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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

#341

Post by mrbungie »

denverllc wrote: post #295
mrbungie wrote: post #178

Earlier quoted context omitted.

Of course AI was involved, you'd expect most mathematicians and researchers to use AI nowadays. This drama is about AI achieving impressive outcomes with little to no human intervention, as that would be signalling AGI.

> This drama is about AI achieving impressive outcomes with little to no human intervention That's not at all what the drama is.

Of course, as any drama, it has been developing into a lot more but the main motivation for OpenAI has been about winning that battle.

Re: On the Navier–Stokes Millennium Prize Problem

#343

Post by efavdb »

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…

>> Keep in mind: natural science is different. It's not always a matter of computation.

Math is like this too. The big problems they've been solving have been identified as interesting only through lots of prior effort.

Re: On the Navier–Stokes Millennium Prize Problem

#344

Post by cherryteastain »

bhouston wrote: post #98

What happens to real fluid in this particular cases? If the singularity is in the physical space? Is this just a result of ignoring things like friction and energy dissipation via heat, etc?

Navier Stokes assumes the fluid is a continuum. The smallest scales that it effectively models [1] are larger than the mean free path of the molecules in the fluid, measured by the Knudsen number [2]. Whenever a phenomenon in the Navier Stokes equations happens in a scale on the order of or smaller than the mean free path, Navier Stokes effectively is unphysical. So, this is a phenomenon in the equation we use to model the fluid, not a physical phenomenon observed in a real fluid.

[1] https://en.wikipedia.org/wiki/Kolmogorov_microscales

[2] https://en.wikipedia.org/wiki/Knudsen_number

Re: On the Navier–Stokes Millennium Prize Problem

#345

Post by vatsachak »

arctic-true wrote: post #35

Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.

Brain has loops and parallel connections.

Loops and parallel connections make transformer go brrr

Re: On the Navier–Stokes Millennium Prize Problem

#346

Post by mrbungie »

scurnus wrote: post #283
mrbungie wrote: post #161

Earlier quoted context omitted.

They are highly capable, no doubt about that, but: 1) We don't really know how they arrived to this result except that they had a lead and that they threw millions of compute at the problem. The article is written in a way that makes you believe that it was just an agent loop with little human intervention, but without any evidence. 2) If the threats are to be believed, it is concerning how far they are willing to go…

1) The article is written in a way that states clearly they threw a lot of compute at the problem. In api cost millions of dollars. 2) Millenium Problems have been the goal every AI company wanted to achieve since their diffusion, all companies have thrown a lot of resource to solve these problems, as they are very famous and scientists spent a lot of time trying to solve them. The first company to solve it will rema…

> 1) The article is written in a way that states clearly they threw a lot of compute at the problem. In api cost millions of dollars.

Did I say otherwise?

> 2) Millenium Problems have been the goal every AI company wanted to achieve since their diffusion, all companies have thrown a lot of resource to solve these problems, as they are very famous and scientists spent a lot of time trying to solve them. The first company to solve it will remain in history, despite all of you finding excuses about it.

I know, but I don't know how that relates to my point, which is about the way they are doing it.

Re: On the Navier–Stokes Millennium Prize Problem

#347

Post by Squarex »

twobitshifter wrote: post #324

>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 is probably billions of increased pre IPO valuation.

Re: On the Navier–Stokes Millennium Prize Problem

#348

Post by mmiyer »

twobitshifter wrote: post #324

>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 is billions added to their valuation. Also of course it costs OpenAI much less than API pricing for inference.

Re: On the Navier–Stokes Millennium Prize Problem

#349

Post by 20k »

olalonde wrote: post #310
colinhb wrote: post #122

Earlier quoted context omitted.

The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys: > I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin…

Playing the devil's advocate here but it's true that OpenAI didn't have to make those offers.

They kind of did though, they were hoping to keep the fact that they may well have plagiarised these researchers unpublished work quiet. They did not want this to turn into a scandal about the fact that they appear to be training on prompts without consent

It makes a certain amount of sense. The internet data is too polluted with AI usage now to be useful, so the only AI free new data source is the prompts people feed into ChatGPT. The only problem is that its clearly plagiarism

Edit:

OpenAI have admitted to training on prompts at the time the breakthrough was made:

https://mastodon.social/@tristanbuckmaster/11723647135247030...

Re: On the Navier–Stokes Millennium Prize Problem

#350

Post by uncomputation »

So what took an autonomous agentic system using a significantly more powerful internal model, totaling multi-millions of dollars of compute in training and inference, was likely to already be solved by a team of a few humans with an orders of magnitude smaller LLM budget, had OpenAI not been foaming at the mouth to jump the shark and claim “AI solves Millenium Problem.”

Also it sounds like the human research effort spanned weeks if not years from Tristan’s statement so it is extremely likely the work and prompts of these human researchers was used in the OpenAI knock-off.

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