Turning a bunch of vague research directions and exploratory prompts into a formalized proof is quite impressive on its own. OpenAI would have no incentive to taint its first math announcement of this magnitude if it knew it were "plagiarizing" another person's work.

People are grasping at straws it seems to dismiss the power of this new model they may have. Hate OpenAI for any reason you want, but denying the capabilities of models has been a losing game for the past 5 years.

> Because the core of the issue is that it may well not have solved it, but instead plagiarised the significant step of the result from other researchers

It's also true however that I haven't seen a single write up trying to discern what did more of the work in those AI chats - the prompts or the responses - bubble to the surface, also since we don't have access to them.

For example, if I prompt Codex with "Make me a website about strawberry cake" and nothing else, and OpenAI announces they have the best strawberry cake minutes before I launch, I'm not sure they plagiarized anything.

We just don't know if this is quibbling over "who prompted first" or if the researchers came up with anything strikingly original by themselves.

It is very unlikely to be plagiarized, and claims of plagiarism are largely unfounded and show a lack of understanding of the situation. They fall apart when reviewing the timeline, and what was actually solved.

This is the timeline:

On June 29, Buckmaster opted out of model training, and stopped allowing his chats to be used as training data with OpenAI https://mastodon.social/@tristanbuckmaster/11723341370570119...

On August 15, Buckmaster and Alpöge found their blow-up for 3D incompressible Euler with forcing https://cims.nyu.edu/~tristanb/statement.pdf

In late August, OpenAI completed a pretrain of its latest internal model. A model derived from this pretrain, built after August 28, found a solution to 3D incompressible Euler without forcing and Navier-Stokes with forcing. https://openai.com/index/navier-stokes-solution/

To explain who solved what (I copied from here: https://x.com/IlinVasily29521/status/2097554700321329393 )

  Tristan + Levent: 3D incompressible Euler with forcing
  OpenAI: 3D incompressible Euler without forcing
  OpenAI: Navier-Stokes with forcing
  No one: Navier-Stokes without forcing

Tristan+Levent ticked the weakest case, OpenAI ticked the two next weakest, then the final case is unsolved. Only the last two are eligible for the Millennium Prize. The Navier-Stokes general case remains unsolved.

Buckmaster disabled model training long before the August 15 breakthrough results, so these chats were not used as training data for OpenAI's model which solved Navier-Stokes.

Additionally, Tristan and Levent only solved the easiest version of the problem and did not have the key insights to solve the harder versions of the problem required for the Millennium Prize.

And OpenAI directly addressed these plagiarism claims, and called them impossible: https://www.nytimes.com/2026/09/10/science/tristan-buckmaste...

"We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training."

> From some estimates I've seen, the compute cost alone would be around $10m, +/-

At market prices. All the estimates I've seen are based on OpenAI API costs. It doesn't mean that's what they paid, or how they paid for it.

But yes, the surprising willingness of humans to solve hard problems in exchange for food and board is underrated.

Once we have an existence proof of a particular technology, it doesn't take long for it to become economically viable and proliferate. And for something as useful as this, theres a strong economic incentive to get it to be as cheap and accessible as possible. Maybe not today, but certainly in a couple years I can imagine this level of intelligence being accessible to someone with a $20/mo plan, or even a free plan.

Interestingly it's this promise of the costs being able to be reduced what incentivizes the actual research.

If you tried to raise 25M to have 20 researchers on a salary for 5 years solving a specific math problem only academics care about, you probably wouldn't get much interest, or you would be able to solve 1 or 2 problems.

If however you promise that the money will go towards a technique that would allow to solve 10 thousand different math problems, and that costs will go down in the future, then you can raise much more than 25M.

Then, of course, one must verify that the verification code is valid, or the purpose of verification is more or less moot.

In a way that works just as well but the incentives are messed up.

And that's before we get into the whole 'salt the earth' way they ended up solving it. For a short period of time it may well have been the least valuable proof in mathematics yet. In their haste it's dubious they actually read the proof, and I don't think anyone has had time yet to truly understand it (the original researchers are best placed to do so, but are they even willing?).

So now it is solved, the proof has been independently verified and nobody has an incentive to investigate further. OpenAI has spent millions to uncover 1 bit of information that so far nobody has learned anything from, and they've demotivated all the people who wanted to.

I don't get how this invalidates the gravity of this achievement. Most mathematicians on the frontier of this stuff were likely using AI (or at the very least were heavily computer assisted) for some time now. Navier stokes was one of the very high profile problems that google Deepmind was working on with academia, for example.

Even with many of our best minds working on it for nearly a century, it _just_ now was solved just as AI became very good at math. Doesn't seem too farfetched to me to assume that AI played an outsized role in solving it. If it was really just a matter of "stitching things together" to solve it (granted, this is a very reductive way to look at it) , I suspect we would've solved this a while ago.

You do realize that regardless of what was in the training data, the final solution included insights no human before had known, right? I share the same concerns regarding academic integrity but it would take a lot of motivated thinking to conclude that what the AI system did was not significant.

Additionally, I'm no physicist but I suspect the possibility of singularities in NS equations is probably one of those 'true but not meaningful' facts. If it took our brightest minds 175 years to craft such a scenario, how relevant can it be in practice? Especially when turbulence exists. Maybe I'm wrong or it has some consequences for pure math though.

You're assuming you'll be the one doing the explaining :-)

It might also be that they won't even ask or wonder, similar to how most don't really do with pre-machining skills.

Or it could be like our "How did they build the Great Pyramid?!"