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An AI system produces a formally checked fluid proof

What changedOpenAI released an AI-generated proof that a smoothly forced three-dimensional fluid can develop an infinite-speed singularity in finite time. The 166-page argument comes with a public Lean formalization. That makes the logic machine-checkable, but mathematicians still need to confirm that the formal statement and interpretation fully match the famous problem.

Repository card for the public Lean certificates accompanying the Navier-Stokes and Euler results

The useful part

Why it matters

A machine-generated result on a 90-year-old Millennium problem is an unusually strong test of whether frontier systems can produce new, checkable mathematics rather than only summarize it.

Keep in mind

Good to know

The mathematical community has not yet completed independent expert review. Formal checking validates the encoded statements and proof steps, not whether the formalization captures every intended interpretation.

Evidence

Primary source

OpenAI

Read the complete 9 September 2026 edition