OpenAI Claims Proof of Finite-Time Singularity in Navier-Stokes Equations

ChainCatcher report: On September 8, OpenAI announced that its internal multi-agent system has successfully proven that the three-dimensional incompressible Navier-Stokes equations can develop singularities in finite time, thereby solving this century-old problem. The proof was driven by an internal model more capable than GPT-6 Astra, with preliminary results obtained on September 5, followed by 17 hours of formal verification in Lean. OpenAI stated that the proof demonstrates how, under smooth external forces, a stationary fluid can evolve into vortex structures that spiral inward and stretch, with finite energy but unbounded velocity growth—corresponding to cases “C” and “D” in the Millennium Prize problem. The entire solution process utilized approximately 10,000 concurrent agents, exchanged about 2.7 million messages, and consumed roughly 130 billion output tokens. OpenAI acknowledged that this effort was inspired by rumors of parallel work by Anthropic employee Levent Alpöge and NYU professor Tristan Buckmaster, noting that their results on the regularity of the Euler equations differ: OpenAI proved the case without external forces, while the other team proved the case with external forces.