Lean use in AlphaProof was something of a crutch (not saying this as a bad thing). Very specialized, very narrow with little use outside any other domain.
On the other hand, if you can achieve the same with general RL techniques and natural language then other hard-to-verify (a whole lot) domains are on the table.
This is a wildly uninformed take. Even today there are plenty of basic statements which LLM’s can produce English language proofs of that have not been formalized.
I said that if language models become capable enough of not needing a crutch, then adding one afterwards isn't a big deal. What exactly do you think Alphaproof is? Much worse LLMs were already doing what you are saying. There's a reason it preceded this and not the other way around.
I’m saying that the view of formalized languages as a crutch is backwards; they are in fact a challenging constraint.
The most extreme version of my position is that there is no such thing as a rigorous natural language proof, and that humans will view the relative informality of 20th and early 21st century mathematics much like we currently view the informality of pre-18th century mathematics.
It was there so the generator wouldn't go off the rails hallucinating and candidates could be verified. And the solving still took days. Take that away and the generator doesn't get anywhere near silver with all the time in the world.
That is the definition of a crutch. The generator was smart enough to produce promising candidates with enough brute force trial and error, but that's it. Without Lean, it wouldn't have worked.