Link: https://www.wired.com/story/openai-navier-stokes-math-discovery-academics/

The Millennium Problems are a set of the most important open problems in mathematics. so far only 2 have been solved: the Poincare Conjecture by Grigori Perelman in 2010 and today OpenAI released this https://openai.com/index/navier-stokes-solution/

The only problem is, that their AI didn't even come up with the solution itself. Mathematicians working on the same problem recently made big strides in solving the Navier Stokes equations, and their chat logs were scraped and used in training data before they could release the proof themselves.

Here is the unpaywalled statements of the Mathematician: https://mastodon.social/@tristanbuckmaster/117233413705701198

Western AI companies have been tackling a bunch of open problems and techbro chuds cannot shut up about it, this is just Marketing and the fact they have to steal real people's work to do so just proves it.
They really want that IPO moneyyy

Everything AI does is with stolen data. What makes this so special?

It’s like if they wrote gta VI in notepad and Microsoft released it saying they made it… so not really different except they didn’t even let the author publish it first

Woah. Navier Stokes has been solved? That's a huge deal. And fuck openai for undercutting the people who made it possible.

Well "solved" is a bit of a weird way to say it. Was it proven as true, or was it disproven? Both of those change things in different ways.

Proven true that it is a stable formula, then that's cool, and we know that issues with fluid simulations based off of that are a software and compute problem.

If it was disproven, then we learn precisely under what specific conditions nature becomes mathematically unpredictable, and then we can start developing different and better models.

My understanding is that it has only been shown to have closed form analytical solution for very simple cases. "Solved" in this case would mean doing the same for more complex geometries. It would mean finding new functions like spherical harmonics or the Bessel Function.

Pay wall

So sad that it has been solved this way. It feels stolen (even if it had not copied work)

Same here. Here's a archive.org link: https://web.archive.org/web/20260910020853/https://www.wired.com/story/openai-navier-stokes-math-discovery-academics/

This feels like when you’re telling a story or a joke and someone swoops in from the sidelines to steal the punchline. Only like 100x worse.

Wait I thought someone in anthropic made some progress on this using Claude which was then leaked to openAI and then they mustered all their resources to do it faster and did it before.

https://x.com/konstiwohlwend/status/2097235335034056835

From what I've read, the Millennium prize proposition was basically "Prove it holds in all cases (sounds to me like a closed form solution), or prove it doesn't hold in all cases", and the proof published by OpenAI proves the latter, i.e. that Navier-Stokes does not hold in some extreme cases.

Steal their work? well, but mathematician worked a lot of years on the problem without a solution, means that their work wasn't correct. Apart scientific papers are accessible by everyone, not only AIs.
Maybe the mathematicians have to think a little more about teamwork, storing their work locally or encrypted, instead claims about copyright and AI stealing their work. But the capabillity of AIs is to be able to find interrelations between millons of datas in hours, something for what humans need decades to do the same. That is the point and also the danger of AI, it get the data it needs from everywhere and web content is open, AI don't have any ethics or respect of copyrights, all web content is information as is.
All you put online is public (or everything online) by definition, there isn't any copyright to avoid it.

This is interesting news but why is it in the privacy comm?

Why is the fact that an AI company is surveilling their users and stealing their work in a privacy comm?

surveilling users? chats are fed into the training data, I believe this is stated pretty clearly on every chat, something like "your chats are used to improve the model'

That's right, surveilling.

Only in certain plans and you can opt out. I assume they were smart enough to opt out but on review I couldn't actually find evidence of that so you may be right...

turns out if you throw hundreds of billions of dollars at math problems, you tend to find solutions, who knew?

the worst part, to me, is the implication that such solutions are a question of capability and not of resources

🎶plagerize
Let no one's else's work evade your eyes
So don't shade your eyes
But
Plagerize
Plagerize
Plagerize
🎶
But of course don't forget to call it... Research

these news site really need to research or write better.

