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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#751

Post by kypro »

reducesuffering wrote: post #359
kypro wrote: post #321

Earlier quoted context omitted.

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 t…

> Genuinely grappling with the implication of where we're headed is usually very crushing.

As someone currently prepping for various AI doom scenarios and who has been dealing with AI-related nightmares for years this is very relateable.

Although, I don't personally think it's this. In my experience the opposite is more true – the majority of high probability doomers seem rather laid back about considering what they believe will happen to the people they love in a few years. Equally I don't get the sense those who don't have such extreme predictions are worried at all. If anything there's not enough emotion.

In my opinion people just don't reason well when it comes to exponentials and are ignorant about things they don't have good mental models of. At least I know I struggle with this.

Re: On the Navier–Stokes Millennium Prize Problem

#752

Post by azan_ »

diehunde wrote: post #611
azan_ wrote: post #328

Earlier quoted context omitted.

Existence of AI capable of solving millennium problem has enormous bearing on everything though.

What kind of enormous bearing? Computers have been able to do things humans can't for decades now.

Are you being flippant?

Re: On the Navier–Stokes Millennium Prize Problem

#753

Post by [deleted] »

enraged_camel wrote: post #632
tedsanders wrote: post #237

Earlier quoted context omitted.

All of those statements sound true, based on what I've heard. - "very little human" input feels ambiguous, and if someone spends a few days prompting a model to solve a super hairy problem requiring a 100-page proof, I can understand reasonable people interpreting that as both "very little" and "not very little" human input - it's all true that a team worked on this, a bunch of compute was burned, and the problem was…

>> I'm not sure how any of this provides evidence that OpenAI took any of their work. Sorry, but the burden of proof lies in the other direction: OpenAI needs to definitively prove that their agents did not look at the existing work that was about to be published. Otherwise OpenAI simply stole the glory and the spotlight (and I'm being charitable here).

[deleted]

Re: On the Navier–Stokes Millennium Prize Problem

#754

Post by DetroitThrow »

tedsanders wrote: post #237
contemporary343 wrote: post #132

Earlier quoted context omitted.

"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a num…

All of those statements sound true, based on what I've heard. - "very little human" input feels ambiguous, and if someone spends a few days prompting a model to solve a super hairy problem requiring a 100-page proof, I can understand reasonable people interpreting that as both "very little" and "not very little" human input - it's all true that a team worked on this, a bunch of compute was burned, and the problem was…

It's unclear if you're suggesting that OpenAI did not train on their input or use their chats as inputs to training on a model that found the solution. Let's not provide an Elizabeth Holmes-esque interview where the question is dodged and words gain new meaning. The question can be answered with "Yes, we trained on their conversations" or "No, we did not train on their conversations".

I'm not coming from a place of distrust here. This should just be definitively answerable given the weight of the claims here. Surely between you, your lawyers, and other members of your team you can just clear this part up.

Re: On the Navier–Stokes Millennium Prize Problem

#755

Post by irthomasthomas »

tzone wrote: post #742
irthomasthomas wrote: post #702

Earlier quoted context omitted.

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?

Clearly The goal was to scoop Anthropic not a single researcher. OpenAI heard the rumor that Anthropic solved an open problem. So they went nuts pulling all plugs to scoop them. Turns out it wasn’t actually Anthropic and just a researcher with a single Anthropic guy friend working on it . Wild times

The researcher told them it was an independent effort, and they still pushed ahead with it.

Re: On the Navier–Stokes Millennium Prize Problem

#756

Post by Kotlopou »

rybosworld wrote: post #689

In chess, a grandmaster just needs to know at what moment in a game there's a critical move to gain a significant advantage over their opponent. They don't need to know the move itself. OpenAI got wind that a millenium problem was being solved. And that feels a bit like the critical move in chess. That is - it was a signal that AI advanced far enough that it would be worth spending a lot of time and resources solving…

Elsewhere in this thread somebody claimed that at some point OpenAI pointed their new model at all the millennium problems and this is where they got some progress. We probably won't see proof of this, but it seems plausible to me -- I assume there's a list of problems that each new model is tested on, and you might as well put the big stuff on the list, if only to see how the model behaves when faced with a problem it knows should be very hard.

The weak point in this is: how do you evaluate if a partial result is promising? If this cost ~$10M as suggested elsewhere in the thread, probably not even OpenAI can just throw that at everything?

Re: On the Navier–Stokes Millennium Prize Problem

#757

Post by 20k »

HDThoreaun wrote: post #658
20k wrote: post #621

Earlier quoted context omitted.

That does not make it ethical

Isnt the entire history of academic progress iterating on work that other academics shared with you? Obviously this situation is spicy but openAI cited their work no?

OpenAI trained on their private unpublished research notes effectively, while also trying to get one of the paper authors fired

Re: On the Navier–Stokes Millennium Prize Problem

#758

Post by efavdb »

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…

I am curious who if anyone will get a reward for this. It would seem unreasonable to give it to the worker who asked the robot to solve it.

Re: On the Navier–Stokes Millennium Prize Problem

#759

Post by tristanj »

whimsicalism wrote: post #691
tedsanders wrote: post #237

Earlier quoted context omitted.

All of those statements sound true, based on what I've heard. - "very little human" input feels ambiguous, and if someone spends a few days prompting a model to solve a super hairy problem requiring a 100-page proof, I can understand reasonable people interpreting that as both "very little" and "not very little" human input - it's all true that a team worked on this, a bunch of compute was burned, and the problem was…

I'm confused, your employer very directly stated that they are unable to confirm that the model was not trained on the conversations.

The models are trained on the conversations of hundreds of millions of people. ChatGPT has several billion conversations every day. I estimate that the model that solved Navier–Stokes was trained on data from nearly a trillion conversations.

It's unknowable and not possible to prove if any one specific conversation was the key to solving Navier–Stokes.

Re: On the Navier–Stokes Millennium Prize Problem

#760

Post by masterspy7 »

aeve890 wrote: post #698
redox99 wrote: post #598

Earlier quoted context omitted.

The amount of goalpost moving is insane. "Yeah it can solve Millenium problems, but can it do it with nothing more than a one sentence prompt?" Also there are proofs where the only human steering was "keep going".

Parent comment is claiming creativity and genius beyond human experts, so why not ask for a fully unassisted AI novel result? Having access to the entire corpus of human knowledge, what else such amazing entity would require to solve a hard problem by its own? Any result of such kind from an AI alone would be enough to refute my argument, yet you don't present any. >Also there are proofs where the only human steering…

https://www.anthropic.com/research/riemann-zeta

>Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress.

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