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On the Navier–Stokes Millennium Prize Problem

openai.com

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Re: On the Navier–Stokes Millennium Prize Problem

#701

Post by danielmarkbruce »

pama wrote: post #183
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.

Not only that, but it used 10k agents coherently over 88 hours to come up with the proof. This is a significant advance.

If you can create a graph of independent work, which you can with many such problems, agents can work together nicely. Again, thank Lean and the tooling around it.

Re: On the Navier–Stokes Millennium Prize Problem

#702

Post by enraged_camel »

biophysboy wrote: post #109
floatrock wrote: post #43

Earlier quoted context omitted.

OpenAI's position: > We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results p…

Why is it unlikely?

Because OpenAI says so, obviously!

Re: On the Navier–Stokes Millennium Prize Problem

#703

Post by irthomasthomas »

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…

If the goal was not to scoop them, why did openai put a massive team on this, working weekends, only after they heard rumors of the solution?

Re: On the Navier–Stokes Millennium Prize Problem

#704

Post by Caracas288 »

pred_ wrote: post #151
tedsanders wrote: post #41

Earlier quoted context omitted.

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…

> we did not read any private chats Your post says “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .” We can discuss what it means to “read” things but obviously the issue here isn't whether you did it manually or automatically. But more importantly, what on earth are you doing threatening real scientists to remove their coauthors, then ma…

If the training toggle is switched on, maybe OpenAI doesn't consider a chat to be private? Therefore making this a 'safe' statement.

Re: On the Navier–Stokes Millennium Prize Problem

#705

Post by demibabs »

boshalfoshal wrote: post #545
20k wrote: post #311

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...

lol, the "other work" was also probably 95-99% AI generated. By a similar breed of OpenAI (and some Anthropic) models, as well. I dont know why this monumental achievement is being drowned out by some arbitrary drama. No matter which way you slice it, AI solved this problem. Doesn't matter if it was some internal OpenAI model, or whether it was Astra + Fable.

Yeah but the mathematicians are claiming that the key insight that made the problem tractable for AI in the first place, came from them.

Re: On the Navier–Stokes Millennium Prize Problem

#707

Post by robryan »

concinds wrote: post #511
Eridrus wrote: post #466

Earlier quoted context omitted.

Seeing mathematicians such as Terry Tao being unhappy with open problems being solved makes me sort of question the usefulness of any of this pure mathematics. If we're not happy that the problems are being solved, why care about this field at all?

His issue is more nuanced than that. Most of the value was in humans reaching new insights or new math during failed attempts to solve these problems, whereas AI is basically "too efficient" in beelining to the goal and discards potential new insights reached along the way. I assume this is solvable.

Surely it is. Ask it to keep a list of all the promising sub paths, reprompt the collections of agents again on these after the main problem has been addressed. Or even release a list of them and let others investigate.

Re: On the Navier–Stokes Millennium Prize Problem

#708

Post by btilly »

The problem that I want to see them tackle is formalizing the classification of finite simple groups.

Everyone uses the classification. Nobody has great confidence in the proof. Nobody understands it. There are attempts to reprove it.

If it can be formalized, that would demonstrate that AI is ready to formmalize all of mathematics.

Re: On the Navier–Stokes Millennium Prize Problem

#710

Post by zem »

AlexErrant wrote: post #243
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…

the projectnash link claims it's mathematically valid, the noahpinion link says that it's invalid and has a marvellous proof that the non-walled section is too small to contain.
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