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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

#331

Post by franktankbank »

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…

What about ripping off the prompts?

Re: On the Navier–Stokes Millennium Prize Problem

#332

Post by o4c »

Resources:

YT playlist on Millennium Prize Problems By Harvard math department in March 2026

https://www.youtube.com/watch?v=3j1VW9REm7s&list=PL0NRmB0fnL...

On Navier-stokes problem definition:

https://www.youtube.com/watch?v=XoefjJdFq6k

https://www.youtube.com/watch?v=ERBVFcutl3M

https://www.youtube.com/watch?v=Ra7aQlenTb8

Re: On the Navier–Stokes Millennium Prize Problem

#333

Post by tantalor »

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…

National Public Radio?

Re: On the Navier–Stokes Millennium Prize Problem

#335

Post by harhargange »

rfgplk wrote: post #121
harhargange wrote: post #115

Just so everyone knows, although openAI pretends that the model generated solution and wrote the paper by itself ""with very little human input"" as Buckmaster himself mentioned in his statement. In reality they have team of researchers guiding the system, along with, probably training on user data, probably Buckmaster in this case, in order to come up with the proof.

This isn't really true.

Check this https://cims.nyu.edu/~tristanb/statement.pdf

Re: On the Navier–Stokes Millennium Prize Problem

#336

Post by tantalor »

echelon wrote: post #53
tiborsaas wrote: post #16

> We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. WOW?

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…

> Are we at the dawn of the singularity now

Singularity doesn't "dawn". That's the whole idea. It happens all at once.

Re: On the Navier–Stokes Millennium Prize Problem

#337

Post by [deleted] »

igleria wrote: post #227
Maxious wrote: post #205

Earlier quoted context omitted.

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

Interesting that they quote the mathematician directly: “there is nothing you can do, I simply do not trust you” but then they proceed to NOT quote themselves themselves verbatim: "I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey."

[deleted]

Re: On the Navier–Stokes Millennium Prize Problem

#338

Post by reverius42 »

fooker wrote: post #113
reverius42 wrote: post #30

Earlier quoted context omitted.

Prompt: cure all cancers and make sure to pretty please not to kill all humans, make no mistakes (This is the alignment problem of course)

So... what do you feel about eliminating (humans with) cancer?

I'm a human so I don't like that proposed solution

Re: On the Navier–Stokes Millennium Prize Problem

#339

Post by QuesnayJr »

anthonypasq wrote: post #192
QuesnayJr wrote: post #158

Earlier quoted context omitted.

Of the seven Millenium problems, Navier-Stokes was the one most thought to be in reach. I'm not sure what the top 3 problems are. You can make a case for the Riemann Hypothesis and P != NP, but I'm not sure what #3 would be. Maybe the Langlands program? (That one is not as precisely stated as the other two.)

the goalposts are on Pluto at this point.

I'm not moving the goalposts. I haven't heard anyone, ever, refer to the Navier-Stokes problem as a top 3 problem in mathematics. People were saying that they thought the solution was in reach a few years ago, before AI was at all capable of research-level mathematics (and the expectation that there was a counterexample).

I am not particularly skeptical of claims about AI, compared to the average here on HN, but that doesn't mean every random piece of hype is warranted. What they did is impressive, even though we now know the only reason they threw so much compute at the problem is that they heard a rumor that someone else was already close. Navier-Stokes is not a top 3 problem in mathematics, and it was the one that was thought closest to being solved.

Re: On the Navier–Stokes Millennium Prize Problem

#340

Post by blake__dev »

cool_dude85 wrote: post #273
blake__dev wrote: post #238

Earlier quoted context omitted.

Yeah I'm surprised they posted a chart, you would think they would keep specifics like that hidden until they're closer to launch

The chart is as non-specific as could be. It improved in some very vague metric by some amount at different (increasing) levels of training.

That's fair, but at least the chart has an axis. :) Since openai just released astra, I was more surprised that they would publicly show any gap to their (presumably SOTA) internal model.
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