Who owns the progress?

On September 8, 2026, OpenAI presented a proposed proof on the Navier-Stokes problem: the formation of a singularity under a smooth external force, formalized in Lean, worked out by around 10,000 agents running simultaneously on an internal model. Two mathematicians, Levent Alpöge and Tristan Buckmaster, had previously worked on a related problem for the Euler equations, using models from both Anthropic and OpenAI, and had put all their drafts into Codex for the whole of the project.

The breakthrough is welcome. Who owns it is not decided by the mathematics, but by who can see the data flow. Right now that is nobody outside OpenAI. The same question faces every company that talks to a model about its own ideas.

My First Objection Was My Own

My first thought was not outrage. It was the objection I usually hear from others, only this time it came from me.

“The mathematicians could have kept working on the problem for the next 750 years. When someone lets 10,000 agents loose on a problem, that is good for humanity. No institute puts up that kind of money for it.”

That is true. And it is still not the interesting question.

I have worked in IT, data and AI for 28 years. I have watched waves arrive that changed the world, and waves that quietly disappeared. In none of them were progress and attribution a trade, where you get one by giving up the other. Anyone who says today that the result counts and the backstory is a footnote is mistaking the size of the bill for an argument.

Progress and attribution are not a trade.

Attribution sounds like vanity. It is the opposite. It is the bookkeeping of where an idea came from, and without that bookkeeping nobody knows which ideas should be funded next. Leaving it out does not skip a courtesy. It erases the map.

So which scientist is the one devoted to humanity? The one who solves his problem, no matter with whom? Or the one who keeps his ideas to himself until he is sure they will not end up in someone else’s model? The answer does not depend on his character. It depends on what he knows about the data flow. Right now, that is nothing.

What Buckmaster Knows and What Nobody Can Verify

Tristan Buckmaster has published a statement, and he says explicitly that he is not accusing anyone of anything. The collaboration was personal, without an institutional agreement. He paid for the tools out of his own research funds, with considerable spending at OpenAI. The pair’s drafts sat in Codex for the whole project. When he asked whether they were being used for training, he got no answer. He does not know whether his data was used.

And then the sentence that stays with me: “If indeed an OpenAI model did close the gap to Navier-Stokes, that is a remarkable thing and it should be said loudly, by them, with the history intact.” The history, for him, includes the prior work of Diego Córdoba and Luis Martínez-Zoroa.

This is a man who does not know what happened to his work and would like to find out. I find that stance more credible than any outrage I read in the week that followed.

There is an irony here that is easy to miss: the two worked on their problem with Claude and put their drafts into Codex, and Alpöge works at Anthropic. Two vendors, two sets of terms, one research project. Anyone who wants to trace the path of those drafts from the outside has to ask two companies that compete with each other.

OpenAI followed up on September 10: its own investigation, it said, had confirmed that Buckmaster’s Codex prompts from the two months before September 8 “could not have influenced the system in any way, including through training.” That is the statement of an involved party about a period it chose itself, without independent review. It is nothing more than that.

OpenAI explicitly recognizes the pair’s priority on the Euler problem with an external force. That does not answer the question about the data flow.

Two months is the period OpenAI chose. Buckmaster speaks of drafts from the entire project. Nobody outside the company can say whether the two periods match.

In a voice note on the case I asked myself a question I have not been able to shake since, because it fits every vendor contract I have read on this subject: But is that really the case? Or is it only true on paper?

The question is legitimate, and no contract answers it. A contract clause says what a vendor promises. It does not say what happens in a training pipeline, who can view logs, and what an internal model saw two months earlier. I do not know whether OpenAI trained on the drafts. I do know that nobody outside can verify it. The second is the problem.

There is one thing I am deliberately not claiming: that the problem is solved. A proposed proof is not an accepted proof. The rules of the Clay Institute require publication, general acceptance in the mathematics community and a waiting period of at least two years. So the breakthrough is welcome and not yet confirmed. Both at once.

The Shadow AI Principle, Read Backwards

I work with these models. I talk to them about my own approaches, about architectures, about arguments for texts like this one. I do it knowing that some of it can leak. I give a model nothing I could not live with if it resurfaced tomorrow in someone else’s context.

None of this is new. Most people use Google, Google Maps, Instagram and WhatsApp, and very few ask what the phone or the provider does with their data. A similar discussion is under way right now about smart glasses.

The differences between the products are real. At OpenAI, training is on by default for personal ChatGPT and Codex accounts and can be switched off. For Business, Enterprise and API it is off by default. For consumer Claude accounts it depends on the setting. Microsoft Foundry does not use data to train the base models without permission, but abuse monitoring can include human review, unless the customer has been approved for modified abuse monitoring, which switches off the storage and the human review.

Those are differences I take seriously. And they are paper until someone can verify them. Which type of account the mathematicians used is not publicly known. Processing, storage, human review and training are four separate operations, and the switch everyone talks about covers only training. The other three run where hardly anyone is looking.

Inside companies I see the same sequence almost every time: an enterprise contract is signed, and the topic is considered settled. The question of whether anyone in the building could ever verify the promise goes unasked, because it is uncomfortable. But it is the only one that counts.

This is where it gets interesting for companies, and not because of the mathematics. In my essay on Shadow AI I wrote down a rule I have seen confirmed in every organization since: whoever pours knowledge in must benefit. Otherwise people keep their ideas to themselves, and the best solutions stay under the desk, known to exactly one person. My book calls them the Secret Cyborgs: high performers who automate their own work and tell nobody, because telling somebody only ever produced more work.

The Buckmaster case is the same principle, read backwards. It is not the employee holding back knowledge. It is the vendor holding back the answer. And science works no differently from a company: when researchers do not know where their drafts go, the riskiest, most original approaches go back into the drawer. Then no number of agents will help, because what they would need never gets typed in.

What happens to a research field in which the route through the model becomes a precondition, while the model answers to nobody? What happens to a company whose best minds entrust their ideas to the assistant but not to their own organization? What happens to a lead you can no longer tell apart from your tool?

The answer to all three questions is the same: it belongs to whoever can see the data flow.

My verdict is therefore not an either-or. Yes to the breakthrough, if it is confirmed, and the rules for that are clear. Yes to the effort: no institute spends that much on a single attempt. Yes also to the 10,000 agents, because they attempted something that generations could not finish.

And still:

If you do not know what leaks, you do not own your progress.

That applies to Buckmaster, who wants to see his backstory told correctly. It applies to OpenAI, whose own investigation remains a claim for as long as nobody from outside is allowed to look in. And it applies to every company that types its strategy into a chat window and mistakes an account setting for a contract.

Tomorrow morning I will talk to a model about my own approaches again. I put nothing in that I would have a bad feeling about: nothing I could not answer for if it leaked. Everything else I put in knowing it could be used for training, for instance. I will not let that keep me from the fruits of AI.

As long as nobody outside can verify what leaks, the question of who owns the progress is not a question of mathematics. It is a question of verifiability, and nobody has answered that one yet.