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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#781

Post by noir_lord »

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/

Recursive self improvement of their upcoming IPO value maybe.

They are fluffy PR pieces otherwise.

Re: On the Navier–Stokes Millennium Prize Problem

#782

Post by calf »

semi-extrinsic wrote: post #709
sobellian wrote: post #669

Earlier quoted context omitted.

Whether or not ways exist to work around the singularities, that they exist is surely of note. Before von Neumann formalized QM people were still doing QM, okay fine. But it's wrong to then say von Neumann was doing no physics of note.

"Does there exist a pathological combination of smooth body forces and initial conditions for this set of PDEs, where singularities appear, which by the way is completely impossible to actually create in the real world unless you are a literal God?" is a question of math, not physics. This is a hill I will die on.

You realize that hill is a mathematical argument, not a physical hill.

Re: On the Navier–Stokes Millennium Prize Problem

#784

Post by elfbargpt »

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…

I have no idea why Sebastian would offer the individuals attribution if OpenAi didn't somewhat knowingly scoop them

Re: On the Navier–Stokes Millennium Prize Problem

#785

Post by AlexErrant »

zem wrote: post #708
AlexErrant wrote: post #243

Earlier quoted context omitted.

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.

Ah derp; that's what I get for moving too fast. Genuine thanks for calling me out on my bullshit. (and this is also why I prefer auditable citations instead of casual "my reading of twitter is...")

I retract the projectnash citation; I grabbed it from the Cool World's youtube description, thinking it was a blog version of the video. It was not. I suggest watching the video instead.

Re: On the Navier–Stokes Millennium Prize Problem

#786

Post by preommr »

danielmarkbruce wrote: post #591
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.

With Lean, math has become a really well suited problem for LLMs. We will likely see large gains for many years from here, just doing more and more rlvr, like continuously, non stop. No need to train from scratch. It really doesn't speak to the general intelligence of models though. It does speak to how good these things can become when a problem space has verifiable rewards, especially when you can verify one step a…

It's crazy how deep Microsoft's bench is (Lean was started there, vscode is another), for everything not directly related to the the ai models (hell, even github for data).

So interesting how everything played out, I remember in the early days when MS came out with the partnership with OpenAI it seemed like they were playing 5d chess and were poised to win big. And it all just fizzled out.

Second biggest fumble after Google.

Re: On the Navier–Stokes Millennium Prize Problem

#787

Post by calf »

raincole wrote: post #163
achierius wrote: post #139

Earlier quoted context omitted.

Have you read the actual statement https://cims.nyu.edu/~tristanb/statement.pdf ? > I should say here why I interpreted their statement the way I did, the in- terpretation I will discuss below. The route to the Clay problem through a smooth force, options c and d in Fefferman’s statement of the problem, is the route Luis and Diego opened and the one Levent and I had quietly chosen to attack. Almost nobody else I know…

Yes, I read the original statement. Buckmaster explicitly stated: > I have not seen OpenAI’s proof. I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything. People saying that he accuses OpenAI stole his proof are putting words into his mouth and I consider that very disrespectful to him. It's basically using Buckmaster as a tool to express their dissa…

Buckmaster is letting the reader connect the dots, it is all the more disrespectful to be disingenuous and say they're nothing there concerning to see or worth further ethical scrutiny given the coincidences.

Re: On the Navier–Stokes Millennium Prize Problem

#789

Post by stratos123 »

root_axis wrote: post #763
stratos123 wrote: post #760

Earlier quoted context omitted.

...obviously it is evidence of the singularity. You're far more likely to see models solving Millenium Prize problems if a singularity is coming than if it's not. One'd have to be doing quite a lot of mental gymnastics to pretend otherwise.

Poor reasoning. You could apply the same logic to any improvement in any field of machine learning.

Not every improvement, no - if progress was steady or slowing down over time, that'd be evidence against. Instead we see what looks a lot like an accelerating growth in capability.

I think you are implying that it's invalid to consider every advance to be evidence "for", and I agree - that'd violate conservation of expected evidence. But not considering any advance to be evidence "for" is also invalid, for exactly the same reason. There has to be some news you may hear that'd make you think a singularity is more likely, and "millenium prize problem solved by an LLM" sure seems like one of those.

Re: On the Navier–Stokes Millennium Prize Problem

#790

Post by mcfry »

cyberax wrote: post #356
tiborsaas wrote: post #103

Earlier quoted context omitted.

2) We are witnessing the intelligence explosion from the first row, wherever this takes us 3) I'm still processing the drama, just found out about it after reading the blog post. If that happened based on private data, that's horrible. If that happened based on public tweets, then it's still abuse of power as OA employees access to compute (launching 10k agents) is quite heavy weight in boxing terms. But apart from A…

> But apart from AI and drama now that we have working solution to Navier-Stokes, what improvements can we expect in engineering? Nothing, really. This mirrors other examples of blowups from the classical physics. It's possible to create a system with just gravitating bodies that exhibits a blowup to infinite speeds in a finite time. The root cause is that, in classical physics, the speed of gravity is instant. In th…

Great comment! I've been trying to understand it more and was hoping to find more people discussing the result, or the implications of the result, and this was the missing piece for me after watching a few videos.
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