There are rumors that a long-standing math problem, one of the Millennium Prize problems, has been solved.
The problem concerns technical properties of solutions to the Navier-Stokes equations [1], a set of equations that describe the dynamics of fluid flow. Popular accounts of the problem are often oversimplified and misleading.
Some reports will speak of the problem as “solving the Navier-Stokes equations.” The task is not to write down a closed-form solution, which can’t be done, or solve the equations numerically, which has been done for decades. The problem is to prove theoretical properties of solutions which are of little interest in practice.
There has been progress toward settling the Navier-Stokes problem. Terence Tao wrote a post on this yesterday.
What’s also interesting is the intrigue around the possible solution. A post this morning says
If I am reading this correctly, Tristan Buckmaster is alleging OAI has a resolution of Navier-Stokes … which maybe used info from Buckmaster and Levent Alpöge’s private Codex sessions.
Buckmaster asked OpenAI whether they used his private sessions and they have not responded. Update: Statement from OpenAI.
Personal note
This topic connects parts of my career spanning decades. My graduate work was in PDEs and I had some interest in the Navier-Stokes equations. Here are some notes I wrote back in the day.
Now I work more with privacy than with PDEs. The question of whether OpenAI uses private data, contradicting their stated policy, is more relevant to my current work than whether the Navier-Stokes equations have global regular solutions.
Related posts
[1] I never know whether to say equation or equations. You’ll hear both. You could think of Navier-Stokes as one vector-valued PDE or three scalar-valued equations.
John, you’re quite a gentleman. The importance of this intrigue you have so diplomatically introduced is..well…appropriately explosive.
Thanks for your post, and as always, for your blog.