OpenAI Blog
GamePad: A learning environment for theorem proving
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OpenAI Blog
Sep 7, 2020
Generative language modeling for automated theorem proving
arXiv Machine Learning
Jun 25
Discovering New Theorems via LLMs with In-Context Proof Learning in Lean
arXiv:2509. 14274v3 Announce Type: replace Abstract: Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving.
arXiv AI
Jun 30
Self-Supervised Theorem Discovery in a Formal Axiomatic System
arXiv:2606. 28747v1 Announce Type: new Abstract: Recent artificial intelligence (AI) systems have shown remarkable progress in mathematical reasoning.
arXiv AI
Aug 28
ProofEvolve: Neuro-Symbolic Evolution for Formal Automated Theorem Proving
ProofEvolve is a neuro‑symbolic framework that evolves formally verified symbolic proof structures alongside neural models to expand the knowledge boundary in automated theorem proving. The neural component proposes variation operators such as decompositions, repairs, and schema recombinations, while the Lean kernel verifies every proof transition, ensuring formal soundness. Across three competition‑level Lean benchmarks, ProofEvolve achieves the highest average solve rate among evaluated proof systems.
arXiv AI
Jul 17
MathCoPilot: An Interactive System for Human-AI Symbiotic Paradigm of Mathematical Research
arXiv:2607. 14582v1 Announce Type: new Abstract: Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition.
arXiv Computation and Language
Aug 27
MathAdv: What Theorem Provers Know, Reason, Formalize, and Generalize
MathAdv is a diagnostic benchmark for formal theorem proving that covers 13 undergraduate- and graduate-level mathematics domains. It includes Lean 4 proofs and up to three auxiliary tasks—multiple-choice questions, fill-in-the-blank problems, and expert-crafted transformations—to probe knowledge, informal reasoning, and robustness to problem presentation. Evaluation of current theorem provers shows formalization is a major bottleneck, performance varies by domain, natural-language guidance can help or hinder models, and equivalent reformulations reveal significant robustness gaps.