Zichen Wang
Publications
Automated Conjecture Resolution with Formal Verification
Recent advances in large language models have significantly improved their ability to perform mathematical reasoning, extending from elementary problem solving to increasingly capable performance on research-level problems. However, reliably solving and verifying such problems remains challenging due to the inherent ambiguity of natural language reasoning. In this paper, we propose an automated framework for tackling research-level mathematical problems that integrates natural language reasoning with formal verification, enabling end-to-end problem solving with minimal human intervention. Our framework consists of two components: an informal reasoning agent, Rethlas, and a formal verification agent, Archon. Rethlas mimics the workflow of human mathematicians by combining reasoning primitives with our theorem search engine, Matlas, to explore solution strategies and construct candidate proofs. Archon, equipped with our formal theorem search engine LeanSearch, translates informal arguments into formalized Lean 4 projects through structured task decomposition, iterative refinement, and automated proof synthesis, ensuring machine-checkable correctness. Using this framework, we automatically resolve an open problem in commutative algebra and formally verify the resulting proof in Lean 4 with essentially no human involvement. Our experiments demonstrate that strong theorem retrieval tools enable the discovery and application of cross-domain mathematical techniques, while the formal agent is capable of autonomously filling nontrivial gaps in informal arguments. More broadly, our work illustrates a promising paradigm for mathematical research in which informal and formal reasoning systems, equipped with theorem retrieval tools, operate in tandem to produce verifiable results, substantially reduce human effort, and offer a concrete instantiation of human-AI collaborative mathematical research.
M2F: Automated Formalization of Mathematical Literature at Scale
Automated formalization of mathematics enables mechanical verification but remains limited to isolated theorems and short snippets. Scaling to textbooks and research papers is largely unaddressed, as it requires managing cross-file dependencies, resolving imports, and ensuring that entire projects compile end-to-end. We present M2F (Math-to-Formal), the first agentic framework for end-to-end, project-scale autoformalization in Lean. The framework operates in two stages. The statement compilation stage splits the document into atomic blocks, orders them via inferred dependencies, and repairs declaration skeletons until the project compiles, allowing placeholders in proofs. The proof repair stage closes these holes under fixed signatures using goal-conditioned local edits. Throughout both stages, M2F keeps the verifier in the loop, committing edits only when toolchain feedback confirms improvement. In approximately three weeks, M2F converts long-form mathematical sources into a project-scale Lean library of 153,853 lines from 479 pages textbooks on real analysis and convex analysis, fully formalized as Lean declarations with accompanying proofs. This represents textbook-scale formalization at a pace that would typically require months or years of expert effort. On FATE-H, we achieve $96\%$ proof success (vs.\ $80\%$ for a strong baseline). Together, these results demonstrate that practical, large-scale automated formalization of mathematical literature is within reach. The full generated Lean code from our runs is available at https://github.com/optsuite/ReasBook.git.