Tao hails AI-assisted blow-up breakthrough on model fluid equations, formalized in Lean

Terence Tao wrote a blog post introducing Levent Alpöge and Tristan Buckmaster's latest breakthrough on the regularity of fluid equations, calling it a remarkable achievement and noting that the argument involved substantial AI input, with the work already formalized in the Lean theorem prover. This direction is connected to the global regularity problem for the 3D incompressible Navier-Stokes equations, one of the Millennium Prize Problems with a $1 million bounty.

Confirmed

• Building on work by Córdoba and Martínez-Zoroa, Alpöge and Buckmaster improved the methods and proved finite-time blowup on three simpler model equations: the incompressible porous medium equation, the 2D Boussinesq equations, and the 3D incompressible Euler equations (as relayed from Tao's blog by @peterjliu and @MannyKayy)
• Tao described the result as "a remarkable achievement" and mentioned that the argument contains substantial AI input (@Hesamation)
• The argument has been formalized in Lean (@peterjliu, @MannyKayy)
• @basedjensen summarized that the field is advancing "remarkably fast": besides Alpöge/Buckmaster's result on Euler with smooth forcing, another team independently proposed related results for the unforced case, and Tao believes a full smooth-solution proof may now be feasible

Why it matters

• This progress follows the route of first proving blowup on simpler model equations, then approaching the full Navier-Stokes problem—substantive progress along the research path toward the Millennium Problem
• The deep involvement of AI in mathematical research (Tao specifically noted substantial AI input in the argument) together with the verifiability enabled by Lean formalization showcases a new paradigm of human-machine collaboration in proving frontier mathematics

2026-09-08 ~ 2026-09-08 · 6 related posts

Full story(13 episodes)→

• Episode 1: Terence Tao Proposes Keeping Some Open Math Problems Off-Limits to AI(2026-09-03, 2 posts)
• Episode 2: Rumors Claim Claude Solved Navier-Stokes; Terence Tao Responds(2026-09-05, 9 posts)
• Episode 3: Rumor: Anthropic Has Solved Navier-Stokes with Claude(2026-09-06, 2 posts)
• Episode 4: Terry Tao slams closed labs' theorem-proving as viral marketing(2026-09-06, 2 posts)
• Episode 5: Claude Did Not Solve Navier-Stokes, Clarifies Terence Tao(2026-09-06, 2 posts)
• Episode 6: AI-assisted proof of irrationality sparks professional-vs-amateur feud in math community(2026-09-07, 9 posts)
• Episode 7: Mathematicians Accuse OpenAI's Astra Math Results of Research Misconduct(2026-09-07, 2 posts)
• Episode 8: Terence Tao's latest AI remarks spark buzz, Gary Marcus calls them 'fire'(2026-09-08, 2 posts)
• Episode 9: Rex Douglass Calls 'Not Real Math' Arguments Goalpost-Shifting in AI Debate(2026-09-08, 5 posts)
• Episode 10: Rumors swirl that Claude may have solved the Navier-Stokes millennium problem(2026-09-08, 3 posts)
• Episode 11: Rumors swirl that OpenAI solved the Navier-Stokes millennium problem(2026-09-08, 25 posts)
• Episode 12: Tao hails AI-assisted blow-up breakthrough on model fluid equations, formalized in Lean(2026-09-08, 6 posts)
• Episode 13: OpenAI Faces Backlash Over Navier-Stokes Credit Dispute(2026-09-08, 4 posts)

• [source] Tao Flags Major Break Toward Navier-Stokes Blowup, Formalized in Lean via Autoformalization Agents — peterjliu · 2026-09-08
• Fluid Regularity Landscape Moving Fast: Tao Says Smooth NS Now Looks Feasible — basedjensen · 2026-09-08
• Terence Tao blogs on Buckmaster and Alpöge's blow-up solutions to fluid equations — LucaAmb · 2026-09-08
• [source] Terence Tao hails AI-assisted math breakthrough, says methods could extend to Navier-Stokes — Hesamation · 2026-09-08

2 near-duplicate retellings: Singularitarian · MannyKayy