New York University mathematics professor Tristan Buckmaster announced three proofs on Tuesday that tackle a major unsolved problem in theoretical mathematics. Working alongside Anthropic mathematician Laurent Alpage, the duo combined OpenAI Codex and Claude AI models to construct the proofs. However, an unusual conflict broke out after OpenAI published its own parallel attempt to solve the exact same equation.

Shortly after Buckmaster released his initial results, OpenAI published a full proof addressing the Navier-Stokes existence and smoothness problem. OpenAI claimed an unreleased next-generation model discovered the proof after running a week-long effort that consumed 200 billion output tokens, costing roughly 22.5 million dollars at current compute rates.

The Navier-Stokes existence and smoothness problem stands as one of seven Millennium Prize problems, carrying a 1 million dollar bounty from the Clay Mathematics Institute for the first confirmed proof. Navier-Stokes equations model fluid mechanics, powering predictions for weather patterns, ocean currents, and airflow across aircraft wings.

While Buckmaster and Alpage were organizing their findings, they learned that outside parties leaked news of their progress directly to OpenAI. When the researchers contacted OpenAI, representatives claimed internal teams had already reached a full proof. Yet when the mathematicians asked when research began and how much human guidance the model needed, OpenAI’s responses became vague.

Buckmaster stated that an entire team at OpenAI threw massive computing power at the problem only after hearing about his initial approach. Internal timelines show OpenAI submitted its first prompt just days after receiving word about Buckmaster’s active research track.

This timeline indicates OpenAI realized Buckmaster’s method held real promise, prompting the lab to use its massive compute budget to rush out a formal proof first.

While many mathematicians actively research Millennium Prize problems, Buckmaster used a distinct technical approach. He found it suspicious that OpenAI adopted his exact mathematical approach right after learning about his active work.

Alpage works directly for Anthropic, though he conducted this research independently rather than on behalf of his employer. The research pair used several tools, relying heavily on OpenAI Codex. Alpage’s connection to Anthropic created friction, and Buckmaster stated that OpenAI executive Sebastien Bubeck asked to remove Alpage’s name from credit lists as part of a proposed compromise.

When Buckmaster threatened to make the dispute public, Bubeck warned him against ruining his professional career, adding that OpenAI would fight back aggressively if forced into an open dispute.

Buckmaster also raised concerns about data privacy. Because he relied heavily on Codex while building his original proofs, OpenAI may have monitored his user inputs to guide its own parallel efforts. While OpenAI terms allow users to opt out of training models on session data, internal teams monitoring Codex interactions could easily view user prompts to replicate novel solutions.

OpenAI denied using private user prompts, publishing a post stating that researchers did not access user data to solve the problem. However, the company admitted that de-identified output data might inform general model performance while insisting its final mathematical calculations differed from Buckmaster’s setup.

Using massive compute budgets to scoop academic researchers creates serious friction between commercial AI labs and independent scientists. As commercial labs monitor user prompts, independent researchers must protect their intellectual property before entering proprietary data into cloud models.