Danus uses fact-graph memory to coordinate AI math agents

Scaling LLM-based agents for research-level mathematics has been a challenge due to the difficulty of coordinating parallel proof searches while keeping intermediate claims organized. In a new paper (arXiv:2607.06447), researchers introduce Danus, an orchestration system built around a shared fact-graph memory. A main agent handles planning and coordination, multiple worker agents execute proof search in parallel, and a stateless verifier validates each mathematical claim before it is admitted into the fact graph. Every verified fact is stored with its proof and logical dependencies, allowing the system to incrementally build long arguments while maintaining a coherent proof state. The main agent periodically summarizes progress and can redirect workers toward promising directions, also enabling interaction with human mathematicians through progress reports.

The team evaluated Danus on six research-level case studies spanning algebraic geometry, singularity theory, and combinatorics. Results demonstrate that the fact-graph memory mechanism enables the system to construct long, detailed mathematical proofs effectively, pointing toward a scalable approach for long-horizon research problems. The system is open source, providing a foundation for further experimentation. By combining parallel search with a centralized memory of verified facts, Danus offers a practical path toward AI-assisted theorem proving and could accelerate discovery in fields that rely on complex mathematical reasoning.