OpenAI's $1M Navier-Stokes Proof May Have Solved the Wrong Problem
Did OpenAI solve the wrong Navier-Stokes problem?
OpenAI's LLM-generated proof of the Navier-Stokes problem exploits an optional external force, a loophole that mathematicians say makes it irrelevant to the real problem. A new proof shows the method can never be extended to solve the full equations, sparking debate over whether the Clay Institute's formulation was flawed and what this means for AI's role in mathematics.
The most important problem is unsolved. The Clay problem is settled, but the main problem for the Navier-Stokes equations is not.
- jonlong
No, OpenAI did not solve the "wrong" Navier-Stokes problem. OpenAI did not solve the hardest version of the problem (unforced blow-up), but did give a solution to the Clay Millennium Prize Problem as written and understood, choosing the explicitly allowed forced option.
SciAm writes "in a sense, the LLM found and exploited a loophole in the framing of the question". This is pure sensationalism. Choosing option (C) (out of an explicit list of four options) is neither a "loophole" nor something "found by the LLM"; everyone involved knew this was the option they were pursuing.
With the grumbling out the way, there is some actual scientific content to the article: there's a strong argument that OpenAI's method will not extend to the unforced case, leaving our understanding of NS incomplete. This negative result is itself new and interesting (and predicated entirely on the solution found by OpenAI)!
- emmelaich
- bmacho
Article says that there are 2 formulations of the NS problem and both are interesting: one is about fluid behaviour with no external forces, other is about fluid behaviour with external forces.
For a counter-example the latter is easier since you can have a tricky external forcefield.
- ChickeNES
So what they are saying is that humans, in this case Charles Fefferman (a math prodigy, going by his history), failed to specify the problem correctly?
- yababa_y
I will admit that when I heard they only had forced blowup I went back to sleep (but I've never been more that cursorily interested in analysis).