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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#101

Post by naasking »

raincole wrote: post #86
echelon wrote: post #53

Earlier quoted context omitted.

This is going to be dramatic in so many different ways. - First off, to reiterate, WOW. - Second of all, when does this end? Are we at the dawn of the singularity now? - People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? - Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can butt…

> People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit. "People" are just misinformed and keep…

> The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit.

Not quite accurate, Buckmaster was taking an approach that nobody else was, and this new proof uses this same approach just weeks after he saved those results to OpenAI workspaces. He asked OpenAI if they used chat logs for training the new model, and they did not confirm or deny.

Asking to remove his collaborator is also totally over the line though.

Edit: although this OpenAI post is not comforting: https://x.com/OpenAI/status/2097375276384567642

Quote: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. "

Re: On the Navier–Stokes Millennium Prize Problem

#102

Post by fooker »

SpicyLemonZest wrote: post #71
paxys wrote: post #37

Earlier quoted context omitted.

What else can they declare really? Yeah the model has training data from previous attempts. Alpöge and Buckmaster also similarly benefited from attempts before theirs.

They could have thought about the problem for like 2 minutes and not done this! I think that literally any academic mathematician could have explained to them, had they asked, why it is considered extraordinarily rude to react to rumors of research progress by desperately rushing to get there first.

> I think that literally any academic mathematician could have explained to them, had they asked, why it is considered extraordinarily rude to react to rumors of research progress by desperately rushing to get there first.

Pretty much all of math and science history is basically this pattern again and again. I'm sure all of that was rude as well.

Re: On the Navier–Stokes Millennium Prize Problem

#103

Post by tiborsaas »

echelon wrote: post #53
tiborsaas wrote: post #16

> We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. WOW?

This is going to be dramatic in so many different ways. - First off, to reiterate, WOW. - Second of all, when does this end? Are we at the dawn of the singularity now? - People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? - Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can butt…

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 AI and drama now that we have working solution to Navier-Stokes, what improvements can we expect in engineering?

Re: On the Navier–Stokes Millennium Prize Problem

#105

Post by cv5005 »

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?

Re: On the Navier–Stokes Millennium Prize Problem

#106

Post by nradov »

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?

Is it spying? I think this usage is disclosed in their terms of service.

Re: On the Navier–Stokes Millennium Prize Problem

#107

Post by rfgplk »

Something I've been going on and on about for months now and no one seems to listen. LLMs today are allowing _anyone_ to access cross-discipline knowledge that was previously entirely inaccessible without a) extremely deep pockets or b) a massively talented and varied team. In fact, contrary to what the masses seem to think LLMs are actually _better_ at hard cutting edge physics/math problems than they are at frontend web stuff (paradoxically). This is why I'm advising most people to start pivoting into much harder to penetrate domains (historically hardware, aerospace, robotics, biotech). Most fields are in their infancy (see the sad state of embedded development) and the gains to be had are massive.

Re: On the Navier–Stokes Millennium Prize Problem

#108

Post by applicative »

paxys wrote: post #37
railgunmerlin wrote: post #25

Does seem like they gloss over Alpöge and Buckmaster's work with the following > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . Which seems a bit irresponsible/rash?

What else can they declare really? Yeah the model has training data from previous attempts. Alpöge and Buckmaster also similarly benefited from attempts before theirs.

This is desperate. They were expressly operating within a program. OpenAI isn't going to recover from this

Re: On the Navier–Stokes Millennium Prize Problem

#109

Post by biophysboy »

floatrock wrote: post #43
beering wrote: post #9

Earlier quoted context omitted.

That is addressed in the article.

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?

Re: On the Navier–Stokes Millennium Prize Problem

#110

Post by jgbuddy »

stabbles wrote: post #84
jgbuddy wrote: post #63

Here's the formalization / lean verification: https://github.com/openai/NavierStokesAndEuler

341k lines of lean without comments

Had no idea this was what lean looked like- that's mind blowing. I'm not even sure how someone would critique this if they wanted to
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