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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#911
post #52

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

Jokes aside, that's a horrible test for AGI. I like to think that I'm sentient, and I could never solve a millenium problem.

The converse is not true.

Re: On the Navier–Stokes Millennium Prize Problem

#912
When considering such foundational challenges to Mathematical Research and plagiarism as discussed here, we should turn to that elder prophet of our age, Tom Lehrer.

Who made me the genius I am today The mathematician that others all quote? Who's the professor that made me that way The greatest that ever got chalk on his coat?

[Chorus] One man deserves the credit One man deserves the blame And Nicolai Ivanovich Lobachevsky is his name Oy, Nicolai Ivanovich Lobach—

[Interlude] I am never forget the day I first meet the great Lobachevsky In one word he told me secret of success in mathematics: Plagiarize

[Verse 1] Plagiarize Let no one else's work evade your eyes Remember why the good Lord made your eyes So don't shade your eyes But plagiarize, plagiarize, plagiarize Only be sure always to call it please, "research"

[Chorus] And ever since I meet this man My life is not the same And Nicolai Ivanovich Lobachevsky is his name Oy, Nicolai Ivanovich Lobach—

[Interlude] I am never forget the day I am given first original paper to write It was on analytic and algebraic topology Of locally Euclidean metrizations Of infinitely differentiable Riemannian manifolds

Боже мой

This I know, from nothing What I'm going to do I think of great Lobachevsky and get idea, haha

[Verse 2] I have a friend in Minsk Who has a friend in Pinsk Whose friend in Omsk Has friend in Tomsk With friend in Akmolinsk His friend in Alexandrovsk Has friend in Petropavlovsk Whose friend somehow is solving now The problem in Dnepropetrovsk And when his work is done Haha, begins the fun From Dnepropetrovsk to Petropavlovsk By way of Iliysk and over Novorossiysk To Alexandrovsk to Akmolinsk To Tomsk to Omsk To Pinsk to Minsk To me the news will run Yes, to me the news will run

[Verse 3] And then I write by morning, night And afternoon, and pretty soon My name in Dnepropetrovsk is cursed When he finds out I published first

[Chorus] And who made me a big success And brought me wealth and fame? Nicolai Ivanovich Lobachevsky is his name Oy, Nicolai Ivanovich Lobachev—

[Interlude] I am never forget the day my first book is published Every chapter I stole from somewhere else Index I copy from old Vladivostok telephone directory This book was sensational! Pravda—well, Pravda—Pravda said: "Жил-был король когда-то, при нём блоха жила”…it stinks But Izvestia! Izvestia said: "Я иду туда, куда сам царь идёт пешком”…it stinks Metro-Goldwyn-Moskva buys the movie rights for six million rubles Changing title to 'The Eternal Triangle' With Ingrid Bergman playing part of hypotenuse

[Chorus] And who deserves the credit? And who deserves the blame? Nicolai Ivanovich Lobachevsky is his name Oy

(Tom Lehrer put all of his work in the public domain prior to his passing. Find versions of his performances on YouTube.)

https://tomlehrersongs.com/disclaimer/

Re: On the Navier–Stokes Millennium Prize Problem

#913

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..

This is the stupidest disclaimer: it's completely unnecessary. Of course the opinions are their own! Whose else would they be? Your mum's?

If someone was speaking on behalf of their employer, they would've used the official channels (such as I dunno an `openai` HN handle, or whatever other channel).

I'm outraged that people think this "opinions are my own" disclaimer is ever necessary.

Re: On the Navier–Stokes Millennium Prize Problem

#914

Earlier quoted context omitted.

there is a proof in lean4 it's correct by construction

How do you know that what is being proved in the lean code is the same as the millennium prize criteria though?

you can get another LLM to verify / if the lean doesn't have `sorry` used to skip certain parts of the proof etc. It's much easier once it's in lean4 because checks like that can be done computationally.

Re: On the Navier–Stokes Millennium Prize Problem

#915

Is this the one that was allegedly based on someone else's actual work & prompts? https://news.ycombinator.com/item?id=49605915 https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd... https://cims.nyu.edu/~tristanb/statement.pdf

Yes, that was the allegation last night. I work at OpenAI, though not on the team that did this, and my understanding is: - we decided to ask our model for Millenium problem solutions because of two reasons: (a) our new model was looking incredibly good and (b) we heard rumors that some Millenium problems had been solved and were curious if our models could solve them (the goal here was not to scoop any particular in…

In fact, the entire outline of the proof is very similar to the external team's proof.

Details may be different, but the use of a very similar tack is very suspicious. Combined with thuggish comments "why would you ruin your career" and "I don't have to be nice" take away pretty much any credibility the OpenAI team's statements might have had.

Re: On the Navier–Stokes Millennium Prize Problem

#916
post #168
post #50

Earlier quoted context omitted.

To my understanding, those mathematicians proved a subset of problems, not the Navier-Stokes problem itself. OpenAI used that subproblem in its proof of NS it seems. The drama comes from where OpenAI got the idea to use that route to tackle NS, since the authors maintain that no one could have plucked it out of thin air like the OpenAI research claim to have done.

This quote from Tao is prescient: “ There does not seem to be anything in principle preventing the methods from extending all the way to Navier-Stokes, and there is even a non-negligible chance that the forcing term could be eliminated entirely, although there are an enormous number of technical difficulties that would ensue in implementing that program. At this point, I would not be surprised if one could batter out…

Navier integration is language in extension:

C to C*

[0]:https://news.ycombinator.com/item?id=49612191

Re: On the Navier–Stokes Millennium Prize Problem

#917

Earlier quoted context omitted.

Recursive self improvement of their upcoming IPO value maybe. They are fluffy PR pieces otherwise.

How can you possible say this sort of thing in context of what looks like a millenium prize being solved. I swear there's nobody blinder than those who won't see.

I. fucking. Wonder. Why.

https://news.ycombinator.com/item?id=49607239

Re: On the Navier–Stokes Millennium Prize Problem

#918

Earlier quoted context omitted.

The implication from their last couple of published articles[1][2] is that they think they’ve achieved “recursive self improvement”. [1] https://openai.com/index/research-acceleration-view-inside-o... [2] https://openai.com/index/an-alien-mind/

Recursive self improvement of their upcoming IPO value maybe. They are fluffy PR pieces otherwise.

This comment was applicable 2 years ago. It isn't any longer.

Re: On the Navier–Stokes Millennium Prize Problem

#919

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.

Agent systems become most credible when they produce artifacts that can be independently checked, not when they merely produce persuasive explanations.

Re: On the Navier–Stokes Millennium Prize Problem

#920

Earlier quoted context omitted.

Recursive self improvement of their upcoming IPO value maybe. They are fluffy PR pieces otherwise.

How can you possible say this sort of thing in context of what looks like a millenium prize being solved. I swear there's nobody blinder than those who won't see.

I don't think we should assume a millenium puzzle has been solved, yet. Astra showed impressive capacity for cheating when it was faced with impossible cybersecurity challenges. It seems equally plausible at this stage that it's found a bug in Lean.
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