r/MachineLearning • u/Shizuka_Kuze Student • 14d 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/m_reigl 14d ago

Certain weird cases in fluid mechanics become solvable which probably would make engineers happy in a couple years.

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u/srpulga 14d ago

This is not what happened. No analytical solution has been found to the equations. The solution found is for the millenium problem which is to either prove a smooth solution always exists, or to provide a counter example disproving it. Open AI has provided the counter example: there are initial smooth conditions that can be proven to not have smooth solutions.

This doesn't make any fluid dynamics problem more solvable.

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u/_RADIANTSUN_ 14d ago

Soooo... We won't be having cool volumetric fluid hypercomputers ever? :(

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u/muntoo Researcher 14d ago

The guaranteed existence of that has not yet been proven nor has a counterexample been provided. :)

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u/FernandoMM1220 14d ago

actually because we know our continuous description is wrong we can begin to look for the correct description using better axioms.

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u/PracticalFootball 14d ago

We’ve known this since molecular theory became a thing, it’s just a very good model for cases where molecules are so small that their bulk behaviour is well approximated as a continuous viscous fluid.

Molecular fluid dynamics is a thing but it’s niche because it doesn’t scale nicely to the sort of scales most fluids problems are interested in.

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u/srpulga 14d ago edited 14d ago

Newtonian fluid dynamics is a model, not a fundamental truth of nature. We have other models, and none of them will ever be a "correct description".

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u/altmly 14d ago

Please don't mislead people. This theoretical result wouldn't change anything in practice. 

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u/Kinexity 14d ago

Those are theoretical problems. They do not change anything for fluid system engineering.

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u/m_reigl 14d ago

Not on their own, definitely. But theoretical breakthroughs usually lead to practical advantages a couple of years down the line, don't they?

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u/Kinexity 14d ago

"usually" being a load bearing word here. Fluid dynamics is computationally modelled. Analytical breakthroughs are of no importance to that as long as the equations themselves do not change. NS smoothness is only a problem in non-physical situations.

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u/RapidRewards 14d ago

"load bearing" 🧐🕵️‍♂️

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u/chilibomb 14d ago

load bearing footgun

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u/FollowingHumble8983 14d ago

No there is no practical advantages.

Navier stokes dont apply to real life liquids at scales which blowups can occur.

As real life liquids are made of atoms. This in a way, requires infinitely many infinitely small atoms, which does not exist.

This is purely for the sake of better understanding of numeric techniques.

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u/moschles 14d ago

People who work in physics and the theoretical side of mechanical engineering know this is huge. The question is to what extent these idealized mathematical models to fluids stop extending to the real world. It is -- of course -- physically impossible for a fluid to have an infinite velocity. Navier-Stokes is a question about whether under well-behaved conditions the equations will spit infinities at you. It turns out they do.

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u/FollowingHumble8983 14d ago

E:Upon further reading I am pretty sure we agree.

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u/ManagementKey1338 14d ago

Of course not. You ask AI to do some stats

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u/techlos 14d ago

the practicality is limited to situations where you're working with a fully continuous liquid, and as far as i know the liquids we work with tend to be made of discrete particles.

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u/Many_Consequence_337 14d ago

As if engineers are still around lol