QED: An Open-Source Multi-Agent System for Generating Mathematical Proofs on Open Problems

We present QED, an open-source multi-agent system that turns human-provided research questions into complete mathematical proofs without further human guidance. Its pipeline is designed to overcome common failures of single-query proof generation by separating planning, proving, and verification: a decomposition agent structures the proof search, prover agents generate candidate arguments, and verifier agents check correctness. In collaboration with domain experts, we evaluated QED on 18 research-level projects of varying difficulty. QED produced five original works across algebraic geometry, fluid PDEs, probability, and inverse problems. Expert assessments regard these works as solid specialized research contributions, with three comparable in difficulty and scope to work commonly published in established specialist mathematics venues. QED is released at https://github.com/proofQED/QED.