No, Navier Stokes was not "solved". We have been using numerical methods to solve these equations approximtely since forever. The exact analytical solutions that exist for special cases are also studied; most often, these are used as baseline for comparison against new theory , new experimental results and new computer simulations. So, we have been "solving" Navier Stokes.

What OpenAI manages to achieve is answering a very specific problem relate to Navier Stoke (sorry for hand waving, not a pure math major). It is something like: given an initial flow condition, does the Navier Stoke equation predict this flow field to blow up or it stays smooth for some finite time? Result: OpenAI manages to come up with a case where the solution blow up.

Mathematically, i bet some math geniuses can expand on this finding as like a "special property" of the Navier Stoke equations.

So no we are still far solving the whole equation analytically.

Somewhere down the article:

While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models⁠.

this is the whole selling-point of locallama and why local models are so rigorously sought after (despite seeming excessive(seemingly needless) spending on rigs )

it would be a better fit for intellectualproperty community . or maybe security. i guess it sorta could be privacy. just not the way most people tend to focus on. intellectualproperty is the bigger issue. but it occured due to lack of privacy .

I'm aware that the data is used to train models. Most people know this, it's stated clearly. That's not the story here. The story is IP theft, not privacy.

This is still a big deal result with a lot of physical significance if it holds up.

Full Navier-Stokes are / were understood to model all of the important physics associated with continuous domain fluids. (Continuous domain here means we approximate the many, many particles of the fluid as a smooth, continuous substance).

In particular, Navier-Stokes are supposed to fully model fluids with turbulence. Turbulence is an everyday phenomenon that you can reproduce for yourself in your kitchen sink, and yet it is extremely difficult to formulate a mathematical function for it. Turbulence appears to be random if you look at it, and yet if it is produced by NS, then it is not random. Solving even the numeric approximations of NS for turbulent flows is difficult because the flows exhibit severe variation in velocity over wide ranges of time and distance scales.

Anyhow, if NS is a good physical theory it has to have a physically realistic solution to every physically-possible set of initial conditions and environmental forcing functions. In math terms this mainly means that all of the velocities, pressures, and forces have to be finite and smooth at all times. Step discontinuities don't really occur in the real physical world (although they do approximately occur).

This result would mean that NS is not the end all final theory for classical continuum fluids. The scenario constructed by OpenAI is claimed to be one that can (at least theoretically) be setup and run in the real world. But if we did that, the real world is certain to do something else besides the infinite flow velocity vortex that OpenAI claims NS predicts. What would really happen in that experiment? Who knows. We're gonna need to find some new physics to find out.

That's the whole debate... If researchers used ChatGPT then they agreed to its terms and conditions, which are shitty and forfeiting privacy, IP and all that comes with it. All the major AI companies are not in the business for the sake or betterment of humanity, but to exacerbate the capitalist model in which you own nothing (funny how that's how communism is sometimes described). I mean the whole drama with Altman and OpenAI, that basically killed the initial nonprofit, humanist goals of Open AI was very revealing. I read a quote the other day that said AI is a means for wealth to access skills and knowledge, while preventing those with skills and knowledge to access wealth.. Couldn't say it any better.

I think this is the real problem here. Chats are being fed to AI. This is horendous. Do we know which chat system was raked by OpenAI.

This is why use of AI needs to be a conscious use. We need to understand that everytime we use it, we are teaching it to improve itself, and if we are feeding it sensitive data, then we are being really stupid.

The original team had used AI to solve the problem. However, they did not want to publish AI slop (think one of the authors actually described their initial proof as such, which is hilarious in hindsight). Then, the not so open to anything but stealing, openai stole their almost finished work and used tons of compute to finish it.

Your reply is incoherent and out of touch with the reality of what happened.

Key and Peele

You mean that the solution didn't converge? Like, what does "blow up" mean?

I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer."

I mean, you kept something secret in Codex. A product purpose built to gather training data. What did you think would happen?