# Euler: Towards Human-Centered Multi-Agent Mathematical Discovery

arXiv: https://arxiv.org/abs/2610.19864 · HTML: https://mlsanity.com/paper/2610.19864/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Educational agents and math problem solving, one of 16 directions in LLM agents and tool use.
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Placed in

- 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, 11 of 11)

- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [The AI Scientist-v2: Workshop-Level Automated Scientific Discovery via Agentic Tree Search](https://mlsanity.com/paper/2504.08066/) (2025)
- [Agentic Context Engineering: Evolving Contexts for Self-Improving Language Models](https://mlsanity.com/paper/2510.04618/) (2025)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [Automated Conjecture Resolution with Formal Verification](https://mlsanity.com/paper/2604.03789/) (2026)
- [Neuro-Symbolic Artificial Intelligence: Towards Improving the Reasoning Abilities of Large Language Models](https://mlsanity.com/paper/2508.13678/) (2025)
- [Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory](https://mlsanity.com/paper/2607.06447/) (2026)
- [MechMath Agent Team: LLM Driven Agents for Mathematical Research](https://mlsanity.com/paper/2607.04394/) (2026)
- [Albilich: Steerable Proof-State Orchestration for LLM-Based Mathematical Research with CAS Integration](https://mlsanity.com/paper/2607.27705/) (2026)
- [Initialization-dependent BFGS trial rates for tilted absolute values](https://mlsanity.com/paper/2609.09872/) (2026)
- [Magenta: Closing the Loop Between Mathematical Reasoning and Lean Verification](https://mlsanity.com/paper/2609.11319/) (2026)

## Abstract (arXiv)

Mathematical research drives scientific discovery, and recent advances in AI for mathematics have shown that language-model agents can solve challenging problems and develop substantial mathematical proofs. Yet much of today's AI-for-mathematics work centers on obtaining a final answer. This emphasis leaves the exploration behind a result difficult for researchers to understand, while long-running investigations face fragmented context and the risk of unsupported claims propagating across reasoning steps. We present Euler, a human-centered mathematical research system built around a shared, structured representation of the research process. Euler organizes mathematical statements, assumptions, proof dependencies, alternative approaches, failed attempts, and verification evidence into connected research graphs. This representation allows researchers to trace how results are developed and supplies agents with persistent, task-relevant knowledge for planning, collaboration, and verification across sessions. Researchers can also select a graph node linked to a saved team state, revisit the agents' earlier reasoning, and explore alternative directions through continued interaction. We illustrate Euler's capabilities through three mathematical research case studies and describe the implemented system and its software validation.