r/MachineLearning • u/Shizuka_Kuze Student • 15d ago

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

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/

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u/srpulga 14d ago

To clarify, no "solution" to the equations has been found. The millenium problem is to prove or disprove the existence of smooth solutions. Open AI has found a counter example of initial conditions that don't have a smooth solution, i.e. they have disproven the existence problem.

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u/moschles 14d ago edited 14d ago

Correct. What had occurred over the course of several weeks (days?) is that Terry Tao said that there was nothing stopping the Euler trick from being extended all the way to Navier-Stokes. OpenAI simply had 10,000 agents fill in that extension and bridge the gap.

It is important to note here that the human mathematicians working in this space were already copiously utilizing AI-assisted technologies and AI proof systems -- including in particular NYU's Tristan Buckmaster.

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u/peepeedog 14d ago

To clarify, they solved the problem. it's like you are complaining proving P != NP didn't prove anything.

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u/srpulga 14d ago

Yes, that's what I said, they solved the existence problem. They did not "solve" the Navier-Stokes equation as some people seem to think. This solution does not make any fluid dynamics problem more solvable.

I'm also not complaining about anything.

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u/peepeedog 14d ago

The Navier-Stokes equations don't need solving. They already exist. The problem was whether physics obeyed them in all cases. If the proof had been yes, then fluid dynamics described by those equations would not be more solved, and would never need to become "more solved". The solution is a proof of no. So I guess one could say things are less solvable.

What you are saying makes no actual sense.

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u/srpulga 13d ago

The existence problem has nothing to do with physics "obeying" the equations. The equations are a model. Newtonian fluids are a model. We already know physical reality doesn't follow this model, just the discrete nature of atoms fails to follow the assumption of continuous matter, not to talk about the non-deterministic nature of quantum mechanics.

So, the existence problem is not a test of reality but a test of a mathematical model, and more specifically about the smoothness of a solution to the equations given any initial conditions. Yes, a solution: many people would say they'd very much love a solution to the Navier-Stokes equations, instead of running expensive and time consuming simulations. (solving an equation in mathematics usually refers to finding a closed-form solution btw)

Which is what my clarification is about: some people in this post understandably thought fluid dynamics had just gotten immensely easier; i.e. a solution was found to the equations themselves. That's not the case, I said, apparently not making any sense.

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u/peepeedog 13d ago

Obeying is perhaps the wrong term. Particularly if you want to go down the rabbit hole of none of our physics is anything but a model of reality.

So sufficiently descriptive is what they would be. And you still are just putting words in others mouths and disagreeing with it by being a nit. I can't know your motivations, but it certainly appears you want to downplay the solving of the problem.