source: Simon Willison: On the Navier–Stokes Millennium Prize Problem
level: technical
openai announced a resolution to the navier-stokes existence and smoothness problem, one of seven millennium prize problems worth one million dollars. the company used an internal model to launch agents on september 1 after hearing rumors that two millennium problems had been solved. the agents reached a solution in about 88 hours, with lean verification taking 17 more hours. the effort involved 4.9 million messages and 300 billion output tokens across all attempted problems.
tristan buckmaster, an nyu professor, and levent alpöge, an anthropic employee, had worked on the problem for almost a year using claude and codex. they had a breakthrough on august 15. buckmaster accused openai of starting after hearing about their work and questioned whether the model was trained on their codex sessions. openai said no specific user data was accessed but could not rule out de-identified data improving models. the proofs differ significantly, with different results in the euler case.
the dispute highlights how rumors of a solution can trigger massive llm spending to get there first, similar to security exploit hunting. openai's token usage at public api prices would cost about fifteen million dollars. the case raises questions about what it means when ai labs say user data improves model performance. for researchers, this shows the risk of using commercial ai tools for sensitive work, as your prompts might indirectly help a competitor solve the same problem faster.
why it matters: this shows how ai labs can rapidly turn rumors into competitive results, raising concerns about data privacy and priority in research.
source: Simon Willison: On the Navier–Stokes Millennium Prize Problem