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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#801

Post by Aaron1011 »

QuesnayJr wrote: post #240
cv5005 wrote: post #105

Maybe a naive question, but how does one know that a particular lean proof is actually a proof of what one thinks? Like, ok the logic checks out and it proves something , but there's still the problem of does this logical result actually prove the initial question that was asked?

Someone has to actually check this. I'm guessing OpenAI had someone check it internally, but it's possible to get it wrong.

In this case, there was already an existing Lean statement of the problem in the formal-conjectures repository, which they re-used: https://github.com/openai/NavierStokesAndEuler/blob/8937a8f4...

Re: On the Navier–Stokes Millennium Prize Problem

#803

Post by biophysboy »

tristanj wrote: post #764
biophysboy wrote: post #109

Earlier quoted context omitted.

Why is it unlikely?

Because the models are trained on hundreds of billions of user conversations, across more than a billion different humans. The conversations are anonymized and not easily traceable back to a specific user. It's unknowable and not possible to prove if any one specific conversation contained the insights for solving Navier–Stokes. We also don't know if the authors unintentionally provided data to OpenAI through alterna…

I understand that AI is not just cut and paste, but some documents will have more influence than others w/ power law scaling. I would be very surprised if this distribution were not extremely steep for arcane math

Re: On the Navier–Stokes Millennium Prize Problem

#804

Post by monster_truck »

Fordec wrote: post #514
monster_truck wrote: post #503

Earlier quoted context omitted.

Based on the leaps in local inference speed in the past month, which have been absurd, I'm p confident we're going to whiplash from compute constrained to storage constrained. Bit apples to oranges, but it reminds me of all the fiber we installed in the late 90s, certain that per-strand capacity increases were years or decades out, only to get massively rugged

I expect the investments into AI driven mathematic discoveries that underpin compression efficiency will be a key investment area. Particularly at the data center scale rather than per device or per file level.

It's not going to be enough. The naive approach of a project I've been working on was pushing >10gbps over the local network, after a ton of work I got it back down under 1... and now it's processing so much more shit that I'm almost past 5 again! It compresses at >3:1 but the latency hit isn't suitable.

I get the impression the only reason there is renewed interest in photonics is because DCs are simply out of room (and power) to rack more servers and switches.

Re: On the Navier–Stokes Millennium Prize Problem

#805

Post by abathologist »

8note wrote: post #679
thorum wrote: post #153

Earlier quoted context omitted.

It reminds me of the Cognitive Dark Forest hypotheses recently shared here: > “You are creating your cool streaming platform in your bedroom. Nobody is stopping you, but if you succeed, if you get the signal out, if you are being noticed, the large platform with loads of cash can incorporate your specific innovations simply by throwing compute and capital at the problem. They can generate a variation of your innovati…

but what do i lose if somebody else is making money? im still having fun making something

Our market economies are based on competition, and most people more than the fun of making things to secure food and shelter.

Re: On the Navier–Stokes Millennium Prize Problem

#806

Post by mr_coffee »

swat535 wrote: post #686
biesnecker wrote: post #616

Earlier quoted context omitted.

I came here to say this, like... wow. I'm pretty sure at at least a few of the places I've worked that would be grounds for immediate termination.

They probably should have added the disclaimer: opinions are my own..

I am sure that will assuage the legal dept. /s

Re: On the Navier–Stokes Millennium Prize Problem

#807

Post by closetheloopdev »

bananzamba wrote: post #790
closetheloopdev wrote: post #662

Earlier quoted context omitted.

I'm not here to judge since I don't have all the facts, but from what they announced: they tried all 6, found a probable lead to Navier-Stokes, concentrated efforts in that direction, and found a solution. I hope the next solved Millennium Prize Problem will have less drama.

But that lead happened to be the same approach Levent and Tristan had found... Meaning they would have found it first if OpenAI hadn't spent millions in compute on following their lead to its conclusion faster than them.

It's forced vs unforced Euler, so it's not exactly the same. Since OpenAI has access to their training data, they can probably scrub through the data to find out whether there have been any mentions of the similar approach, and whether it only comes from Tristan Buckmaster or if it is in the training data before that. They'll probably have to kick off another fleet of agents to scrub through the training data to answer that.

To be clear, I only talked about the mentioning of the approach to solving it and not of the proof in the training data.

Re: On the Navier–Stokes Millennium Prize Problem

#808

Post by hellohello2 »

traes wrote: post #543
jakevoytko wrote: post #3

For full context, here's the HN thread from the other side of the "Concurrent Work" section: https://news.ycombinator.com/item?id=49605915 Unlike the vanilla read of the OpenAI press release, it is much more unfiltered and outlines some particularly aggressive behavior by specific OpenAI employees

Which seems to be entirely true by their own admission! [0] Both the comments about him risking his career and about Levent's authorship seem to have indeed occurred. > 2) I never ever asked for Levent to be removed from authorship of his own work (as indicated by my text). I was surprised to learn during the call with Tristan that they had only solved Euler and not Navier-Stokes; after learning this we brainstormed…

Hm. Looks like its possible everyone behaved terribly here unfortunately. :/

I remained impressed by ChatGPT however!

Re: On the Navier–Stokes Millennium Prize Problem

#809

Post by abathologist »

hmate9 wrote: post #5
minimaxir wrote: post #2

> Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens Don't even try to do the math on how much that would cost at normal API prices. And we don't even know how much more expensive this internal-only model would be!

Napkin math if we assume gpt 6 astra on max is >$15 million (just for output tokens) for those wondering.

This could fund 10 top income mathematicians for 8 years (based on https://careers.usnews.com/best-jobs/mathematician/salary ). Imagine what kinds of results we'd have to transform the foundations of science if we were giving brilliant minds this kind of funding to do nothing but research for most of decade....

Instead, we get slop proofs that are technically correct as PR stunts to enable corrupt kleptocrats, and most likely will drive research into culs-de-sac.

Re: On the Navier–Stokes Millennium Prize Problem

#810

Post by senordevnyc »

applicative wrote: post #91
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…

Its funny, it is uniquely with this one act that I have turned forever on OpenAI, which I hitherto defended up and down against nonsense charges. I dedicate my life to its complete destruction beginning today.

Wow, the origin of a supervillain! /s
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