  We introduce ProofNet, a benchmark for autoformalization and formal proving
of undergraduate-level mathematics. The ProofNet benchmarks consists of 371
examples, each consisting of a formal theorem statement in Lean 3, a natural
language theorem statement, and a natural language proof. The problems are
primarily drawn from popular undergraduate pure mathematics textbooks and cover
topics such as real and complex analysis, linear algebra, abstract algebra, and
topology. We intend for ProofNet to be a challenging benchmark that will drive
progress in autoformalization and automatic theorem proving. We report baseline
results on statement autoformalization via in-context learning. Moreover, we
introduce two novel statement autoformalization methods: prompt retrieval and
distilled backtranslation.
