Navier news and milestones

"Hey, the news is talking about how AI has proven the breakdown of a solution to one of the 'Millennium Prize Problems(1)', a super-difficult math problem with a million-dollar b…

OpenAI's claimed proof of the Navier-Stokes problem is a mathematical tour de force, but any real-world applications may be years away-if they ever arrive at all

Physicists and mathematicians are going beyond the classic equations of fluid dynamics to understand turbulence - often with the help of AI.

On September 1, 2026: LANCE: I'm surprised you haven't blogged about OpenAI solving 10 open math problems. BILL: If I post every time an op...

Inside OpenAI's Navier-Stokes proof: an exact covariance bound, a Lean proof and an 8DB research test that keeps conclusions tied to their evidence.

OpenAI's claimed Navier-Stokes blowup proof, unpacked for readers with undergraduate maths and physics: the construction, what Lean does and doesn't verify, and the ethics.

The Millennium Prize Problems were unveiled by the Clay Mathematics Institute (CMI) at a meeting in Paris in 2000 to celebrate

OpenAI's Sébastien Bubeck gives his side of the Navier-Stokes credit dispute and apologises for a remark. Sam Altman backs him.

When OpenAI released their proof that solutions to the Navier-Stokes equations can blow up in finite time, they also released a formal proof in Lean 4.

On the Navier-Stokes Millennium Prize Problem introduces an impressive result from OpenAI, who used an unreleased model to produce a resolution to the Navier-Stokes existence and…

How much information can be searched, structured and verified before a human lawyer has to look at it?

There's been a lot of buzz about Navier-Stokes. If you're not a math major and not super familiar with computational fluid dynamics. Here is the guide that you've been looking fo…

A concentrating 3D vortex. Trails spiral in as the core slims. Illustration, not a solver.

I spent much of the weekend talking with the team who did this work. Seb--and everyone else--acted with integrity and generosity throughout.Initially we believed the other team h…

I would like to clarify a few things:1) The screenshot is my reaching out to Levent to coordinate our releases. I hope it's clear from the message that we came in with the best p…

Improve the model for everyone

A landmark announcement by the frontier AI lab has been overshadowed by accusations of impropriety.

Navier-Stokes equations. What's the problem? What progress is being made? Is there Ai espionage going on?

There's some exciting very recent work by Alpöge and Buckmaster, building upon prior work by Córdoba and Martínez-Zoroa, in the general topic around the infamous global regularit…