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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#311

Post by onidj »

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…

>- Do "normies" even know what's happening?

Absolutely not. Even to a lot of techy/nerdy people it's still just a chatbot that they sometimes use to help them at work. Even on here people will do whatever they can to downplay.

The lack of fucks given is staggering.

Re: On the Navier–Stokes Millennium Prize Problem

#312

Post by olalonde »

colinhb wrote: post #122
dorjoycb wrote: post #13

It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774

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.

Re: On the Navier–Stokes Millennium Prize Problem

#314

Post by bibimsz »

armchairhacker wrote: post #216
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…

Let's wait until AI solves a longstanding practical problem before "dawn of the singularity" (which could be tomorrow, but still).

feels like moving the goalpost. is the achievement impressive or isn't it?

Re: On the Navier–Stokes Millennium Prize Problem

#316

Post by recitedropper »

AlexErrant wrote: post #242
recitedropper wrote: post #10

Sad turn of events for our world. After watching the behavior of the most senior OpenAI researchers on twitter, I feel even less confident in them as a team to be shepherding this much capital and compute. The dark forest awaits..

1. What does the dark forest have to do with this? Because "the most senior OpenAI researchers" are shitposting on social media, we've an answer to the Fermi paradox??? 2. The dark forest is fun for scifi stories, but is mathematically bunk anyway https://www.noahpinion.blog/p/the-dark-forest-hypothesis-is-... https://www.reddit.com/r/IsaacArthur/comments/1l06cnk/cool_w... https://www.projectnash.com/aliens-the-fermi…

I elaborated on my use of "dark forest" in another reply. We're headed for a dark forest--not amongst interstellar civilizations, but in intellectual work.

I agree that we have not solved the Fermi paradox; I disagree that comments highlighting immature behavior from people who wield enormous power in our world are unproductive.

Re: On the Navier–Stokes Millennium Prize Problem

#317

Post by lukewarm707 »

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…

"There's no reason to believe that anything they did in ChatGPT led to our solution"

do you think that the model's proof was unrelated to being fed a solution that was close to completion?

any comment on openai allegedly trying to drop attribution for alpöge and then threatening buckmaster?

Re: On the Navier–Stokes Millennium Prize Problem

#318

Post by CobrastanJorji »

igleria wrote: post #184
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…

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.

As soon as I thought "man, this sounds like some evil sociopath shit," my second thought was "oh, Sam Altman must have been personally involved."

Re: On the Navier–Stokes Millennium Prize Problem

#319

Post by core_dumped »

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.

What about this isn't true?

Re: On the Navier–Stokes Millennium Prize Problem

#320

Post by kypro »

simianwords wrote: post #136
aizk wrote: post #52

People had joked a couple years ago "Well if they solve a Millenium problem it's AGI"... Well here we are.

> I have a couple friends who did the Math tripos at Cambridge (so a pretty high level!) who work in tech and have unanimously said they have 0% expectations of an LLM doing a millennium problem anytime soon https://news.ycombinator.com/item?id=38433655 > Let's talk when we've got LLMs proving the Riemann Hypothesis (or any mathematical hypothesis) without any proofs in the training data. I'm confident in my belief t…

As someone with a background in AI and who has been playing around with neural nets for decades at this point, it's been genuinely amazing watching extremely intelligent people make confident predictions about AI capabilities and progress, then be so completely wrong.

There's a kind of theory of mind for AI (specifically neural nets) which I now realise I seem to have which is very hard to explain to people who haven't felt the magic of these algorithms. In fact, the algorithmic details almost doesn't matter at all. When you have a generalised learning algorithm really the only essential components are – compute, data and time. So long as you can scale these you can be certain you will also scale capabilities. There is never any exception.

That said, the capabilities neural networks tend to progress in step-functions rather than scale in correlation with compute, data and time, because algorithmic improvements tend to come every ~5 years and bring a significant step change in capability (or efficiency depending on what you measure).

I think people like Dario and others working at frontier labs see and understand this very clearly. And I suspect it's also why they worry about AI risk because even if you ignore the significant increases in compute and data these models are being trained with, it's concerning that it only took two real algorithmic improvements to take us from mostly useless predictive language models to AGI-level intelligence – and we're due another step change.

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