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PaperclipPerfector  2d ago (text post)   7907 thread views

Culture War Roundup for the week of September 7, 2026

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Navier-Stokes Millenium Problem Solved by GPT

OpenAI says they solved the Navier-Stokes Millenium Prize problem with an internal model that is more powerful than GPT6, so a GPT 7 candidate or something close. OpenAI has been on fire lately really casting a shadow on Anthropic. First the hugging face incident, now the first to crack the Millenium prize problems.

As for the solution to the problem, they are claiming that smoothness is disproved and that the equations do break down.

A fundamental open question for these dynamical equations has been whether the continuum approximation of the fluid can break down. Specifically, can the Navier–Stokes equations for a three-dimensional incompressible fluid with constant density develop a “singularity,” even when the motion starts smoothly? Here, a singularity means the dynamics lead to speeds in the fluid growing without bound within a finite amount of time. The development of a singularity would have to happen despite the presence of viscosity, which tends to smooth out motion. Because a real fluid cannot move infinitely fast, this would mark a breakdown in how the equations model the fluid. To continue modeling the system, one would then need to track the behaviour of each particle individually.

They say that the equation can develop a singularity, which apparently means it is not a perfect model.

This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time.

This is very exciting to me as I believe it to be the first scientific result of an AI model. Previous results have been basically irrelevant to the sciences. However, this result is of course still completely symbolic in nature, which is not surprising because LLMs are not embodied enough to collect data and analyze it autonomously.

While they are generating amazing PR recently, I will say GPT-6 is somewhat disappointing for coding. It is not the same leap that 5.5 to 5.6 sol was. It would appear that the models are getting better at running very long context chains while efficiency improvements and refinements in lower level tasks are lacking. Still, it's great work from OpenAI and it's plausible to me that if there's no singularity in general by 2030, there will be for mathematicians. They will no longer be meaningful for producing math, rather they will only be humans who understand it.

You know what, I'm past caring. At least caring enough to make a fuss about things, or spend my limited time under the untamed sun trying to convince people to see the writing on the wall.

Yeah, we just found a solution to Navier-Stokes. I know just enough to say that that's a Big Deal. It's one of many Big Deals lately, each bigger than the last.

Anyone is welcome to plot the trendlines. I'm going to continue having fun and doing things IRL while that adds anything over what the bots can do. Good luck everyone, make sure to enjoy yourself.

As one of those people who, in your view, refuses to see the writing on the wall, I'm not sure why you would even be worried about my coming over to your side. Even if you could convince me and all the other AI skeptics out there, what, exactly, am I supposed to do with this information?

I am known to have altruistic tendencies. If that isn't enough, I dislike it when people are wrong about things, and find it satisfying to at least try and correct them. Also, there was some scope for coordinating a solution instead of having it imposed on us. Maybe it's not too late.

What are you going to do with this information? Entirely up to you. What would you do with the knowledge we're going to be raptured, or that an asteroid has a 30% chance of hitting the Earth in a few years?

What would you do with the knowledge we're going to be raptured, or that an asteroid has a 30% chance of hitting the Earth in a few years?

Go to the pub and wait for it all to blow over?

That's what you would do if the asteroid was going to hit in a few hours, not a few years. We need some way to live while we wait, and with uncertainty about whether the asteroid is really going to hit at all.

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