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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#451

For full context, here's the HN thread from the other side of the "Concurrent Work" section: https://news.ycombinator.com/item?id=49605915 Unlike the vanilla read of the OpenAI press release, it is much more unfiltered and outlines some particularly aggressive behavior by specific OpenAI employees

To be fair, the first solved Millennium Prize Problem, the Poincaré conjecture, also had its fair share of drama!

Re: On the Navier–Stokes Millennium Prize Problem

#452
post #208
post #106

Earlier quoted context omitted.

Is it spying? I think this usage is disclosed in their terms of service.

If it happened it's plagiraism. Consent to see data isn't consent to claim priority.

I mean... none of these humans have priority. The result is due to the team of LLM agents.

Re: On the Navier–Stokes Millennium Prize Problem

#453
post #446

Earlier quoted context omitted.

Sure, even a 20% chance at 1 million payday after 5-6 years of fulltime work on a project with zero practical application doesn't touch the, say, 200k/year guaranteed our best mathematicians would have to forgo to devote their intellect to the problem.

Are these mutually exclusive? Why would you have to forego that salary to work on this problem? This is one of the most prestigious and meaningful problems in all of mathematics, which is why it has such a high prize amount attached to it - why would a university not support a mathematician working on such a prestigious and important problem in lieu of something else?

Publish or perish? We're talking devotion here -- so no time to do anything (like edit proofs) other than try to solve the problem.

[Edit: my only point here is that the prize is probably not driving human effort to the limit.]

Re: On the Navier–Stokes Millennium Prize Problem

#454
post #53

> 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…

It's incredible to me that every single time there's a new model people scream "singularity" from the rooftops and every time they are wrong.

This is an impressive result, but there is absolutely zero evidence of "the singularity".

Re: On the Navier–Stokes Millennium Prize Problem

#455

Earlier quoted context omitted.

If I was a company with a zero data retention contract involving OAI I would be asking for a third party audit of such claim of zero retention like, yesterday.

Could they say they don't retain, but do something "transformative" like use their own AI to summarize and paraphrase user sessions?

Yes, and that’s exactly what I believe they are doing

Re: On the Navier–Stokes Millennium Prize Problem

#456
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.

The _gall_ to say something like this. Do you perhaps think we are all stupid?? This very blogpost claims not to know if their work was used as input for this model. I don't even understand how that is possible, surely you can know if something is part of the training data, even if you are in the dark about what impact it actually made, qualitatively. The moon....

> Knowing most of the recipes we use, there's really no reason to think such contamination happened.

Yeah sorry but I don't trust you. I don't trust people or companies that have shown themselves to be dishonest before. Especially when the previous paragraph is comparing plagiarism and training data contamination with, _the phases of the moon_.

Might even be you're actually telling the truth, but the boy that cried wolf and all that.

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As an aside, I would bet very good money at how most (all?) these companies are flouting their ZDR.

Re: On the Navier–Stokes Millennium Prize Problem

#457

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…

It's astounding that the thought to dissociate one of the mathematicians from the proposed publication was driven by their corporate institutional affiliation - and that that exclusion was suggested by a scientist themselves! This is like a researcher from CMU saying to an NYU researcher that their collaborator, being from MIT, is a problem - this is as ridiculous as that! Progress in humanity's knowledge now has to…

The scientist allegedly making that request comes from a machine learning background. Perhaps he's not familiar with the culture in mathematics regarding authorship. That sort of squabbling over author priority would be unconscionable to mathematicians.

Re: On the Navier–Stokes Millennium Prize Problem

#458
post #46
post #15

"While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." I think they should be able to unravel whether or not any sessions by Tristan or Levent went into the training data for this model.

If they could then it wouldn't be de-identified data...

Well you could search for elements similar to the proof / problem in the training data, even if it's de-identified, right? OpenAI can probably do better than Ctrl-f "Navier Stokes".

Re: On the Navier–Stokes Millennium Prize Problem

#459
This is a great day to re-read Ken Thompson's "Reflections on Trusting Trust":

>To what extent should one trust a statement that a program is free of Trojan horses? Perhaps it is more important to trust the people who wrote the software.

https://www.cs.cmu.edu/~rdriley/487/papers/Thompson_1984_Ref...

Re: On the Navier–Stokes Millennium Prize Problem

#460
post #329

Earlier quoted context omitted.

So, physical fields? I’m not catastrophic regarding jobs yet as I have an optimistic view of humanity in general and its ability to meaningfully survive, but the more time I spend thinking about the future of work, the more I’m leaning toward broad general abilities rather than distinct talents. To your point, I no longer need comprehensive knowledge of any particular subject, but what is absolutely valuable is “gene…

We are very likely at the begging of the next industrial revolution.

This one won’t create significant amount of new jobs though.
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