Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory

2026-07-07

AI Summary

This work proposes a multi-agent collaborative framework grounded in a shared fact graph to tackle research-level mathematical problems requiring extended, complex reasoning. Orchestrated by a central planning agent, multiple worker agents concurrently explore proof pathways, while a stateless verifier ensures the correctness of all propositions committed to the fact graph. Serving as a global memory mechanism, the fact graph enables logical dependency tracking, incremental construction of long-chain arguments, and dynamic redirection of search efforts. The system further incorporates automated summarization and a human-in-the-loop interface. Evaluated on six challenging cases from algebraic geometry, singularity theory, and combinatorics, the framework successfully generates rigorous, complete proofs, demonstrating its scalability and efficacy in advanced mathematical reasoning.

Abstract

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.

Problem

• mathematical reasoning
• agent orchestration
• fact-graph memory
• proof search
• research-level problems

Innovation

• fact-graph memory
• mathematical reasoning agents
• orchestration system
• parallel proof search
• verified claim management