Even then this seems much more promising to me compared to other areas. Writing theorem statements is much much easier than coming up with proofs so it's not a big deal if a human has to do that. And once that's done getting a correct proof out of an LLM/AI model can be done fully automatically (assuming you do get a proof out of it though!)
> Even then this seems much more promising to me compared to other areas. Writing theorem statements is much much easier than coming up with proofs so it's not a big deal if a human has to do that.
Not at all. Theorem crafting is hard. What's easy is standing up and proving a mathematical strawman which may or may not have any relation to the original problem.
I'm not sure this is true. Encoding theorems in dependent types takes a lot of expertise.
Even without the Lean technical details, a lot of math theorems just don't mean anything to most people. For example, I have no idea what the Navier-Stokes theorem is saying. So, I would not be able to tell you if a Lean encoding of the theorem is correct. (Unless of course, it is trivially broken, since as assuming False.)
There is no "Navier-Stokes theorem". There is a famous class of open problems whether Navier-Stokes equations are well-posed (have solutions that don't explode in finite time) for various initial data, but that type of question is completely irrelevant for any practical purposes.
I do share the feeling though. As a non-expert, I have no idea what the existing, allegedly practically relevant, formalizations of distributed algorithms actually guarantee.
