Stellar colosseum coordinates ai agents for complex math problem solving
Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science
Artificial IntelligenceComputation and LanguageMachine Learning
Summary
Solving long and complicated math problems is hard because it needs many steps that depend on each other. The authors created Stellar Colosseum, a system that uses multiple AI models working together to explore different ways of solving a problem before picking the best path. It breaks proofs into smaller parts, checks their correctness, and uses feedback to improve the whole proof. This approach helps tackle difficult problems more reliably than trying to solve everything at once.
What this means in practice
- •For software engineers: Generate and verify complex algorithmic proofs to improve reliability in software development tasks.
- •For competitive programmers: Automatically solve challenging programming contest problems by combining proof-based reasoning with execution feedback.
Authors
Honghao Lin, David P. Woodruff, Yuan Deng, Jieming Mao, Song Zuo, Vahab Mirrokni
Abstract
Language models can produce plausible short proofs, but may still be unreliable on long-horizon research problems, where progress depends on a sequence of uncertain and interdependent decisions. We introduce Stellar Colosseum, a model-agnostic harness for allocating inference across research in mathematics and theoretical computer science. Colosseum explores alternative strategies before proof construction, uses a readiness gate to decide when a route is mature enough to decompose, represents the proof plan as interdependent section-level subproblems, and routes verifier findings back to the affected part of the argument. Across these stages, it generates candidates in parallel, attacks them with targeted falsification, and combines candidates and their critiques into a single research artifact through overlapping random-sample tree aggregation. The Colosseum workflow has also been integrated into Google Antigravity's Teamwork framework as the Long Proof pattern. We demonstrate the capabilities of Colosseum through open-ended research and evaluations on theorem-proving and competitive programming benchmarks. Using Colosseum with Gemini 3.1 Pro, we obtain several new results that address open problems arising from papers published at top venues such as FOCS and JMLR. On TCS-Bench, a benchmark of research-level theorem-proving tasks drawn from papers published at FOCS, STOC, and SODA, Colosseum achieves 71.0% accuracy using Gemini 3.1 Pro and Gemini 3.7 Flash. In a separate Codeforces evaluation using Gemini 3.1 Pro, the proof-oriented pipeline with execution feedback solves 218 of 222 problems.