The Navier–Stokes Millennium Prize Problem • Hacker News Board

Re: The Navier–Stokes Millennium Prize Problem

#101

Post by Blikkentrekker » Wed, Sep 09, 2026, 7:16 AM UTC

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.

That they do it is just concerning to me in that it says that home-ran models just aren't good enough. Surely researchers like this have the processing power to run them at home, they just don't have the processing power to train models of comparable level.

This is something I feared would happen and where open source would be left behind. Maybe they can do something with crowd-sourcing computational power from volunteirs. They were after all able to get Leela Chess Zero to be comparable to AlphaZero by training from volunteer processing power but it seems to me we live in a world now where the best models keep their stuff closed.

In imagine generation too. I'm not sure how well Stable Diffusion can compete in following instructions with all those advanced models that are kept secret.

Re: The Navier–Stokes Millennium Prize Problem

#102

Post by alangibson » Wed, Sep 09, 2026, 7:16 AM UTC

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…

This is not the simplest explanation.

The most direct line from problem to proof is OpenAI building off of conversations the mathematicians had with their AI.

Re: The Navier–Stokes Millennium Prize Problem

#103

Post by karmasimida » Wed, Sep 09, 2026, 7:16 AM UTC

Use Bedrock or any kind of big tech hosted version of the frontier labs can be a solution. I think if secrecy is of utmost importance to you, then do not send data to first parties

Re: The Navier–Stokes Millennium Prize Problem

#104

Post by rzzzt » Wed, Sep 09, 2026, 7:17 AM UTC

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.

They wouldn't appear in weights but could be added to the context. My conversations regularly go "regarding your Java problem"... which was a separate item in the history from earlier. As long as I only see these (and nobody else sees mine), it can be helpful.

Re: The Navier–Stokes Millennium Prize Problem

#105

Post by a_bonobo » Wed, Sep 09, 2026, 7:17 AM UTC

teiferer wrote: post #95

skylurk wrote: post #47

Earlier quoted context omitted.

> 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…

This ties back into AI, too, right?

I always like to bring up how many decades of research, how many hundreds of years of entire PhD-theses, how many sleepless nights were used up to generate all the protein structure data that made up the corpus of Protein Data Bank - that was then hovered up by the AlphaFold team, and guess who got the Nobel Prize...

Re: The Navier–Stokes Millennium Prize Problem

#106

Post by teiferer » Wed, Sep 09, 2026, 7:19 AM UTC

jwr wrote: post #61

I always thought it was enough to switch off the "Improve the model for everyone" setting on chatgpt.com: "Allow your content to be used to train our models, which makes ChatGPT better for you and everyone who uses it. We take steps to protect your privacy." But apparently there is also an entire completely different route "Do not train on my data"? Does this mean that before I submitted the "Do not train on my data"…

That's because what people enter into LLMs is the last gold there is out there. Everything else is already scraped or ensloppified.

Maybe next step is to filter your input client side through an unknown number of obfuscators where you ask LLMs to rephrase your question (onion router idea) such that no single provider can be certain that this is human input and not some slop feedback loop.

Re: The Navier–Stokes Millennium Prize Problem

#107

Post by FeepingCreature » Wed, Sep 09, 2026, 7:20 AM UTC

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.

LLMs can learn from one sample.

Re: The Navier–Stokes Millennium Prize Problem

#108

Post by 20k » Wed, Sep 09, 2026, 7:21 AM UTC

karmasimida wrote: post #100

npiano wrote: post #78

Earlier quoted context omitted.

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

OpenAI have admitted their new model they used was trained on prompts at around the time that researcher was working on it, so it seems self evident that it was used as part of the millennium solution

Re: The Navier–Stokes Millennium Prize Problem

#109

Post by pansa2 » Wed, Sep 09, 2026, 7:23 AM UTC

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.

> one should not use LLM services for confidential or proprietary information

That’s obvious, isn’t it? Just like you wouldn’t upload your confidential documents to an online spellchecker, or your proprietary code to an online compiler?

Re: The Navier–Stokes Millennium Prize Problem

#110

Post by teiferer » Wed, Sep 09, 2026, 7:23 AM UTC

Simran-B wrote: post #68

I don't get the sales pitch, spend 15 million dollars to win a 1 million dollar price? Showing of the model's capabilities - okay, but it's not like it solved the problem on its own, and apparently not particularly efficient. Are there practical applications that justify the investment?

How is that any different from any other academic research? Every PhD candidate solves problems essentially nobody cares about. They don't even get $1M, they get nothing.

There are two benefits though.

One is recognition. Cred. The PhD candidate gets to put a ", Ph.D." behind their name, opening doors to future academic employment or other endeavors where people value titles. The AI lab gets to say their tech solved sth that humanity wanted bad for a long time. Both cases with substantial financial upside (higher income for Mr. PhD and higher company valuation for the AI lab).

The other one is that this is how scientific progress works. $1M or not. That number was just a PR campaign by the math community to point to some goals. It's clear that it would cost more than $1M to get there.