Whether smooth 3D fluid solutions can blow up in finite time concentrated analytic, numeric, and now AI-assisted work.
Euler (inviscid) and Navier–Stokes (viscous) equations model continuum fluids. Since Leray (1934), global 3D regularity remains open in the Clay-prize sense.
In the 2020s, advances on blow-up scenarios, near-singular constructions, and assisted verification brought discussion toward conditional results and external forcing.
The pre–September 2026 landscape included both classic analysis programs and large-scale computational experiments.
Tristan Buckmaster and Levent Alpöge resolved a forced-Euler blow-up variant; OpenAI recognized their priority after September rumors.
OpenAI describes ~10,000 concurrent agents, hundreds of billions of tokens, and Lean formalization after finding a singularity with smooth forcing.
OpenAI claims an analytic proof and Lean formalization of a 3D Navier–Stokes singularity; it does not claim the Clay Prize and awaits math review.