ReasFlow: Assisting Reasoning-Centric Scientific Discovery in Applied Mathematics via a Knowledge-Based Multi-Agent System

Existing autonomous research systems focus on empirically driven domains, while theory-driven discovery, which requires rigorous proofs and deep domain knowledge, remains underexplored. Key challenges include verifying theoretical reasoning at scale, insufficient LLM reasoning capabilities for frontier exploration, and the scarcity of procedural heuristics. We introduce ReasFlow, an end-to-end multi-agent system that integrates (i) an internal verification loop for auditing logical derivations, and (ii) an automated knowledge retrieval and self-improvement mechanism that proactively surfaces both declarative facts and overlooked heuristics, substantially reducing expert intervention. ReasFlow unifies literature survey, algorithm design, theorem proving, experimentation, and manuscript writing. Applied to five novel research tasks in distributed optimization with minimal human prompts, ReasFlow consistently outperforms state-of-the-art open-source baselines under rigorous LLM-based review.