AI's Next Mathematical Conquest: Which Millennium Prize Will Fall?
An OpenAI model has presented a possible solution to the Navier-Stokes problem, one of the seven Millennium Prize Problems. This has led mathematicians to speculate on which of the remaining five problems AI might solve next. Only two of the original problems have been solved so far, including the Poincaré conjecture in 2003.
The Navier-Stokes problem concerns the behavior of fluid flows and whether smooth, physically valid solutions always exist for the equations governing them. Its potential resolution by an AI model marks a turning point, as just a year earlier such systems struggled with Olympiad-level problems. The remaining five Millennium Prize Problems include the Birch and Swinnerton-Dyer conjecture, which links elliptic curves to the number of rational points they contain—a question with deep ties to cryptography and Fermat’s last theorem. OpenAI has hinted at progress on another unsolved problem, though it has not named which one, fueling intense speculation across mathematical forums and conferences.
If AI continues to crack such foundational problems, the pace of mathematical discovery could accelerate dramatically, but it may also shift the role of human mathematicians from solvers to verifiers and interpreters. This could affect funding priorities, educational curricula, and the perceived value of pure research. Society may benefit from faster breakthroughs in fields like fluid dynamics and cryptography, yet it could also raise questions about trust in machine-generated proofs and the equitable distribution of prestige and prizes.