# Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory

arXiv: https://arxiv.org/abs/2607.06447 · HTML: https://mlsanity.com/paper/2607.06447/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 7 of its 49 references that are in the map.
- First posted on arXiv 7 Jul 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Builds on (most cited first, 7 of 7)

- [Meta-Harness: End-to-End Optimization of Model Harnesses](https://mlsanity.com/paper/2603.28052/) (2026)
- [Towards Autonomous Mathematics Research](https://mlsanity.com/paper/2602.10177/) (2026)
- [Automated Conjecture Resolution with Formal Verification](https://mlsanity.com/paper/2604.03789/) (2026)
- [AI co-mathematician: Accelerating mathematicians with agentic AI](https://mlsanity.com/paper/2605.06651/) (2026)
- [QED: An Open-Source Multi-Agent System for Generating Mathematical Proofs on Open Problems](https://mlsanity.com/paper/2604.24021/) (2026)
- [First Proof Second Batch](https://mlsanity.com/paper/2606.18119/) (2026)
- [Matlas: A Semantic Search Engine for Mathematics](https://mlsanity.com/paper/2604.17484/) (2026)

## Built on by (most cited first, 8 of 8)

- [Albilich: Steerable Proof-State Orchestration for LLM-Based Mathematical Research with CAS Integration](https://mlsanity.com/paper/2607.27705/) (2026)
- [Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science](https://mlsanity.com/paper/2609.15983/) (2026)
- [Andy: A Mathematical Agent for Rigorous Proof and Autonomous Research](https://mlsanity.com/paper/2608.15052/) (2026)
- [EULER: Exploring Underused Links with Evidence-Checked Return for Multi-Agent Mathematical Discovery](https://mlsanity.com/paper/2609.00032/) (2026)
- [TCSAlgBench: Benchmarking Automated Proving for Research-Level Theoretical Computer Science](https://mlsanity.com/paper/2609.35606/) (2026)
- [Continual Graph Memory for Mathematical Research Agents](https://mlsanity.com/paper/2610.02945/) (2026)
- [Cost-Efficient Theorem Proving via Agent Orchestration in Program Verification](https://mlsanity.com/paper/2610.09681/) (2026)
- [Euler: Towards Human-Centered Multi-Agent Mathematical Discovery](https://mlsanity.com/paper/2610.19864/) (2026)

## Abstract (arXiv)

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.