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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

#711

Post by jiggawatts »

rfgplk wrote: post #107

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 fronten…

I can't find a good way to articulate this point to other people. What the LLMs lack in depth in a speciality field they more than make up for in breadth!

It feels like the "tide is rising" where the minimum level of skill applied to every aspect of everything will inexorably rise to "whatever an LLM can do", which is already pushing past PhD level.

Re: On the Navier–Stokes Millennium Prize Problem

#712

Post by danielmarkbruce »

vatsachak wrote: post #357
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

No, it won't. How do you verify some causal claim in biology?

The reason AI is doing so well in math proof writing is that it can verify every idea it has, quickly.

Re: On the Navier–Stokes Millennium Prize Problem

#713

Post by hackinthebochs »

root_axis wrote: post #454
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

#714

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

#715

Post by plaidfuji »

Jtariiiii wrote: post #607
MichaelDickens wrote: post #541

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

#717

Post by vemacs »

Jtariiiii wrote: post #607
MichaelDickens wrote: post #541

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

#718

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

#719

Post by 8note »

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 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

#720

Post by 7373737373 »

dakolli wrote: post #429
Fordec wrote: post #378

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

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