News for hackers. Stuff that matters.
Re:On the Navier–Stokes Millennium Prize Problem by jgbuddy on Tuesday September 08, 2026 @01:36PM (#49613664)
Here's the formalization / lean verification: https://github.com/openai/NavierStokesAndEuler
Re:On the Navier–Stokes Millennium Prize Problem by stabbles on Tuesday September 08, 2026 @01:41PM (#49613748)
341k lines of lean without comments
Re:On the Navier–Stokes Millennium Prize Problem by kzrdude on Tuesday September 08, 2026 @02:30PM (#49614614)
The construction is that there is one file you need read and verify, the challenge file. If you've verified that file and trust that your lean compiler works correctly, the proof will be correct.

That file should be https://github.com/openai/NavierStokesAndEuler/blob/main/Com... in this case (286 lines).

Re:On the Navier–Stokes Millennium Prize Problem by jgbuddy on Tuesday September 08, 2026 @01:47PM (#49613863)
Had no idea this was what lean looked like- that's mind blowing. I'm not even sure how someone would critique this if they wanted to
Re:On the Navier–Stokes Millennium Prize Problem by frotaur on Tuesday September 08, 2026 @02:05PM (#49614175)
The point of lean proofs (as it stands) is simply one bit of information: that a given mathematical statement is indeed true.

It's a way to be absolutely certain (modulo bugs in the lean kernel) that a proof you came up for a statement is indeed correct. It is really not meant to be analyzed, much less now that they are fully llm written.

Re:On the Navier–Stokes Millennium Prize Problem by aizk on Tuesday September 08, 2026 @03:07PM (#49615210)
Well, how do we know there aren't errors in their construction within the lean code? Does it just "not compile" or something, or is it deeper / more fundemental than that.
Re:On the Navier–Stokes Millennium Prize Problem by Jblx2 on Tuesday September 08, 2026 @09:23PM (#49619546)
Re:On the Navier–Stokes Millennium Prize Problem by frotaur on Wednesday September 09, 2026 @04:27AM (#49623173)
that's essentially it, if the proof is incorrect it does not compile which signifies a problem in some step.