Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

On the Navier–Stokes Millennium Prize Problem

openai.com

Post reply on HN
Print view View original

801–810 of 1001 posts

Re: On the Navier–Stokes Millennium Prize Problem

#801

Post by cyberax »

mcfry wrote: post #791
cyberax wrote: post #356

Earlier quoted context omitted.

> But apart from AI and drama now that we have working solution to Navier-Stokes, what improvements can we expect in engineering? Nothing, really. This mirrors other examples of blowups from the classical physics. It's possible to create a system with just gravitating bodies that exhibits a blowup to infinite speeds in a finite time. The root cause is that, in classical physics, the speed of gravity is instant. In th…

Great comment! I've been trying to understand it more and was hoping to find more people discussing the result, or the implications of the result, and this was the missing piece for me after watching a few videos.

Here's the paper about the blowup for the gravitating bodies: https://www.jstor.org/stable/2946572?origin=crossref

There's a Wiki article about it: https://en.wikipedia.org/wiki/Painlev%C3%A9_conjecture

Re: On the Navier–Stokes Millennium Prize Problem

#802

Post by drpixie »

lanthissa wrote: post #14

5 million messages, 300b output tokens, done in 5 days, and achieving something humans couldn't. the first "Country of geniuses in a datacenter" moment.

That is how the PR reads, but is not at all what happened.

A team of highly trained and skilled people used an AI tool, through many many instructions (prompts), to produce a specific mathematical theorem. The tool is impressive, the result (possibly/probably) interesting, but the PR skips the vital role of the humans (for the usual PR reasons).

Re: On the Navier–Stokes Millennium Prize Problem

#803

Post by covidwasfake »

TomJansen wrote: post #799
dyauspitr wrote: post #529

Earlier quoted context omitted.

I had a lot of fun during Covid. I loved the working from home. The fact that most outdoor places were sparsely populated, jobs were plentiful and prices were low. Covid was awesome.

Yeah Covid was awesome, say that to the people who died from it, or who committed suicide because of the lockdown depression

[dead]

Re: On the Navier–Stokes Millennium Prize Problem

#804

Post by [deleted] »

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…

[deleted]

Re: On the Navier–Stokes Millennium Prize Problem

#805

Post by Aaron1011 »

QuesnayJr wrote: post #241
cv5005 wrote: post #105

Maybe a naive question, but how does one know that a particular lean proof is actually a proof of what one thinks? Like, ok the logic checks out and it proves something , but there's still the problem of does this logical result actually prove the initial question that was asked?

Someone has to actually check this. I'm guessing OpenAI had someone check it internally, but it's possible to get it wrong.

In this case, there was already an existing Lean statement of the problem in the formal-conjectures repository, which they re-used: https://github.com/openai/NavierStokesAndEuler/blob/8937a8f4...

Re: On the Navier–Stokes Millennium Prize Problem

#807

Post by biophysboy »

tristanj wrote: post #768
biophysboy wrote: post #109

Earlier quoted context omitted.

Why is it unlikely?

Because the models are trained on hundreds of billions of user conversations, across more than a billion different humans. The conversations are anonymized and not easily traceable back to a specific user. It's unknowable and not possible to prove if any one specific conversation contained the insights for solving Navier–Stokes. We also don't know if the authors unintentionally provided data to OpenAI through alterna…

I understand that AI is not just cut and paste, but some documents will have more influence than others w/ power law scaling. I would be very surprised if this distribution were not extremely steep for arcane math

Re: On the Navier–Stokes Millennium Prize Problem

#808

Post by monster_truck »

Fordec wrote: post #515
monster_truck wrote: post #504

Earlier quoted context omitted.

Based on the leaps in local inference speed in the past month, which have been absurd, I'm p confident we're going to whiplash from compute constrained to storage constrained. Bit apples to oranges, but it reminds me of all the fiber we installed in the late 90s, certain that per-strand capacity increases were years or decades out, only to get massively rugged

I expect the investments into AI driven mathematic discoveries that underpin compression efficiency will be a key investment area. Particularly at the data center scale rather than per device or per file level.

It's not going to be enough. The naive approach of a project I've been working on was pushing >10gbps over the local network, after a ton of work I got it back down under 1... and now it's processing so much more shit that I'm almost past 5 again! It compresses at >3:1 but the latency hit isn't suitable.

I get the impression the only reason there is renewed interest in photonics is because DCs are simply out of room (and power) to rack more servers and switches.

Re: On the Navier–Stokes Millennium Prize Problem

#809

Post by abathologist »

8note wrote: post #680
thorum wrote: post #153

Earlier quoted context omitted.

It reminds me of the Cognitive Dark Forest hypotheses recently shared here: > “You are creating your cool streaming platform in your bedroom. Nobody is stopping you, but if you succeed, if you get the signal out, if you are being noticed, the large platform with loads of cash can incorporate your specific innovations simply by throwing compute and capital at the problem. They can generate a variation of your innovati…

but what do i lose if somebody else is making money? im still having fun making something

Our market economies are based on competition, and most people more than the fun of making things to secure food and shelter.

Re: On the Navier–Stokes Millennium Prize Problem

#810

Post by mr_coffee »

swat535 wrote: post #687
biesnecker wrote: post #617

Earlier quoted context omitted.

I came here to say this, like... wow. I'm pretty sure at at least a few of the places I've worked that would be grounds for immediate termination.

They probably should have added the disclaimer: opinions are my own..

I am sure that will assuage the legal dept. /s
Post reply on HN