Buckmaster Says Keep Your Best Ideas Out of ChatGPT

NYU mathematician Tristan Buckmaster told CNBC that he still uses OpenAI and Anthropic tools most days, and that he still will not type his own original research ideas into them. OpenAI denies his account of how his work reached a Navier-Stokes result ahead of him. The remark landed in the middle of the largest single release of machine-written mathematics any lab has attempted.

What did Buckmaster actually tell CNBC?

He uses the tools constantly. He draws the line at unpublished ideas.

Buckmaster appeared on CNBC's Squawk Box on October 8, 2026, to discuss the fight over OpenAI's math findings. Models are fine for cleaning up code, checking algebra and tightening a proof that already exists. A new idea stays on his side of the wall, and has for a while.

He pointed at a structural squeeze underneath the personal rule. The number of open mathematical problems is effectively unlimited, while the window in which a PhD student or postdoc can build a career on one of them is finite. If a lab can clear hundreds of problems in a day, a decade of scaffolding built around scarcity becomes harder to defend, and that is a question about careers rather than about software.

Buckmaster was blunt about the motive he attributes to the company. "The fact they would front run their customers, it shows their disdain for their customers," he said. In September, OpenAI announced a proof of the Navier-Stokes existence and smoothness problem. Buckmaster said he and Levent Alpoge had spent roughly a year working toward the same target, and the New York Times ran the episode as a clash over a $1 million proof.

Where exactly is the line Buckmaster is drawing?

The line runs between work that is already public and work that is not yet public. Buckmaster is a professor of mathematics at New York University's Courant Institute, where he arrived in 2023 after a doctorate at Leipzig in 2014, seven years at Princeton and one year at the University of Maryland. He holds dual Australian and British citizenship and US permanent residency.

He is not an AI abstainer. He is an AI user with a policy.

His field is also the one where model assistance has already produced finished, checkable results.

On September 7, 2026, Buckmaster and Levent Alpoge, a mathematician at Anthropic, announced solutions to the three-dimensional incompressible Euler equations that start smooth and lose regularity in finite time. Companion papers cover the inviscid Boussinesq system and the porous media equation on the two-dimensional torus with Matei Coiculescu. All three were formalized in the Lean proof assistant, and Buckmaster said nothing in principle prevents the method from reaching Navier-Stokes.

What did OpenAI release, and what was actually proven?

OpenAI published 722 machine-generated mathematics manuscripts, and independent verification covers only part of them. The release landed on October 6 and 7, 2026 in a public GitHub repository, produced by an internal model the company has not released. The papers fall into 372 families of results spanning number theory, algebraic geometry and other fields. OpenAI said it tested roughly 8,000 open problems, at a success rate near 5 percent and about three hours of GPU-level computation per solved problem.

Not every manuscript was formalized in Lean. Three were withdrawn within about a day, leaving 719.

The gap between formal checking and mathematical acceptance drew sharp criticism. Terence Tao and the Association of Human Mathematicians said in a joint statement that the release ignored recommendations from OpenAI's own Mathematical and AI Advisory Group, and that publishing more than 700 files at once is not an academic achievement but a display of power. They called on mathematicians to end collaborative work with the company.

TechCrunch reported that only ten of the remaining manuscripts exposed the model's reasoning, which is why the process matters as much as the results. Scott Aaronson noted that no human has fully understood most of them. Until somebody reads them, this is a claim about capacity rather than a body of settled mathematics.

Does OpenAI actually keep what you type into ChatGPT?

On a personal account, it may, unless you switch training off. OpenAI's published policy says content from individual ChatGPT and Codex use may be used to train its models. Users can turn off "Improve the model for everyone" under data controls, or select "do not train on my content" in the privacy portal, and either switch alone is sufficient for new conversations.

Codex carries a separate "include environments" setting for training on full environments, which the ChatGPT toggle does not change. Business, Enterprise, Edu and API inputs are excluded from training by default, and temporary chats are purged after 30 days.

Opt out, then hit the thumbs-up button, and the whole thread can still train a model.

OpenAI states that submitting feedback on a response means the entire conversation attached to that feedback may be used to train models even after opting out. Buckmaster's caution is not that the policy is hidden. It is that the default is permissive, and that a research pipeline can be extracted from prompts without anyone ever promising confidentiality.

What does this mean for AI tokens and crypto markets?

It is a governance story first and a token story second, but crypto trades the second one every hour. The AI token sector was worth roughly $19 billion at the end of the first quarter of 2026 and around $22 billion by mid-year. TAO, FET and RENDER are the largest names in that basket, and all three repriced after Nvidia chief Jensen Huang framed the market in April as compute demand meaning tokens come out.

That trade runs on narrative velocity, not quarterly earnings.

It also cuts against the decentralisation argument.

Buckmaster's remarks sit inside that narrative rather than outside it. A model clearing hundreds of open problems in a day, run by a small internal team with no public weights and no disclosed training set, is a harder pitch for decentralised compute marketplaces than a model straining to render an image. Centralised labs hold the training data, the checkpoints and the talent, and now compete to publish proof volume as a product. For traders the variable is not whether one result is correct, but whether headlines keep pulling capital in.

What to watch next

Three things: whether the remaining Lean files hold up, whether institutions write disclosure rules, and whether formal verification becomes standard. Independent checking of hundreds of manuscripts will take months, and the first widely cited failure of a formalized result will set the tone for everything after it. More withdrawals are likely if errors surface, and the gap between "Lean verified" and "accepted result" will keep being argued in public.

No public dataset exists for what the internal model was trained on.

Institutional response matters as much as the mathematics itself.

Universities decide whether model-assisted proofs count for hiring, promotion and grants, and whether disclosure of assistance is required. Buckmaster's own papers disclose that large language models assisted and that Lean verified them, which sets a concrete floor rather than an abstract principle. On the commercial side, watch whether training exclusion and output rights harden into standard contract language. OpenAI's terms of use were last dated January 1, 2026, and its service terms were updated on September 29, 2026.