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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

#981

Post by achierius »

anon109 wrote: post #586
jijijijij wrote: post #486

Earlier quoted context omitted.

> Should I just say fuck it, and go hitchhiking across Europe with some friends? Yes. Assuming you are young and haven't had such experience. The world is changing not just because of AI. Everything is unstable right now. You may regret not enjoying the remainder of stability and economic viability prior generations had. It's not like you can expect to get ahead by powering through education. Either your career persp…

Have you people gone insane?

There is a land war in Europe for the first time in generations. The only reason you can say that big things aren't happening is because you're lucky enough to live where they're happening.

Re: On the Navier–Stokes Millennium Prize Problem

#982

Post by achierius »

DudleyBluffles wrote: post #636
JPC21 wrote: post #597

Earlier quoted context omitted.

Just don't. If you read the story here carefully, you see that AI was used to work from theory built by others which showed that the Euler equations possesed finite-time blow-ups. But to make that step, actual good understanding for mathematics was needed. My experience with software has been the exact same.

I fear this is only temporary and due mostly to the complexity of the problem. Consider the recent counter-example to the Dinitz–Garg–Goemans conjecture: > https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0... The prompts for the chat above are: > Construct a counterexample to general (non-planar) case of Dinitz Garg Goemans conjecture. You should do a breakthrough and find a structured counterexample. > [g…

You're probably correct. FWIW most people with math degrees haven't gone on to do math research regardless, so in that regard this isn't a big change.

Re: On the Navier–Stokes Millennium Prize Problem

#983

Post by achierius »

backtr4ck wrote: post #949
colesantiago wrote: post #7

Is this truly the beginning of the AGI era? Running agents and prompting excessively to produce 'slopcode' to solve mathematical problems and generate a solution. If this is what anyone calls 'slop' then slop has no meaning. I'm all for it on the use case of solving mathematical breakthroughs!

No AGI here, it's just extreme brute forcing. AI doesn't understand fluids dynamics, it just slops it's way to the solution.

If you don't need to 'understand' to do this, then maybe what you call 'understanding' is less important than you think. When people in the real world reach for a tool, what they care about is whether or not it'll produce results, not whether or not it has the capacity for interior phenomenological experience.

Re: On the Navier–Stokes Millennium Prize Problem

#984

Post by an0malous »

ameliaquining wrote: post #639
an0malous wrote: post #559

Earlier quoted context omitted.

The things you don’t care about are highly relevant to that claim

Elaborate?

If the model started from work that Tristan Buckmaster had already done, and was aided by an entire team of mathematicians as he alleged, then it's not as capable as you seem to be precluding

Re: On the Navier–Stokes Millennium Prize Problem

#985

Post by frozenseven »

diomedes wrote: post #877
frozenseven wrote: post #473

Earlier quoted context omitted.

There was a recent rumor about the Hodge Conjecture. I'd keep an eye on that one. But like the other person who replied, I'm also rooting for Yang-Mills. That has massive potential for unlocking a series of physics results.

interesting, i haven't heard anything about that. i don't know much about the hodge conjecture, all i really know is that it's incredibly abstract and obtuse - not sure if that has any implication for solvability by an AI though. do you have any source for the hodge rumor? curious to learn more

So far it's just anonymous accounts on X and Reddit during the past few days, no "official leak" or anything like that. But the rumors about Navier-Stokes being solved started the same way. If somebody really solved it, the incentive is to come forward soon before being scooped by another team. We'll see.

Re: On the Navier–Stokes Millennium Prize Problem

#986

Post by dekhn »

JumpCrisscross wrote: post #896
dekhn wrote: post #855

Earlier quoted context omitted.

We don't have any proof of that at all. Please stop rushing to judge without data.

> We don't have any proof of that It’s fair to give benefit of doubt to Buckmaster given OpenAI is currently being very credibly sued by Apple for openly stealing others’ original work in another context.

A prior of "one large company is current involved in an unrelated lawsuit with another large company" is pretty weak; the case is undecided and about an entirely different kind of IP theft.

In short I think a lot of people are jumping to conclusions without supporting evidence and that's really not helping the situation.

Re: On the Navier–Stokes Millennium Prize Problem

#987

Post by [deleted] »

tedsanders wrote: post #624
Imnimo wrote: post #254

Earlier quoted context omitted.

>we did not read any private chats The question I am interested in is not "did we read private chats", but "was this new model trained using any of Tristan and Levent's chats, regardless of whether they were marked private". Can you comment on that?

If they opted out of training, then we definitely did not train on them. If they did not opt out, then I don't personally know if training signals came from their chats, and I don't think we'd be able to tell without their cooperation in identifying them. And even if signals were trained on in some manner, I highly doubt it made a difference to a problem as challenging as the NS proof. Reasons for my doubt: - I know…

[deleted]

Re: On the Navier–Stokes Millennium Prize Problem

#988

Post by jdm2212 »

alightsoul wrote: post #975
jdm2212 wrote: post #728

Earlier quoted context omitted.

It'd be corporate suicide for them to be caught violating zero-data-retention commitments. But also if you're really paranoid you can just use ChatGPT on Azure or AWS, where nothing is flowing back to OpenAI at all.

Zero data retention commitments? Technically generating synthetic data off of user data on the fly, counts as zero retention of user data! And it technically means they didn't lie either, because they didn't keep user data, they kept their own, synthetic data. That is what they already do with reasoning when they provide summaries/sanitized versions of it to prevent "distillation attacks" even via the API. They gener…

This is flatly false. ZDR means the customer request is processed and nothing about its content remains on the model provider's servers.

Re: On the Navier–Stokes Millennium Prize Problem

#990

Post by sobellian »

HarHarVeryFunny wrote: post #969
sobellian wrote: post #549

Earlier quoted context omitted.

Even under your interpretation, OAI pushed a button and solved NS. Yes, that is very impressive. Are you kidding me? Imagine building an automated system that can solve NS.

> OAI pushed a button and solved NS Not exactly... From here: https://cims.nyu.edu/~tristanb/statement.pdf "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 thei…

The evidence we have (not much) leaves the facts severely under-constrained. All the below are consistent with what we observe:

- OpenAI lying their face off for marketing purposes

- Buckmaster sore about getting beaten to NS, misrepresenting what was told

- Buckmaster not being an expert in ML, not understanding what he was told and hearing what he wanted to hear as it vindicated him

- Others...

OAI claimed that none of the people on their team were domain experts. So it's more akin to Deep Blue than Stockfish (actually slightly better than Deep Blue which did hire domain experts) but nevertheless represents a highly sophisticated automatic theorem prover.

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