Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment
cs.AI, cs.DM, cs.MA
Submitted: 2026-08-24
Updated: 2026-09-14
Comments: 47 pages, 16 figures, 3 tables. Source code: https://github.com/dualverse-ai/station. Agent dialogues and proofs: https://dualverse-ai.github.io/station_data_v2/
Code: https://github.com/dualverse-ai/station
License: http://creativecommons.org/licenses/by-nc-sa/4.0/
The gist: We study autonomous mathematical discovery in the Station, an open-world multi-agent environment in which AI agents from different model families pursue a shared research goal without a central
Terminology
Abstract
We study autonomous mathematical discovery in the Station, an open-world multi-agent environment in which AI agents from different model families pursue a shared research goal without a central coordinator or scripted pipeline. Agents choose their own research directions, conduct experiments, collaborate and publish papers. These papers accumulate into a shared body of knowledge that later agents can read, cite and extend. We evaluated the Station on 12 mathematical construction problems from the AlphaEvolve study and two additional case studies. Five of the 12 problems yielded results novel relative to the prior literature: a new infinite family of finite field Kakeya sets, new exact 604-point kissing configurations in eleven dimensions, improved bounds for the discretized Kakeya needle and sign uncertainty problems, and a substantially improved lower bound for Erdős's minimum overlap problem. Agents also discovered novel infinite families for Book Ramsey numbers. Their research extended beyond searching for high-scoring constructions: agents developed explanations of their findings and proved theorems outside the assigned tasks. These explanations guided further discoveries and were preserved in the agents' papers, making the underlying insights easier for external researchers to understand and build upon. All presented discoveries are supported by exact constructions or proofs formally verified in Lean. We release the source code, full agent dialogues, papers and verification code, providing a transparent record of how these discoveries emerged.
Sources
- AlphaEvolve: A coding agent for scientific and algorithmic discovery
- A solution to Crouzeix's conjecture
- The Station: An Open-World Environment for AI-Driven Discovery
- Mathematical exploration and discovery at scale
- Sharp density bounds on the finite field Kakeya problem
- The minimum overlap problem revisited
- Structured Scaling of AI Discovery Across Diverse Scientific Domains
- AI-Assisted Discovery of Convex Relaxations via Dual Agents
- Highly symmetric lines
- Harnessing the Collective Intelligence of AI Agents in the Wild for New Discoveries
- Classification of independent sets in signed Johnson graphs and applications to kissing arrangements
- Structure of kissing arrangements in ${\mathbb R}^{12}$ and a place for the $841$st sphere
- Measuring Progress in Reasoning Toward Mathematical Discovery with Automatic Verification
- An optimal uncertainty principle in twelve dimensions via modular forms
- Connection between the Lieb--Thirring conjecture for Schroedinger operators and an isoperimetric problem for ovals on the plane
- On an isoperimetric inequality for a Schrodinger operator depending on the curvature of a loop
- One-dimensional projective structures, convex curves and the ovals of Benguria & Loss
- An improved bound for the ground state of a Schr\"odinger operator on a loop
- Improved Lower Bound for Difference Bases
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