Explore open math problems with a multi-agent system
Submission history. Task: Submission history Access Paper: View PDF HTML (experimental) TeX Source Current browse context: References & Citations NASA ADS Google Scholar Semantic Scholar BibTeX formatted citation Bookmark Author Venue Institution Topic arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.; tools: custom-built or unnamed agent. Human role: The original post does not say how a person stayed involved.; limitations: The workflow requires a robust formal verification system like Lean to validate agent-generated proofs, as autonomous discovery carries high risks of hallucination or logical errors. Integration depends on agents from different model families being able to interpret and build upon each other's published papers within the shared environment. The system operates without a central coordinator, meaning success relies on emergent collaboration rather than scripted pipelines, which may lead to unpredictable resource usage or redundant efforts..
Tools
custom-built or unnamed agent
Published on Agent Work Atlas:
Overview
Submission history
Workflow
Submission history Access Paper: View PDF HTML (experimental) TeX Source Current browse context: References & Citations NASA ADS Google Scholar Semantic Scholar BibTeX formatted citation Bookmark Author Venue Institution Topic arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Reported result
The system produced novel mathematical results in five of the twelve assigned problems, including new infinite families of finite field Kakeya sets and improved bounds for Erdős's minimum overlap problem. Agents also discovered novel infinite families for Book Ramsey numbers and generated explanations and theorems outside the assigned tasks. All discoveries were supported by exact constructions or proofs formally verified in Lean, with source code, dialogues, and papers released for transparency.
Human role
The original post does not say how a person stayed involved.
Limitations
The workflow requires a robust formal verification system like Lean to validate agent-generated proofs, as autonomous discovery carries high risks of hallucination or logical errors. Integration depends on agents from different model families being able to interpret and build upon each other's published papers within the shared environment. The system operates without a central coordinator, meaning success relies on emergent collaboration rather than scripted pipelines, which may lead to unpredictable resource usage or redundant efforts.
Try it
I want to replicate the 'Station' multi-agent mathematical discovery workflow for a specific open problem in combinatorics. Inputs: - Target Problem: [Insert specific mathematical conjecture or construction problem, e.g., 'Find a new lower bound for the Ramsey number R(5,5)'] - Verification Tool: Lean 4 environment with standard mathlib. - Agent Configuration: Two distinct LLM agents (e.g., Agent A: Reasoning-focused, Agent B: Code-generation focused). Steps: 1. Initialize a shared workspace where agents can read and write 'paper' files. 2. Prompt Agent A to propose a construction strategy and Agent B to implement it in Lean. 3. Run an iterative loop: Agent A critiques Agent B's code, Agent B refines the proof, and both update the shared paper. 4. Stop when a formal proof is verified in Lean or after [Max Iterations]. Deliverables: - A Lean 4 file containing the verified proof or counterexample. - A markdown 'paper' summarizing the discovery process. Safeguards: - Do not publish or submit any results without human review of the Lean verification output. - If the agents fail to converge after [Max Iterations], halt and report the state of the shared knowledge base. - Ensure no external API calls are made during the experiment to maintain reproducibility.
Source reports are not independently verified. Publication date is the catalog publication date, not the original article date.