In September 2026 OpenAI announced that its agents had proved a breakdown result for the Navier–Stokes equations — one of maths' million-dollar Millennium problems. The night before, mathematician Tristan Buckmaster published a statement alleging that news of his and a colleague's unpublished work on a closely related problem had reached OpenAI — work done partly with OpenAI's own tools. OpenAI denies using it. Whatever the facts turn out to be, the shape of the dispute is new: when your work-in-progress runs on a vendor's model, the vendor can also be your competitor.
Buckmaster and Levent Alpöge say they had a machine-checked proof of a related result by late August, and that word of it leaked to OpenAI, which started its own large-scale run on 1 September. OpenAI says its methods differ significantly and that their work played no part. Its public wording on whether their usage data could have had any influence changed several times over the following week, before settling on a firm no.
Nobody outside the two sides knows what happened in the private conversations, and this briefing doesn't take a side. The point is that neither party could settle it quickly — not the researchers, and not the vendor looking at its own systems. If that's hard for the vendor, it's impossible for you.
AI labs now do first-party work in the same fields their customers do: maths, code, science, and soon your industry's equivalent. Meanwhile your pricing models, product designs, deal strategy and unreleased code flow through their models as prompts. A prompt that describes your next product is an R&D document, whatever the interface makes it feel like.
Retention periods, whether data trains future models, who can read logs for abuse monitoring, and what counts as “de-identified” or “derived” data differ by vendor and by tier — consumer, team and enterprise plans often differ sharply. Read the contract, not the marketing page, and assume a personal account on a staff member's phone carries the weakest terms in the building.
The mathematicians' strongest evidence was a dated, machine-checked artefact they controlled. The business equivalent is ordinary engineering hygiene: work committed to your own version-controlled repository, specifications with dates, decisions written down where you hold the history. If a dispute comes, your logs are the evidence — the vendor's logs are theirs.
Treat this like data residency: an input-supply-chain question answered before procurement, not after a claim. Classify what may go to which tier of which vendor, the way you already classify personal information.
Deeper: Version control as the ledger →Not just training: research, product decisions, evaluations. Ask for the answer in the contract, in writing.
Including abuse-monitoring access and “de-identified” or aggregated data.
Personal accounts and free tiers are the usual leak. Give staff a sanctioned tool so they don't need one.
In your repositories and document systems, not only in a chat history the vendor hosts.
For crown-jewel R&D, an open-weight model on infrastructure you control removes the question entirely.
The full story — what was claimed, what Lean verification does and doesn't prove, the 719-manuscript release and the three papers withdrawn a day later — is in the tree.
Deeper: When the machine proves →Where owning beats renting — including the location of your data and models when the work is sensitive.
Read briefing →The other provenance question: what went into the model, and why it belongs on the same register as POPIA.
Read briefing →Your AI vendor is becoming a participant in your field, not just a supplier to it. Treat what you type as R&D, read the terms that govern it, keep your own dated record of your work, and keep the crown jewels on infrastructure you control.