Ask Me Anything | October 2026

In October 2026, OpenAI announced that an internal AI system had produced a proof that the 3D Navier-Stokes equations can blow up in finite time—a Millennium Prize problem. Sean Carroll opens the AMA by noting that while the result is deservedly big news, it tells us little about actual fluids, since the continuum approximation breaks down well before any true singularity. More interesting to him is what the announcement reveals about how AI is changing mathematics and physics, and about the messy, under-examined process behind it.

What the Navier-Stokes "Proof" Actually Means

Carroll emphasizes that the Navier-Stokes problem is a math problem, not a physics one. From a physicist's perspective, a singularity in fluid equations is exactly where the approximation stops being valid. But as a mathematical achievement, it's significant—though still contested. The proof was checked by a program called Lean, which formalizes and verifies logical steps, but Carroll notes that Lean itself can make mistakes or interpret things differently than intended. There is also controversy over whether the proof OpenAI released is identical to the one Lean checked. More troublingly, Carroll points out that many human mathematicians have been collaborating with LLMs to work on the same problem, and it is unclear whether OpenAI's model was trained on those conversations or whether OpenAI resear