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PaperclipPerfector  2d ago (text post)   7376 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.

I think in terms of psychological impact this kind of thing just isn’t important to most people. We’re going from a world where 99.9[99]% of people don’t contribute intellectually to the advancement of the human race to a world where 100% don’t. That affects the tiny minority who genuinely aspired to be in and believed they could be in the former group (even they were mostly destined for disappointment, AI or not), but not really everyone else.

Well, I suspect they'll care when they start ending up unemployed, or when the world reconfigures itself faster than they can blink. In the meantime, I'm sure ignorance is bliss.

That’s the thing though. As the other response says, ‘knowing’ (not really, but let’s say ‘having an idea of the scale of’) what’s coming doesn’t really help you in any way.

I disagree. Knowing that human endeavor is going to end up redundant in less than a decade has some obvious implications as far as I'm concerned.

I wouldn't quit my job to retrain in something else, the opportunity cost will never be recouped. I have to worry less about saving up for college for my kids - they never need to attend one for credentialing purposes. Any health related concerns that would take decades to kick in become far less pressing.

It should drastically change your priorities and medium and longterm planning. That's happened to me. But I prepare for as many scenarios as I can, and at least in my case, I don't need to do anything particularly out of the ordinary.

That being said, I should max out my ISA. I am not immune to procrastination.

What medium or long term planning is it changing for you? It’s not like a big drought or a tsunami or even a civilizational breakdown (or major war) where you can theoretically prepare if you have the means. I know people who are prepping, some at considerable cost, but they’re prepping for some kind of fantasy The Road type future which now seems unlikely. ASI will be far more powerful and wide reaching, its power will stretch beyond geography and the limits of our own civilization. Even the example you give (say, deciding not to commit to an expensive degree or career move) doesn’t necessarily make sense. If none of it matters, maybe you decide to do that masters in philosophy or take the job in some remote and low paid location anyway, just for fun.

As for human endeavor, I think things will be fine (absent x risk, which it now seems is impossible to control and so with which we are at the mercy of fate) if everything is automated. There will always be interesting things to do - think of the amateur woodworkers making flimsier furniture than IKEA, but having a great time doing so. Most of us will never be (close to) the best at anything, so ‘the best’ going from being a human to an AI doesn’t affect us in the same way that it does Terence Tao.

If we have a worst-case scenario, or just any of the really bad ones, we're fucked. A hidden bunker will just mean you die last.

If things go swimmingly, then the worrying would have been pointless - in hindsight.

That means I think it still makes sense to follow general, option-preserving strategies. That covers the increasingly unlikely "business as usual" worldlines, and shelters against socio-economic/political upheaval as the changes (good, bad or meh) promulgate.

In my context, that means I just continue being a doctor, progressing through training so I keep making more money. Money is the most general of strategies. It can be exchanged for goods and services, including more durable barter goods if shit really hits the fan.

If none of it matters, maybe you decide to do that masters in philosophy or take the job in some remote and low paid location anyway, just for fun.

I like money, you know. And want a family, which is expensive. I can't stress enough how the "correct" course of action depends on someone's priorities, which I am really not in a position to dictate. If you want to go be a hobo on a tropical beach, be my guest. My approach minimizes my hindsight regret.

I continue deriving some amount of satisfaction from my career, and regardless of how this ends, I'll say that I did something important while that meant something.

I wasn’t arguing against the ‘business as usual’ strategy at all, for what that’s worth - after all, that’s what I’m doing.

But I was curious about the additional or different preparations you’ve made / steps you’ve taken that you referenced. The changes to plans.

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