# Discovering mathematical concepts through a multi-agent system

arXiv: https://arxiv.org/abs/2603.04528 · HTML: https://mlsanity.com/paper/2603.04528/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 67 references that are in the map.
- First posted on arXiv 4 Mar 2026.

## Builds on (most cited first, 13 of 13)

- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Autoformalization with Large Language Models](https://mlsanity.com/paper/2205.12615/) (2022)
- [Formal Mathematics Statement Curriculum Learning](https://mlsanity.com/paper/2202.01344/) (2022)
- [Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving](https://mlsanity.com/paper/2507.23726/) (2025)
- [Ablation Studies in Artificial Neural Networks](https://mlsanity.com/paper/1901.08644/) (2019)
- [Lean Copilot: Large Language Models as Copilots for Theorem Proving in Lean](https://mlsanity.com/paper/2404.12534/) (2024)
- [Aristotle: IMO-level Automated Theorem Proving](https://mlsanity.com/paper/2510.01346/) (2025)
- [Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the ErdHos Problems](https://mlsanity.com/paper/2601.22401/) (2026)
- [Machine learning and information theory concepts towards an AI Mathematician](https://mlsanity.com/paper/2403.04571/) (2024)
- [The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale](https://mlsanity.com/paper/2512.07087/) (2025)
- [What makes math problems hard for reinforcement learning: a case study](https://mlsanity.com/paper/2408.15332/) (2024)
- [Mathematical conjecture generation using machine intelligence](https://mlsanity.com/paper/2306.07277/) (2023)

## Built on by (most cited first, 1 of 1)

- [NeuroClaw Technical Report](https://mlsanity.com/paper/2604.24696/) (2026)

## Abstract (arXiv)

Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this observation. Our system, conceived with research in mind, poses its own conjectures and then attempts to prove them, making decisions informed by this feedback and an evolving data distribution. Inspired by the history of Euler's conjecture for polyhedra and an open challenge in the literature, we benchmark with the task of autonomously recovering the concept of homology from polyhedral data and knowledge of linear algebra. Our system completes this learning problem. Most importantly, the experiments are ablations, statistically testing the value of the complete dynamic and controlling for experimental setup. They support our main claim: that the optimisation of the right combination of local processes can lead to surprisingly well-aligned notions of mathematical interestingness.