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Millennium Prize Problems status board

Clay still marks Navier–Stokes Unsolved. Quanta reported a Lean-checked blow-up claim on 8 Sep 2026. One page that keeps those facts separate and shows all seven Millennium problems.

Updated 9 Sept 2026
Waves of cloud stacked in a Kelvin–Helmholtz pattern at sunset over Hartford
Hero image for the Navier–Stokes / Millennium Prize status page. · Paul Danese · Wikimedia Commons

Clay Millennium Prize · Navier–Stokes

Is Navier–Stokes solved?

Short answer: Clay’s prize page still says no. Quanta’s September 2026 coverage says researchers announced a formalized “blow-up” proof. This page shows both facts so you do not mash them into one word.

Checked 2026-09-09.

Waves of cloud stacked in a Kelvin–Helmholtz pattern at sunset over Hartford

Fluids make patterns like this in the sky. The Millennium Prize question is about the equations that try to describe that kind of motion.

Photo: Paul Danese / Wikimedia Commons (CC0)

Two facts that both stay true

Quanta Magazine

8 Sep 2026

Lean-checked blow-up announcement

News layer: a claimed singularity

Quanta reported that OpenAI researchers announced a Lean-checked proof that the 3D Navier–Stokes equations can blow up. The same article covers a parallel AI-assisted effort, fights over who did what, and OpenAI declining Clay’s prize.

What “blow-up” means here

Diagram of fluid flow regimes past circular cylinders, from smooth to turbulent

A blow-up would mean the math model allows a spot of infinite speed in finite time. That is a claim about the equations, not about water in a sink.

Photo: John H. Lienhard IV / Wikimedia Commons (public domain)

The prize question asks whether an idealized fluid, following these equations with smooth forces and no walls, can ever develop a point that spins infinitely fast in finite time. That singularity is the blow-up. Quanta’s story is about researchers claiming they proved such a singularity exists. Clay has not changed its Unsolved badge.

What to say if someone asks

Clay still lists Navier–Stokes as Unsolved for the Millennium Prize. In September 2026, Quanta reported a Lean-checked blow-up claim that mathematicians are still sorting, including credit. Say both parts. Do not answer with a single yes or no.

All seven Millennium Prize problems

Tap a row for the one-line status. The highlighted row is the live fight.

  • Clay: Unsolved. Quanta (8 Sep 2026): Lean-checked blow-up claim, prize not claimed.

Sources