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The Navier–Stokes Millennium Prize Problem

simonwillison.net

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Re: The Navier–Stokes Millennium Prize Problem

#131

Post by Bluestein »

keremk wrote: post #70

Occam's Razor says: "They heard this problem is solved or about to be solved amongst the rest of the other problems. They prioritized this and put substantial compute with their newest model and solved it." I know everyone loves juicy rumors, theories etc. but honestly that is the simplest and most plausible explanation given the state of AI improvement now. Obviously spending 15 million on a problem is not a slam du…

There's also an elephant here in this room: Quite "coincidental" one of the coauthors worked for the competition. Of course GPT would know this fact. And OAI has every incentive to particularly monitor those accounts.-

Re: The Navier–Stokes Millennium Prize Problem

#132

Post by jojva »

PowerElectronix wrote: post #116
keremk wrote: post #70

Occam's Razor says: "They heard this problem is solved or about to be solved amongst the rest of the other problems. They prioritized this and put substantial compute with their newest model and solved it." I know everyone loves juicy rumors, theories etc. but honestly that is the simplest and most plausible explanation given the state of AI improvement now. Obviously spending 15 million on a problem is not a slam du…

Funny how they did not solve any of the other problems, just the one where there was already solutions to the NS with some restrictions in their chats, and their solution seems to derive from those.

They explain in the article that they eventually redirected all their resources towards NS.

Re: The Navier–Stokes Millennium Prize Problem

#133

Post by lhd1 »

civvv wrote: post #15

LLM’s seem very good at solving mathematical problems of which there is an enormous amount of exisiting work/attempts in their training data. This is an amazing capability, but does not convince me that these models are «thinking» or «reasoning» in the way a human does. A human mathematician could in theory categorize/discover an entirely new field of mathematics tomorrow, based purely on their «human intelligence»,…

This is also what I've been thinking. The result itself is amazing but it's not like this was completely unexpected. There has been a huge amount of progress on the problem in the last 10 years without which it seems unlikely today's full resolution would have been possible. It is not clear what strategy was taken but it sounds like it borrowed heavily from the two spanish mathematicians. Experts will scrutinize the proof and it will be interesting to see if anything truly original or unexpected was done, outside of known techniques, a move 37.

Re: The Navier–Stokes Millennium Prize Problem

#134

Post by iLoveOncall »

The main thing to take away from this whole story is that frontier labs have hired teams of mathematicians with the sole purpose of solving open problems.

If this doesn't show you that the fantastical claims of their LLM's ability to solve problems on their own are bullshit, I don't know what will.

It's pretty clear all of this is a marketing effort only, and they pass human results as LLM findings.

We already know that the supposedly industry-changing Mythos and Fable results were actually complete BS and they're just your run of the mill model. There's nothing at all to suggest this is any different, and once we get this "unreleased model" (aka bob from the math department), we'll see it was all lies again.

Re: The Navier–Stokes Millennium Prize Problem

#135

Post by nicce »

latent-person wrote: post #124
nicce wrote: post #41

Earlier quoted context omitted.

As long as the proofs itself are correct. How long they were this time? Edit: at least ~600,000 lines https://stanfordtechreview.com/articles/openai-buckmaster-na...

To claim something verified in Lean is wrong, you need to either argue that the theorem was stated incorrectly, or that there is a bug in Lean (assuming no `sorry` etc, which is checked by comparator). The number of lines needed to prove it is irrelevant (other than checking for a bug in Lean gets harder).

That is the point. Someone must verify that the Lean matches the actual theorem, precisely as it should be interpreted.

Re: The Navier–Stokes Millennium Prize Problem

#136

Post by andersmurphy »

georgemcbay wrote: post #54
andersmurphy wrote: post #27

Earlier quoted context omitted.

You'd think theft would still be illegal regardless of what a privacy policy says.

> You'd think theft would still be illegal regardless of what a privacy policy says. I wish that were true, but I live in the United States and it is 2026. The President of the United States rug-pulls memecoin crypto and regularly pardons people like Paul Walczak (who was convicted of massive payroll fraud) in exchange for large donations. I wouldn't make any assumptions about what is considered theft anymore, at lea…

I mean the fact that comments like this get downvoted is wild.

Re: The Navier–Stokes Millennium Prize Problem

#137

Post by Cider9986 »

johanvts wrote: post #99
sdcfgy wrote: post #14

My take home from this entire drama is that one should not use LLM services for confidential or proprietary information as they all seem to be run by assholes. And you’re sending them everything you are doing. Would you send your lab notebook to an asshole? Hell no. I say that as a mathematician (on paper) who perhaps surprisingly doesn’t give a crap about the problem itself.

Or use Lumo from Proton. Are there any other privacy first companies offering LLMs?

Lumo seems the most reputable. There's confer.to, duck.ai, and nanogpt.

Re: The Navier–Stokes Millennium Prize Problem

#138

Post by hn993302 »

sdcfgy wrote: post #14

My take home from this entire drama is that one should not use LLM services for confidential or proprietary information as they all seem to be run by assholes. And you’re sending them everything you are doing. Would you send your lab notebook to an asshole? Hell no. I say that as a mathematician (on paper) who perhaps surprisingly doesn’t give a crap about the problem itself.

Or if you're going to trust one of them, maybe it shouldn't be OpenAI

Re: The Navier–Stokes Millennium Prize Problem

#139

Post by piker »

pietz wrote: post #128

I find the claims from OpenAI somehow more relatable and reasonable. - They threw compute on a problem another team/company was rumored to have solved to see what their secret model could do. - The texts I read do make it seem like OpenAI wanted to talk and share credit generously. - Imagine working on a frontier math problem with someone at Anthropic and not only do you use Codex but also through a non-business acco…

It’s fishy though that they heard one of seven problems was about to be solved and threw perhaps 15 million bucks at the right one.

[Edit: they said "two of": "On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. .. we launched an effort ... on all open Millennium Prize problems".]

Re: The Navier–Stokes Millennium Prize Problem

#140

Post by Rebuff5007 »

keremk wrote: post #70

Occam's Razor says: "They heard this problem is solved or about to be solved amongst the rest of the other problems. They prioritized this and put substantial compute with their newest model and solved it." I know everyone loves juicy rumors, theories etc. but honestly that is the simplest and most plausible explanation given the state of AI improvement now. Obviously spending 15 million on a problem is not a slam du…

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