Did OpenAI solve the wrong Navier-Stokes problem?
4 hours ago
- OpenAI claimed to solve the Navier-Stokes problem, a $1-million Clay Institute prize, but the proof uses an external force, which many mathematicians consider an unnatural loophole.
- The Navier-Stokes problem asks whether the equations can 'blow up' (produce infinite flow speeds) under realistic conditions, but OpenAI solved a variant that includes an external force like gravity.
- Recently, three mathematicians proved that OpenAI's method cannot be extended to the full problem without external force, showing the loophole is permanent.
- The Clay Institute's original problem statement includes an option allowing external force, so OpenAI's solution is technically valid for that version.
- LLMs excel at finding explicit blowups but struggle with proving impossibility, giving humans an edge in the full problem.
- The controversy has sparked debate about whether the Clay problem statement should have included external force, and raises questions about AI's role in mathematics.