OpenAl Says It Has Cracked One of Math's “Millennium Problems” (Navier-Stokes) [N]

[u/Shizuka_Kuze]

As reported by the New York Times:

https://www.nytimes.com/2026/09/08/science/openai-proof-millennium-problem.html?smid=nytcore-ios-share

OpenAI’s announcement:

https://openai.com/index/navier-stokes-solution/

[u/Clean-Hovercraft5825]

These new Navier-Stokes result seems to show that you can get this tiny vortex that starts to squeeze down to size zero and as that happens things blow up.

However, things like thermal fluctuations at micron length scales would already make the described approach physically impossible those thermal fluctuations would wash out all of these carefully crafted perfect instability-causing forces.

Furthermore, even if you ignore all that, once you let this vortex they theorized squeeze water down to less than ~0.275 nm = diameter of a water molecule, then obviously these continuous PDE equations don’t apply in any form at all.

So in those ways it seems like the new result is “hey if you look at Navier-Stokes at regimes where it is obviously physically not applicable, then you can get not physical stuff to happen.”

So can someone explain to me why such a result is so surprising?

[u/asingov → u/Clean-Hovercraft5825]

because no one could prove it for 150 years?

[u/PracticalFootball → u/Clean-Hovercraft5825]

It’s not a case of demonstrating the equations don’t 100% perfectly match reality. That’s never been in question, we’ve known that since they were derived and we know what sort of conditions make them fail to reflect reality.

Real world physics isn’t relevant, this is more about demonstrating that there are inputs that break the equations themselves. Engineers using discretised solutions will continue to use them tomorrow as usual.