Problem
Research questions and friction points this paper is trying to address.
automated proof discovery
multi-agent orchestration
open research problems
language models
mathematical reasoning
Cogentic: Multi-Agent Orchestration for Automated Proof Discovery
🤖 AI Summary
This study addresses the limitation of single-pass generation in large language models when tackling open mathematical problems that require long-horizon exploration, overcoming technical obstacles, and preserving intermediate progress. To this end, it proposes a Gemini-based multi-agent orchestration framework in which an orchestrator assigns competing conjectural directions and coordinates independent provers through iterative proving and adversarial verification cycles. A persistent ledger is maintained to accumulate intermediate reasoning steps, thereby overcoming bottlenecks associated with long-horizon reasoning. The proposed approach yields novel mathematical results on five open problems spanning online learning, auction theory, and other domains. These findings have been independently verified by domain experts, demonstrating the framework’s effectiveness in addressing the challenges of long-range collaborative reasoning for complex mathematical problem-solving.
📝 Abstract
We present Cogentic, a multi-agent harness for automated proof discovery on open research problems. While frontier language models can generate strong mathematical ideas in a single shot, single-shot generation is often insufficient for open problems that require exploring multiple competing conjectures, overcoming subtle technical obstructions, and retaining intermediate progress over a long horizon. Cogentic addresses these challenges through an iterative prove--verify loop in which an orchestrator allocates a population of independent provers across distinct proof directions, subjects their output to adversarial verification by several specialized components, and promotes confirmed intermediate results into a persistent verified ledger that later rounds build on. The harness is designed to be able to solve research-level math and theoretical computer science problems. Using Gemini as the base model, Cogentic produced novel results on five open problems across online learning, auction theory, and mechanism design. Each result was independently verified by domain experts and is developed in full in companion papers. We list these results, and new ones as they are verified, at https://sites.google.com/view/cogentic .
Innovation
Methods, ideas, or system contributions that make the work stand out.
Multi-Agent Orchestration
Automated Proof Discovery
Prove-Verify Loop
Adversarial Verification
Verified Ledger
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