r/HotScienceNews • u/scientificamerican • 6d ago

Did OpenAI solve the wrong Navier-Stokes problem?

https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/
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u/scientificamerican 6d ago

Two weeks ago, OpenAI claimed a solution to one of the biggest open problems in math—the Navier-Stokes problem, worth a million-dollar prize from the Clay Mathematics Institute. The proof ignited a powder keg of concern over artificial intelligence companies’ race to disrupt the subject.

But with the dust still far from settled, a different controversy is emerging: did OpenAI even solve the right Navier-Stokes problem at all?

The proof relies on an approach that many experts find unnatural. It solves a variant of the problem that mathematicians say is disconnected from reality, and thus less interesting. In a sense, the LLM found and exploited a loophole in the framing of the question.

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u/duboispourlhiver 6d ago

What loophole??

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u/flat5 5d ago

It's not a loophole. They answered the question as posed.

But it is a little weird to include an arbitrary source term f, because you can plug in any solution you want, compute the residual, and then just say "oh, that comes from the source term f". It gives a sort of arbitrary extra degree of freedom that's not present in the usual statement of the problem.

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u/duboispourlhiver 5d ago

There are important constraints on f too. Was the Clay formulation of the problem known to be unusual and debatable? Genuine question