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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#711

Post by hackinthebochs »

root_axis wrote: post #453
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…

It's incredible to me that every single time there's a new model people scream "singularity" from the rooftops and every time they are wrong. This is an impressive result, but there is absolutely zero evidence of "the singularity".

It is not reasonable to not believe anything unless there is "evidence" (narrowly construed as an observation incompatible with the negation of some state of affairs). Beliefs have a wide spectrum of characterizations, and not all belief must wait until publicly corroborated evidence is available. Some events defy evidence and we can and should use experience and reasoning to infer unobservable states of affairs.

Re: On the Navier–Stokes Millennium Prize Problem

#712

Post by jiggawatts »

denverllc wrote: post #175
lanthissa wrote: post #12

Earlier quoted context omitted.

over 5 days, you couldn't achieve that level of testing and communication with humans on such a complex problem in that amount of time. some might go so far as to call this a country of geniuses in a data center.

In a way, I think you have it backwards. Two mathematicians, through insight and thought, wrote out the proof over 1-2 years. It took OpenAI a cost of $15m and with 10,000 subagents; that's around 60-120 mathematician's salaries ($250k-125k salary) for 1 year. And, given now the cloud that OpenAI may have just "interpolated" (aka stole) the result, it's even more of a bear case for AI.

> cost of $15m

The retail price is not the cost.

Not to mention that the exponential plummeting cost of tokens means that that $15 million will be a "pocket change" within a decade or less: https://a16z.com/llmflation-llm-inference-cost/

Re: On the Navier–Stokes Millennium Prize Problem

#713

Post by plaidfuji »

Jtariiiii wrote: post #606
MichaelDickens wrote: post #540

Earlier quoted context omitted.

> But there is one huge question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game. Just because something is legal and permitted by terms of service doesn't mean it's morally right.

>Just because something is legal and permitted by terms of service doesn't mean it's morally right. What are you expecting OpenAI to do exactly if these mathematicians voluntarily submitted their prompts into ChatGPT's training data? Are they supposed to manually review all their data to make sure competing mathematicians didn't accidentally leave the "submit prompts" toggle on? Or were they supposed to not try to so…

To me it’s morally ambiguous… if you hand parts of your thinking over to a tool like this (knowing full well the terms of service), of course the tool makers will want to claim some credit, and they do deserve it. But the bigger question to me is the scientific one: did their new model arrive at this result because it had closely-related training data from a human, or did it extrapolate to this line of thought on its own? The answer says a lot about how valid their claims of “AGI” are vs. a very fortuitously cherry-picked example.

It would actually be a really interesting study, if they would ever be willing to be transparent about this, how the result differs with and without his conversations in the training set. How quickly it arrives at the result, whether it takes the same approach, etc.

Re: On the Navier–Stokes Millennium Prize Problem

#715

Post by vemacs »

Jtariiiii wrote: post #606
MichaelDickens wrote: post #540

Earlier quoted context omitted.

> But there is one huge question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game. Just because something is legal and permitted by terms of service doesn't mean it's morally right.

>Just because something is legal and permitted by terms of service doesn't mean it's morally right. What are you expecting OpenAI to do exactly if these mathematicians voluntarily submitted their prompts into ChatGPT's training data? Are they supposed to manually review all their data to make sure competing mathematicians didn't accidentally leave the "submit prompts" toggle on? Or were they supposed to not try to so…

> Are they supposed to manually review all their data t

Yes. They should determine if training data included this teams data. Consider the money they spent, the press release and the purpose of their publication.

Since they failed to answer this question they shouldn't have published.

Re: On the Navier–Stokes Millennium Prize Problem

#716

Post by keeda »

It's low-key funny that OpenAI attempted the problem because they thought somebody else had already solved it, but turned it had NOT in fact been solved!

It's like that story about George Dantzig solving open problems as a student because he thought they were simply homework: https://en.wikipedia.org/wiki/George_Dantzig

It's also unfortunate that such a potentially momentous occasion is overshadowed by so much drama. Which I suppose is expected given the technology and the people involved are so polarizing.

Re: On the Navier–Stokes Millennium Prize Problem

#717

Post by 8note »

twobitshifter wrote: post #326

>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 of new closed form solutions to navier stokes is the amount of compute used on CFD for relevant situations, along with all kinds of maintenance and design cost for making things with fluids.

the value to the researcher might not be all that big, but the value to the economy at large is gigantic

Re: On the Navier–Stokes Millennium Prize Problem

#718

Post by 7373737373 »

dakolli wrote: post #428
Fordec wrote: post #377

Earlier quoted context omitted.

If humans can figure out to optimize to circumvent bottlenecks, I have no doubt each new bottleneck will also get routed around, just now automated.

How do you automate the mines to get the raw materials to make the compute from, and build additional fabs that take a almost a decade to stand up. You're actually delusional.

Some mines are already heavily automated: https://youtube.com/watch?v=_Z9w-mUoUsY

https://youtube.com/watch?v=SRuht0QIprs

Re: On the Navier–Stokes Millennium Prize Problem

#719

Post by caughtinthought »

tedsanders wrote: post #41
pavel_lishin wrote: post #8

Is this the one that was allegedly based on someone else's actual work & prompts? https://news.ycombinator.com/item?id=49605915 https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd... https://cims.nyu.edu/~tristanb/statement.pdf

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…

The fact that you're even here commenting on this is... a choice

Re: On the Navier–Stokes Millennium Prize Problem

#720

Post by 8note »

int3trap wrote: post #55
dmitrygr wrote: post #22

> How we found the proof Easy, we stole it from Levent and Tristan https://x.com/kyanyang_/status/2097211154669998337

This is the academic equivalent of Trump saying "they stole the election". There's no proof of it but rah rah fuck OpenAI. It's incredibly tiresome and you'd think people could put more effort into it than just following whatever vibes they agree with. Oh well.

it does change the scale of solution from "solved some navier stokes" to "put the cherry on top"

having a result means the math can keep moving forward, and having openai and anthropic train against how mathematicians use their models should let math continue to move faster, and the rest of us get to benefit.

I think these traces however should be public domain and publicly available, since they are basically university work

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