OpenAI Claims Navier Stokes Proof as NYU Mathematician Alleges Idea Leak
OpenAI claims a Navier Stokes proof after a $22.5 million AI push, while NYU mathematician Tristan Buckmaster alleges leaked ideas and credit pressure.
Summary
On September 8, 2026, NYU professor Tristan Buckmaster announced three proofs, including a preliminary Navier Stokes result, developed with Levent Alpöge using mainly OpenAI Codex plus Anthropic's Claude. Alpöge is an Anthropic mathematician but conducted the work independently. OpenAI then published what it called a full proof of the Navier Stokes existence and smoothness problem, one of seven Clay Mathematics Institute Millennium Prize problems worth $1 million each. The fluid mechanics equations are widely used but theoretically unresolved. OpenAI said an unreleased next generation model tackled several unsolved problems during a weeklong run producing 300 billion output tokens, equivalent to $22.5 million at current Astra rates.
Buckmaster said the pair learned their progress had reached OpenAI while finalizing their results. He said OpenAI eventually acknowledged its first prompt came days later, although OpenAI says its September 1 effort followed rumors that two Millennium problems had been solved and confirms discussions with the pair. Buckmaster questioned OpenAI's simultaneous use of their uncommon smooth force route, options c and d in Fefferman's formulation, pioneered by Luis and Diego. He alleges Bubeck proposed removing Alpöge's credit and warned that publicity could ruin Buckmaster's career. Because Codex interactions may train OpenAI models unless users opt out, Buckmaster also raised possible leakage through his usage. OpenAI says no researchers or agents saw the work and no specific user data was accessed, but cannot exclude deidentified usage improving its models. It says the proofs differ significantly, including forced versus unforced Euler results. Buckmaster wants fuller disclosure, intensifying disputes over AI research credit, data provenance and compute advantages.
Positives
- OpenAI published a claimed full solution to a $1 million Millennium Prize problem involving the Navier Stokes equations.
- Buckmaster and Alpöge produced three proofs, including preliminary progress on a central problem in theoretical mathematics.
- Codex and Claude both contributed to Buckmaster and Alpöge's work, demonstrating cross platform AI assistance in advanced mathematics.
- OpenAI says its proofs differ significantly from the pair's work, including forced versus unforced results in the Euler case.
- Public releases from both sides expose the proofs, methods and provenance dispute to broader scrutiny.
Risks & concerns
- Buckmaster alleges OpenAI began its push only after information about his unpublished progress reached the company.
- OpenAI's 300 billion output tokens represented $22.5 million in compute at Astra rates, highlighting a major resource imbalance.
- Bubeck allegedly sought to remove Alpöge's credit and warned Buckmaster that publicizing the dispute could ruin his career.
- Codex interactions may be used for model training unless users opt out, creating uncertainty about confidential research entering future models.
- OpenAI cannot rule out deidentified product usage improving the model that generated its proof.
- The teams' simultaneous choice of an uncommon smooth force route leaves the proof's intellectual provenance disputed.