observe it happening much less do anything about it. Why should we believe your claims when they depend on an ability you don't actually have?

Re: On the Navier–Stokes Millennium Prize Problem

#878

Post by camel-cdr »

chilmers wrote: post #152
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.

The implication from their last couple of published articles[1][2] is that they think they’ve achieved “recursive self improvement”. [1] https://openai.com/index/research-acceleration-view-inside-o... [2] https://openai.com/index/an-alien-mind/

I found this post interesting in that reguard: https://www.lesswrong.com/posts/thXohzXrWCA2EhZCH/mateusz-ba...

Re: On the Navier–Stokes Millennium Prize Problem

#879

Post by mzs »

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?

This is precisely what I would write after just learning that yes it did.

Re: On the Navier–Stokes Millennium Prize Problem

#880

Post by spongebobstoes »

tim-kt wrote: post #815
joshka wrote: post #761

Earlier quoted context omitted.

I worked at OpenAI previously, but don't know any of the people involved in this. My guess was it was probably this was more a nerd snipe than any action from OpenAI that was a "massive team" being put on it. Literally someone looking at this and asking "I wonder if our models are good enough yet". It's easy to assume that having access to massive compute amounts means significant coordination, but this assumes that…

They said that a customer would have paid around 15 million for the required compute. I can't imagine that this was not a significant internal spending even with "free" tokens.

just because you can't imagine it doesn't mean it's not true
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