  We explore the use of expert iteration in the context of language modeling
applied to formal mathematics. We show that at same compute budget, expert
iteration, by which we mean proof search interleaved with learning,
dramatically outperforms proof search only. We also observe that when applied
to a collection of formal statements of sufficiently varied difficulty, expert
iteration is capable of finding and solving a curriculum of increasingly
difficult problems, without the need for associated ground-truth proofs.
Finally, by applying this expert iteration to a manually curated set of problem
statements, we achieve state-of-the-art on the miniF2F benchmark, automatically
solving multiple challenging problems drawn from high school olympiads.
