# Continual Graph Memory for Mathematical Research Agents

arXiv: https://arxiv.org/abs/2610.02945 · HTML: https://mlsanity.com/paper/2610.02945/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Agent memory systems, one of 16 directions in LLM agents and tool use.
- Builds on 14 of its 34 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Placed in

- LLM agents and tool use / [Agent memory systems](https://mlsanity.com/agents/agent-memory-systems/)

## Builds on (most cited first, 14 of 14)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [A-MEM: Agentic Memory for LLM Agents](https://mlsanity.com/paper/2502.12110/) (2025)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [CoEvoSkills: Self-Evolving Agent Skills via Co-Evolutionary Verification](https://mlsanity.com/paper/2604.01687/) (2026)
- [G-Memory: Tracing Hierarchical Memory for Multi-Agent Systems](https://mlsanity.com/paper/2506.07398/) (2025)
- [Automated Conjecture Resolution with Formal Verification](https://mlsanity.com/paper/2604.03789/) (2026)
- [Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory](https://mlsanity.com/paper/2607.06447/) (2026)
- [Albilich: Steerable Proof-State Orchestration for LLM-Based Mathematical Research with CAS Integration](https://mlsanity.com/paper/2607.27705/) (2026)
- [ISM:Self-Improving Strategy Memory for Continual Mathematical Reasoning](https://mlsanity.com/paper/2606.31191/) (2026)

## Abstract (arXiv)

Using frontier agent harnesses to tackle mathematical research problems has emerged as an effective means of advancing mathematics. However, solving frontier problems in mathematics may require a massive number of agents working in parallel for extended periods to construct proofs, thereby generating an enormous volume of intermediate proof results. Organizing these intermediate results throughout a long-horizon proof-search process and reusing knowledge gained from prior explorations remain major challenges. We present Ansatz, a mathematical research agent built around Continual Graph Memory, a graph-based, evolvable, cross-problem mathematical research memory system that explicitly organizes the entire proof search process and reuses information from exploration trajectories of previous problems. Specifically, we develop a unified graph memory that represents all intermediate exploration results, including facts, plans, and counterexamples, together with edges that explicitly represent the relationships among them; dependency-aware retrieval supplies precisely targeted local context; an evidence-sensitive curator updates the research frontier and distills lessons from prior attempts; and scoped recall surfaces earlier statements and negative findings for local re-proving rather than uncritical reuse. Experiments cover runs across all ten First Proof Second Batch problems, together with four component studies. Ansatz reports closure on all ten research tasks, demonstrating its ability to sustain and resume long-horizon mathematical search. Beyond these problems, Ansatz also produces solutions to the Jamison caterpillar conjecture and ErdHos Problems 289, 348, and 488 without human intervention, and makes partial progress on several open problems, illustrating its strong ability to solve open mathematical research problems.