cross-posted from: https://hexbear.net/post/9497419
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
Woah. Navier Stokes has been solved? That's a huge deal. And fuck openai for undercutting the people who made it possible.
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.
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.
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.
So sad that it has been solved this way. It feels stolen (even if it had not copied work)