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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

#271

Post by nradov »

imbusy111 wrote: post #83
Reubend wrote: post #66

It's great that important discoveries like this can now routinely be accompanies by formalized proofs. The fact that it's being released alongside a Lean proof from Day 1, rather than the Lean proof being released months or years later, is super helpful for verifying that it's correct.

I feel sorry for whoever has to read and understand the solution. It looks like the typical convoluted unreadable mess I see the models generate for software. It might be technically correct, but gaining insight from it is just intellectual hell.

There's an opportunity to build a Lean "optimizer" which automatically simplifies existing proofs.

Re: On the Navier–Stokes Millennium Prize Problem

#272

Post by arodev »

rfgplk wrote: post #138
imbusy111 wrote: post #83

Earlier quoted context omitted.

I feel sorry for whoever has to read and understand the solution. It looks like the typical convoluted unreadable mess I see the models generate for software. It might be technically correct, but gaining insight from it is just intellectual hell.

Skill issue. Also lean is meant to be executed, not read.

i think they're talking about the writeup

Re: On the Navier–Stokes Millennium Prize Problem

#273

Post by 20k »

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…

Drama aside, this solution would be a counterexample disproving the smoothness postulate, which means that it leads to nothing new unfortunately. We already had working solutions to navier stokes, the only thing we didn't know is if the equations possessed a technical property

Its a bit like solving p = np with a negative result. Its an incredibly difficult problem, but it doesn't lead to anything at all on its own. This is why people are talking about the fact that the solution methodology is much more interesting than the solution - the tools used to crack something like this may lead to solving more useful problems

Re: On the Navier–Stokes Millennium Prize Problem

#275

Post by demirbey05 »

From Levent Alpöge : https://x.com/__alpoge__/status/2097383870773748190?s=20

>so far the proof looks more along the lines of another euler blowup proof we had, off of whose ansatz naming we were making really stupid puns like “smooth criminale”, unlike the much better “ideal fluids explode”, Tristan

There are too many ambiguities around OpenAI. Unanswered questions making this ambiguity more.

Why they didn't properly explain to Tristan about usage of their data.

Re: On the Navier–Stokes Millennium Prize Problem

#276

Post by magicalist »

tedsanders wrote: post #181
lambda wrote: post #130

Earlier quoted context omitted.

Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there ma…

To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effec…

> identify any of their de-identified data that came from their usage of ChatGPT

"de-identified" seems more of a euphemism than normal in this context, given the very unique work they were doing.

Re: On the Navier–Stokes Millennium Prize Problem

#277

Post by colinhb »

Maxious wrote: post #205
igleria wrote: post #184

Earlier quoted context omitted.

I´m waiting on the other side version, because I know there is no justifiable way to talk to a person like they did. Sociopathic behaviour.

OpenAI version of events conceed some of the words alleged to have been used may have been used https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310

May be unfairly jaded or just well calibrated given the body of evidence, but I can't help but think of another quote about OpenAI leadership:

> Not consistently candid

Re: On the Navier–Stokes Millennium Prize Problem

#279

Post by stefap2 »

munificent wrote: post #217
stefap2 wrote: post #180

Earlier quoted context omitted.

This just pushes knowledge work further up the ladder, toward larger and more complex problems. If there are no knowledge workers, who is going to interpret these results, validate them, decide what matters, and put them into practical use? Rather than eliminating knowledge work, advances like this could create entirely new layers of problems to solve and opportunities to pursue, which will create even more jobs and…

> This just pushes knowledge work further up the ladder, toward larger and more complex problems. You really think it makes sense for you to be higher on the "solving complex problems ladder" than the machines that solved fucking Navier-Stokes? I envy your self-confidence.

Maybe I should have been clearer. My point is that solving something like Navier–Stokes just pushes knowledge work further ahead, onto a new set of bigger and more complex problems. Navier–Stokes is a Millennium problem today, but once problems like that become solvable, they can open the door to entirely new classes of problems we haven’t even thought of yet.

Re: On the Navier–Stokes Millennium Prize Problem

#280

Post by dgellow »

tedsanders wrote: post #181
lambda wrote: post #130

Earlier quoted context omitted.

Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there ma…

To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effec…

> As a parallel example, can we prove the phase of the moon had no impact on the NS solution? No, not without a bunch experiments run at different phases of the moon.

That reads as incredibly dismissive and condescending. What makes you think you’re in a position to communicate like that when engaging on such a sensitive topic?

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