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PaperclipPerfector  2d ago (text post)   7021 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.

Imagine a car.

For a long time, it was a purely theoretical car. Spending any amount of time theorizing about its safety features was a charming activity for undersocialized nerds.

Then it moved. Slowly enough that you could walk alongside it. It was a mild curiosity, at best, to most.

Then it started picking up speed. The acceleration was increasing too, and some of us found that concerning. You could plot the bloody thing. I can't stress enough how little of this required a revelation.

I was around when we were trying to design safety features for a vehicle that didn't exist yet. Later, I was politely asking people to take notice when the ride started getting bumpy.

About a year and a half ago, I became somewhat frantic. Did people really not see what was coming? I spent far too much time arguing about it. I should have saved my breath.

Six months ago, with Mythos? The steering wheel came off. And I considered myself done with trying to convince anyone of anything.

I have the misfortune of occasionally reading someone explaining that the car can't be dangerous because of how the engine works. Or that it's a beat up sedan, and we should only worry about F1 cars. And don't you know that the speed of limit is a hard limit on velocity? Or that our current transmission systems break down at 570 km/h?

I'm sure there's a reply to that. I've probably written one before. If writing doesn't work, look out a window before it's all a blur.

Can people see an inch beyond their noses? Apparently not.

These days, I'm doing my best to strap myself in. I have no idea how much good that will do, but I've only got so much time and attention, and I'd like to spend some of it on the assumption that I have a future.

I don't know where the road ends. But some people are about to wish for airbags, and I find that a "told you so" is a small consolation.

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