The Proof Was a Collaboration

The headlines about Navier-Stokes this September asked whether an AI had solved it. The story underneath is a collaboration: two mathematicians and models from two rival labs, working one line of attack across tools that do not talk to each other. Collaboration like that is the problem we work on.

What happened

Tristan Buckmaster is a mathematician at NYU’s Courant Institute. Levent Alpöge is a mathematician on the technical staff at Anthropic. For about a year they worked toward the Navier-Stokes problem, one of the seven Millennium Prize Problems, in what Buckmaster’s statement calls a purely personal collaboration, with no involvement from either employer.

They started from a program built by Diego Córdoba and Luis Martínez-Zoroa and used language models to push it further. On August 15 they had blow-up results for the Boussinesq and Euler equations, two simpler relatives of Navier-Stokes. A week later the proof passed in Lean, a program that verifies mathematics line by line. The paper and the Lean code went up late on September 7.

The next day, OpenAI said that about 10,000 of its agents had settled Navier-Stokes itself in 88 hours. As we write, that claim has not been independently confirmed. The two sides also disagree about credit and about data. That argument is not ours to settle, and this post is not about it.

How they worked

Two people and two labs’ tools. Buckmaster’s statement names them: Anthropic’s Claude and OpenAI’s Codex, used throughout. Scientific American reports that Claude found the Euler blow-up. Alpöge sent Buckmaster the proof the models had written. Codex did much of the rewrite for human readers, and every draft of the project went into their Codex sessions.

None of those tools knows about the others. Claude and Codex are separate products, and each keeps its own conversation. So the collaboration ran on what collaboration across separate tools always runs on: copy, paste, send, and explain again. A person carried every handoff, between the two models and between the two people.

The models were not the obstacle. The first proof they wrote was unreadable to people, and Buckmaster told an audience at NYU that it made no difference to the machines: “all the different LLM models understand this complete gibberish.” The models could read each other. Nothing but the two people connected them.

Collaboration is the hard part

Buckmaster wrote that the results matter less than the fact that a mathematician and a model can now do this much in a month. We would add one thing. This was not one mathematician and one model. It was two people, several models from two labs, and a program that came from two more people and that no model proposed. The next results will have more of each.

We see the same thing in product teams. AI made each person on a team faster. It did not make the team faster, because an agent sees one person’s prompt and nothing else. The work slows down in the gaps: between people, and between tools.

What we are building

Cyborg is multiplayer for AI: one shared place where a team and agents from every lab work in the same thread.

• Everyone in one thread. Anyone on the team can start a mission, and everyone in it reads the same conversation and can direct the agents.
• Every lab in it. Claude, Codex and Gemini agents work side by side in a mission, on your own accounts and keys. One agent can hand its turn to another, so nobody carries work from one tool to the next.
• People guiding. Agents do the work and check each other. When a call belongs to a person, the agent asks and waits.

Not only for software

We started with product teams because that is the work we know, and Cyborg today is built around it: a company signs up, and a mission works on a code repository.

The shape is not special to software. A research group is a few people who hold the judgment, several models with the stamina, and a result that has to pass a check stricter than anyone’s confidence. Scientists, researchers and mathematicians are already collaborating with each other and with models from more than one lab. They are doing it in separate windows.

That is something we can help with. Our ultimate goal is to empower any group of people to collaborate with each other and with agents, and to achieve results faster.

If you do research with more than one person and more than one model, write to us at hi@cyborgs.team and tell us how you work.

Agents working, People guiding.