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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.A 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. 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