In the OpenAI Math Drop some papers have Lean proofs, others don't, including L = RL = BPL. Why is it hard to formalize results on complexity classes? Let's consider an example, Lautemann's proof that BPP is in \(\Sigma^p_2\). It's a beautiful proof because it comes down to a single formula. I gave the full proof in a 2025 post, but to remind you, here is the setup. Let \(B\) be in BPP, accepted by a probabilistic polynomial-time Turing machine \(M\) with error bounded by \(2^{-n}\). Let \(A(x,r)\) be true iff \(M(x)\) using random tape \(r\) accepts. \(A(x,r)\) is deterministically...