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The Navier–Stokes Millennium Prize Problem

simonwillison.net

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Re: The Navier–Stokes Millennium Prize Problem

#91

Post by l5870uoo9y »

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…

Given that the solution took a somewhat “unusual” approach, I find it even more unlikely that an AI model would have come up with this on its own.

Re: The Navier–Stokes Millennium Prize Problem

#92

Post by josalhor »

405error wrote: post #77
josalhor wrote: post #23

I think this drama was blown up a bit out of proportion. The entire discourse I am seeing online seems to revolve around this: > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models I mean... yeah? What do you expect? What else can they say? How could you prove a negative in this case? I do not want to comment on specific OAI employee chat messa…

I can give you some context. 1. Terence Tao's mastodon explains the way this problem was solved does not in itself contribute much. LLMs (and in this case) produce massive, often unintelligible proofs that do not further understanding. It is often that in pursuit of solving these problems, many other discoveries are made. 2. There is a more serious question about scooping. If OAI is using chat data from researchers t…

1. I know, but that is somewhat irrelevant to my question 2. I am indeed a CS PhD student (well, I am finishing now)

> If OAI is using chat data from researchers to make discoveries, essentially every researcher who chats with an LLM can get scooped

But they make very clear that they do train on this if you do not disable the setting. We can comment on the fact that this is opt out instead of opt in, but this discourse of OAI sniping the solution out of some researchers hands seems to be running on the best case speculation of the researchers having perfectly handled all their chats and discussions with other researchers and the worse case of OAI not having full pipeline control and I think that is an unfair assumption.

Re: The Navier–Stokes Millennium Prize Problem

#93

Post by Fordec »

josalhor wrote: post #81
Fordec wrote: post #57

Earlier quoted context omitted.

A very simple "these two pipelines don't connect up in our architecture, here's our internal high level network diagram combined with our data ingestion opt-out feature flag that we will stand by in court" as opposed to "yeah, we don't even entirely know how our own customer facing systems are connected to our training pipeline, but it probably didn't happen".

Have the other researchers opted out? On all their accounts? Through the entire time? And did they discuss this with anyone else? And did those people ask ChatGPT stuff? And did they disable it? If I was OpenAI, I would be very careful about my wording here when making claims of "we have never trained on any of their ideas directly or indirectly".

All very good questions that could end up in a court of law with a Millenium Prize on the line. In a competent world, these are very answerable from logs and considering the news cycle this is creating, should be able to be pulled up and made into a public postmortem in short order. You know, if it's all been above board that is. And if the researchers don't wish for that information to be public knowledge, it can be shared with the researchers promptly for a retraction of their statements lest some libel gets litigated.

Re: The Navier–Stokes Millennium Prize Problem

#94

Post by AlphaSite »

junofan wrote: post #22
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.

Their privacy policy for normie subscribers says in plain English they use your Personal Data for research. I think it’s pretty unreasonable to use the service and expect otherwise.

There’s an opt out so I’m blade for now.

Re: The Navier–Stokes Millennium Prize Problem

#95

Post by teiferer »

skylurk wrote: post #47
bob1029 wrote: post #24

> ... we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors ... I've observed this exact effect last week. I made a discovery regarding a stepwise performance improvement in a codebase. I shared the benchmark results with a peer and within 12 hours they replicated the same. We had both been looking for this for years. I think giving someone hope that an answer exists might as…

> I think giving someone hope that an answer exists might as well be the same thing as giving them the answer these days. If you read the history of major scientific discoveries, this has been the case for a long time. There are many things that were independently discovered by different people at nearly the same time. Once people know something is solved or solvable, it gets a relentless amount of focus.

Maybe that shows how scientific discoveries come to be. It's not a genius sitting alone in their chamber for a decade and then suddenly they emerge with this huge thing. That's Hollywood fiction. Scientific progress is the colaborative effort of countless researchers over long periods of time, communicating, exchanging ideas, many of them wrong, tweaking, trying, thinking, arguing. When a breakthrough happens then it's the tip of a mountain of work that came before it. If two individuals stand on that mountain and feel there is something somewhere then it's not too strange that they take the last step at roughly the same time because conditions were right. The preconditions were in place at that time, the results required for this were available and the focus was on this specific thing.

I'd say it illustrates well that this last piece, the person celebrated for the achievement, is disproportionally overvalued and the rest of the work they are standing on is disproportionally ignored.

Re: The Navier–Stokes Millennium Prize Problem

#96

Post by grey-area »

feverzsj wrote: post #49
tosh wrote: post #2

> My two favourite hypothetical questions regarding this used to be: > If I'm running Codex and one of my API keys accidentally gets consumed in the context, what are the chances that someone else might ask for an API key in the future and get mine back? (I asked someone at OpenAI once and they called this the "regurgitation" problem and assured me that they take great pains to prevent that... but wouldn't describe h…

LLM can't be trained that easily. More like actual human are checking your logs and stealing valuable things from you.

Or searching anonymised logs for mentions of this problem and using that as part of the context or training.

This would work just as well and have plausible deniability.

Re: The Navier–Stokes Millennium Prize Problem

#97

Post by awestroke »

_bobm wrote: post #89

Hah, what is the infrastructure which takes user sessions (chats with API keys, directions, navier-stokes math/progress) and regurgitates this into pre-training, RL, fine-tuning data? Or better, in-context data? People talk about the "compute" but what about the "storage"? Is storage exponentially greater, or soon to be, than the compute? Is the storage going to slow down growing to some constant rate, i.e. all peopl…

AI companies use heuristics to filter sessions, then llms to further filter, then use various techniques too anonymize the session, then process it and add it to various datasets for further selection and refinement. they don't need huge storage for this.

Re: The Navier–Stokes Millennium Prize Problem

#98

Post by thesz »

imjonse wrote: post #36
nicce wrote: post #20

Can’t wait to see the human verifying the results and then figure out that the AI model actually cheated and the results are not correct.

the proofs were verified in Lean, so unlikely.

But still possible [1].

[1] https://leodemoura.github.io/blog/2026-8-1-postmortem-for-ke...

Re: The Navier–Stokes Millennium Prize Problem

#99

Post by johanvts »

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?

Re: The Navier–Stokes Millennium Prize Problem

#100

Post by karmasimida »

npiano wrote: post #78
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…

Why is that simple or plausible? Why is simpler or more plausible than lifting an almost-finished solution from a researcher's account?

Because it is not finished. Their follow up claim is that OpenAI’s approach looks like another proof they had been working on the side, but hasn’t published yet
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