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PaperclipPerfector  2d ago (text post)   7020 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.

Although this is clearly groundbreaking and historic and I’m not downplaying it in any way, at a glance this seems to be in line with the other major AI mathematics results we’ve seen lately, which mostly fall into the categories of either “noticing links between existing papers in the literature that no one had noticed before”, or “pulling a specific counterexample/construction out of the impossibly vast search space”. I don’t at all have the technical knowledge to evaluate how unexpected this result was, how close it is to existing methods/approaches, etc, but that’s what it looks like to my untrained eyes. I think we’re still waiting for that qualitative breakthrough where AI generates valuable new ideas ex nihilo that really change the way people think about a given domain; I think we’re still waiting for that qualitative breakthrough in math and in every other field. There’s a distinction between say, solving an individual problem and leaving it there, vs inventing something like Galois theory that spawns many new fundamental research directions. If a subject matter expert DOES think this paper will change the lay of the land in fluid dynamics (beyond just the significance of the result itself), please chime in.

It’s mostly a moot point though since all these questions are actually pretty easy to test empirically. If OpenAI and Anthropic are still employing humans, then there’s clearly still work to be done.

That does sound like downplaying it, your preamble notwithstanding.

But, sure, we don't have an AI Grothendieck yet. It's been a full three hours since OpenAI announced a solution to Navier Stokes; but, what's it done for us lately, I think we've hit a wall, etc.

Give it a year, or six months, or three, who knows, and we'll be in a different place.

He has a point. Most of the stuff I've heard of (I am not a mathematician) is proof by counterexample which doesn't per se expand the space of what we can do. I suspect the AI+researcher combo is still significantly more important than just AI for the stuff that actually transfers beyond mathematics.

Centaurs are unstable. Before long, AI+human combos are left behind by even stronger AIs, so strong that adding a human to the loop just makes it worse; the human slows the AI down, becoming a liability. In chess, that took ten years. How long will math take? Perhaps another year or two.

I know that this is what people say, but it's predicated on a scenario where the Venn diagram of AI capabilities (at a useable price even) becomes a strict superset of human capabilities. At the moment this hasn't happened even in software where AI cannot maintain a codebase long-term; studies showing that AI outcompetes centaurs are usually on short-term discrimination tasks like medical diagnoses.

I think it's quite likely that this scenario comes to pass, but it hasn't yet, so we'll see.

In some fields it's been this way for decades (hello air defense!); in others I suspect it will be a very long time before centaurs are replaced.

My sense is that even very smart LLMs are very gullible. I think it will be some time before centaurs aren't invaluable in conducting opposed work, which is the most important work of all. Pivoting models away from general purpose work towards specialized tasks may help here, even if that doesn't seem to be something the primes want to admit.

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