Solving (Some) Formal Math Olympiad Problems

We built a neural theorem prover for Lean that learned to solve a variety of challenging high-school olympiad problems, including problems from the AMC12 and AIME competitions, as well as two problems adapted from the IMO.[1] The prover uses a language model to find proofs of formal statements. Each time we find a new proof, we use it as new training data, which improves the neural network and enables it to iteratively find solutions to harder and harder statements. We achieved a new state-of-the-art (41.2% vs 29.3%) on the miniF2F benchmark, a challenging collection of high-school olympiad problems. Our approach, which we call statement curriculum learning, consists of manually collecting a set of statements of varying difficulty levels (without proof) where the hardest statements are similar to the benchmark we target.