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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

#351

Post by mmiyer »

twobitshifter wrote: post #327

>The groups varied in size, and the group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents… The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched. The Millenium Prize is $1M, what is the ROI? (Edit: since I was not clear, and confused some - I mean for a hypothetical of a third party paying commercial rates to u…

The ROI is billions added to their valuation. Also of course it costs OpenAI much less than API pricing for inference.

Re: On the Navier–Stokes Millennium Prize Problem

#352

Post by 20k »

olalonde wrote: post #313
colinhb wrote: post #122

Earlier quoted context omitted.

The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys: > I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin…

Playing the devil's advocate here but it's true that OpenAI didn't have to make those offers.

They kind of did though, they were hoping to keep the fact that they may well have plagiarised these researchers unpublished work quiet. They did not want this to turn into a scandal about the fact that they appear to be training on prompts without consent

It makes a certain amount of sense. The internet data is too polluted with AI usage now to be useful, so the only AI free new data source is the prompts people feed into ChatGPT. The only problem is that its clearly plagiarism

Edit:

OpenAI have admitted to training on prompts at the time the breakthrough was made:

https://mastodon.social/@tristanbuckmaster/11723647135247030...

Re: On the Navier–Stokes Millennium Prize Problem

#353

Post by uncomputation »

So what took an autonomous agentic system using a significantly more powerful internal model, totaling multi-millions of dollars of compute in training and inference, was likely to already be solved by a team of a few humans with an orders of magnitude smaller LLM budget, had OpenAI not been foaming at the mouth to jump the shark and claim “AI solves Millenium Problem.”

Also it sounds like the human research effort spanned weeks if not years from Tristan’s statement so it is extremely likely the work and prompts of these human researchers was used in the OpenAI knock-off.

Re: On the Navier–Stokes Millennium Prize Problem

#354

Post by curt15 »

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.

They're also counting on more casual observers to extrapolate optimistically from successes in high profile math theorems to the company's economic value.

Re: On the Navier–Stokes Millennium Prize Problem

#355

Post by famouswaffles »

kzrdude wrote: post #296
famouswaffles wrote: post #29

Earlier quoted context omitted.

>Does OpenAI have a policy of not claiming math prizes like this Wouldn't be surprising if they did. The prize money isn't worth the almost certainly negative PR.

I don't see how it would be negative PR. If anything, the love these breakthroughs and use it in their PR campaigns.

They don't need to collect the monetary prize to announce the result and use it for marketing.

On the other hand, trying to collect the prize would probably not go uncontested.

Re: On the Navier–Stokes Millennium Prize Problem

#356

Post by cyberax »

tiborsaas wrote: post #103
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…

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 the case of Navier-Stokes, the fluid is incompressible. So technically any force that you apply to it is supposed to instantly affect everything else. This can be exploited to create these blowups. In reality, no fluid is incompressible, and it takes time for any action to affect the material.

It's just that Navier-Stokes equations are so slippery that it's hard to pin their behavior down. They basically just restate the momentum conservation law for a continuous medium.

Re: On the Navier–Stokes Millennium Prize Problem

#357

Post by vatsachak »

hdivider wrote: post #112

My take: 1. It shows what even this wave of AI can actually do. 2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model. 3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including informat…

Lol what? Everything is computation.

The natural sciences will soon start breaking too.

I will concede that AI seems likely to not invent a "research program" anytime soon.

It has no taste

Re: On the Navier–Stokes Millennium Prize Problem

#359

Post by reducesuffering »

kypro wrote: post #321
simianwords wrote: post #136

Earlier quoted context omitted.

> I have a couple friends who did the Math tripos at Cambridge (so a pretty high level!) who work in tech and have unanimously said they have 0% expectations of an LLM doing a millennium problem anytime soon https://news.ycombinator.com/item?id=38433655 > Let's talk when we've got LLMs proving the Riemann Hypothesis (or any mathematical hypothesis) without any proofs in the training data. I'm confident in my belief t…

As someone with a background in AI and who has been playing around with neural nets for decades at this point, it's been genuinely amazing watching extremely intelligent people make confident predictions about AI capabilities and progress, then be so completely wrong. There's a kind of theory of mind for AI (specifically neural nets) which I now realise I seem to have which is very hard to explain to people who haven…

> extremely intelligent people make confident predictions about AI capabilities and progress, then be so completely wrong.

The ability for the human mind to rationalize conclusions to maintain denial in the face of a very scary future is immense. Genuinely grappling with the implication of where we're headed is usually very crushing. It's not easy to engage with the possibility, and very intelligent people will use those smarts to feel safe.

Re: On the Navier–Stokes Millennium Prize Problem

#360

Post by tedsanders »

Analemma_ wrote: post #129
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.

In OpenAI's case, if they were genuinely unsure, they wouldn't have said anything. "We cannot rule out" means they absolutely 100% for-sure did look at the existing prompts and bootstrapped from that, and they are trying to get ahead of the disclosure with this weasel-wording.

Also possible: we're 99.999% sure, but a lawyer said to be safe and strictly accurate, we should stick in a sentence in saying we can't be perfectly sure, since it's infeasible for us to prove it.

I promise you that if we took their work from ChatGPT and stuck in a bunch of weasel words to give the opposite impression while remaining technically true, I would quit on the spot.

(I work at OpenAI.)

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