Solving some formal math olympiad problems
This is pretty cool!To be fair, however, these proofs are using several of the automatic proving methods built into Lean, like linarith, nlinarith, field_simp, and so on. Each of these are hundreds of lines of manually tweaked heuristics.It's still quite interesting. I think if we had a good integration of AI methods into the Lean runtime itself the theorem prover could be excellent. You could have a cooperative model where the human mathematician writes down statements, and the AI fleshes out a proof or catches typos that you make. Right now Lean has similar functionality but the automatic proving isn't as good as it could be.I just wish the Lean community wasn't stuck on the Lean 3 -> Lean 4 migration for the past year. I'm getting flashbacks of Python 2 -> Python 3 ....