Leheng Chen

Jihao Liu, Guoxiong Gao, Zeming Sun et al.

Recent LLM-based mathematical reasoning agents have begun to tackle research-level problems and, in several cases, have contributed to the resolution of open problems. However, scaling and orchestrating such agents effectively remains challenging, due to the difficulty of coordinating parallel proof search while keeping intermediate claims organized and reliable. In this paper, we propose Danus, an orchestration system for research-level mathematical reasoning centered on a shared fact graph as a global memory-management mechanism. Danus consists of a main agent that performs planning and coordination, multiple worker agents that carry out proof search in parallel, and a stateless verifier that checks proposed mathematical claims before they are admitted into the fact graph. Each verified fact is stored together with its proof and logical dependencies, allowing the system to build long arguments incrementally while keeping the shared proof state organized. The main agent periodically summarizes the evolving proof state, redirects workers across promising directions, and supports interaction with human mathematicians through progress reports. We evaluate Danus through six research-level case studies in algebraic geometry, singularity theory, and combinatorics, illustrating how the fact-graph memory mechanism enables Danus to construct long, detailed mathematical proofs. Our results suggest that fact-graph-based orchestration provides an effective route toward scaling mathematical reasoning agents for long-horizon research problems. Danus is open source at https://github.com/frenzymath/Danus.

Haocheng Ju, Guoxiong Gao, Jiedong Jiang et al.

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.

Haocheng Ju, Leheng Chen, Peihao Wu et al.

Retrieving mathematical knowledge is a central task in both human-driven research, such as determining whether a result already exists, finding related results, and identifying historical origins, and in emerging AI systems for mathematics, where reliable grounding is essential. However, the scale and structure of the mathematical literature pose significant challenges: results are distributed across millions of documents, and individual statements are often difficult to interpret in isolation due to their dependence on prior definitions and theorems. In this paper, we introduce Matlas, a semantic search engine for mathematical statements. Matlas is built on a large-scale corpus of 8.07 million statements extracted from 435K peer-reviewed papers spanning 1826 to 2025, drawn from a curated set of 180 journals selected using an ICM citation-based criterion, together with 1.9K textbooks. From these sources, we extract mathematical statements together with their dependencies, construct document-level dependency graphs, and recursively unfold statements in topological order to produce more self-contained representations. On top of this corpus, we develop a semantic retrieval system that enables efficient search for mathematical results using natural language queries. We hope that Matlas can improve the efficiency of theorem retrieval for mathematicians and provide a structured source of grounding for AI systems tackling research-level mathematical problems, and serve as part of the infrastructure for mathematical knowledge retrieval.