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PaperclipPerfector  2d ago (text post)   7262 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.

Given that this is the culture war thread, I think it's in the interest of this forum to also mention the controversy over the topic.

A mathematician is alleging impropriety on the part of OpenAI. Please forgive the formatting. I'm pulling it straight from the pdf.

I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.

Two proposals were offered to me. The first was that we post our Euler result, and that OpenAI post its Navier-Stokes result the next day. The second was that, after posting Euler, I alone write a paper presenting the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it. Sebastien twice asserted that he wanted Levent removed from authorship, and said it would all be simple if only it were not the case that, and it was so annoying that, Levent works at Anthropic. It was also said that if OpenAI posted after us, they would say that we deserved the Clay Prize, and that we were the “closest humans to the problem”. I declined both offers.

I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”

I'm not going to comment on the veracity of the claims, nor am I going to comment on the math itself.

I will say, however, that I will be meeting with a few other developers and a representative from our corporate risk team today to discuss contingencies if these allegations prove true.

The model did it on its own, and the people in charge of the company are not in charge of the model. Just like huggingface.

What's interesting to me is that, based on what is alleged, it looks to me like the mathematician was also using AI:

We used several LLMs throughout: Anthropic’s Claude, OpenAI’s Codex, especially with GPT-5.6 Sol and, more recently, Astra. The latter was only used for writeups and auditing our arguments.

Furthermore, he alleges that the idea that the OpenAI team let the AIs solve it by themselves is wrong:

Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute had been used.

Finally, it appears that the team may have been set up to steal his (AI-assisted) work...

I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI. I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.

[As an aside: people are fixating on whether or not OpenAI used his data on the training, which seems to me to be missing the suggestion that they may have heard of the approach that he used?]

...in order to keep Anthropic from getting any credit!

The first was that we post our Euler result, and that OpenAI post its Navier-Stokes result the next day. The second was that, after posting Euler, I alone write a paper presenting the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it. Sebastien twice asserted that he wanted Levent removed from authorship, and said it would all be simple if only it were not the case that, and it was so annoying that, Levent works at Anthropic.

From what I can tell this is a "win" for AI in the sense that AI was used by both teams working on the problem, a "loss" for AI in the narrow sense that humans also put in a lot of work instead of just typing in "lol solve Navier-Stokes" [this is only a loss for AI if you, for some reason, don't think merely assisting humans in solving generational math problems is not a glorified enough W], and a lot of the heat generated by it isn't about whether AI did it or not [in either case, it was a human-assisted-by-AI effort, or AI-assisted-by-human effort, if you prefer] but rather if OpenAI can use it to rack up PR points or not.

Thanks for linking the statement, saved me a search for it.

[this is only a loss for AI if you, for some reason, don't think merely assisting humans in solving generational math problems is not a glorified enough W]

The problem is AI fanatics literally use this as their doomsday goal post. It's never "Expert + AI" spend large amounts of compute and combined intellectual prowess to solve hard problem, create bio weapon, hack every system in the world etc. It's always "I'm worried some pleb is going to type "lel give me smallpox x10, make it incurable, make no mistakes"". By that same metric this is a loss for them because it did require a "centaur". Hell it really required a humanoid-hydra-centaur where its a dozen human heads on a single horse torso.

As always, maximalists gonna maximilize, nobody ever got famous/stood out from a crowd by making measured, subdued, realistic predictions. Follow the incentives.

Apply the intermediate value theorem. If AI started 2026 much worse than human mathematicians, and (hypothetically) by the end of 2026 AI is much better than human mathematicians, then at some point in 2026 AI capabilities pass through the point at which they are useful but still need human mathematician assistance to reach their full potential.

Yes, I think this is right.

And I actually think this is a good result for AI:

  • New breakthrough made with AI!
  • But with human researcher assistance
  • And lots of compute

If you put those pieces together, they paint a picture of a better future where you still have your job but maybe an AI-assisted pharmaceutical cures your cancer, and some disgruntled terrorist in a lab running a jailbroken local model is going to have a much harder time making smallpox x10 than that AI-assisted team of PhDs is going to have synthesizing a cure. That's...pretty great! I can be excited about that future!

But to your point about incentives, I think OpenAI wants to blur the line between "we threw a million monkeys at a typewriter to solve a fabled mathematics problem" and "you can do this on your computer at home" in part because of marketing (and ideological hype about the future of AI). They want investors to think that what they will get in their browser at home is the same product as the one that solved Navier-Stokes, which is misleadingly true.

Somewhat relatedly, OpenAI recently reported that their project to build an automated "research intern" was a success...that now cost them $600 per day per median researcher to run. I don't think this means that OpenAI's automated investor is worthless - in some fields it might be worth every penny! - but it's not going to be replacing the literal ~free labor interns that I work with and once was.

So I think there's a convergence between how OpenAI wants you to see their product and how the doom-mongers want you to see their product. They are both framing it in grandiose, infinite-return-on-investment (either negative or positive) terms and not asking you to look too hard at all of the little nitty gritty details such as "where would an escaped AI swarm get enough compute to subsist outside of its servers?" or "how much is it going to cost me to solve Navier-Stokes at home when the investor cash dries up?"

I just hope judges aren't taken in by this particular charade when it starts having actionable implications. Never mind legislators.

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