STAR-P\'olyaMath: Multi-Agent Reasoning under Persistent Meta-Strategic Supervision

TL;DR

STAR-PólyaMath is a multi-agent reasoning framework that uses meta-level supervision and structured interaction to improve mathematical problem-solving over extended reasoning chains, achieving state-of-the-art results.

Contribution

It introduces a persistent Meta-Strategist and an orchestrated state machine to address reliability issues in long-horizon reasoning tasks, surpassing existing benchmarks.

Findings

Achieves perfect scores on AIMEs, Putnam, and HMMT.

Outperforms baseline GPT-5.5 on Apex 2025 with 93.75% accuracy.

Demonstrates that framework orchestration improves performance independently of model diversity.

Abstract

Frontier AI models and multi-agent systems have led to significant improvements in mathematical reasoning. However, for problems requiring extended, long-horizon reasoning, existing systems continue to suffer from fundamental reliability issues: hallucination accumulation, memory fragmentation, and imbalanced reasoning-tool trade-offs. In this paper, we introduce STAR-P\'olyaMath, a multi-agent framework that systematically addresses these challenges through meta-level supervision and structured Reasoner-Verifier interaction. STAR-P\'olyaMath is structured as an orchestrated state machine with nested challenge-step-replan loops, governed by a reasoning-free Python orchestrator that separates control from inference and bounds error propagation through trace-back and re-planning. Our key innovation is a persistent Meta-Strategist that maintains cross-attempt memory and exercises meta-level control by issuing high-level strategic guidance or mandatory directives, so the system can escape unproductive loops rather than stagnate or over-rely on tools. STAR-P\'olyaMath achieves state-of-the-art results on all eight top-tier competition benchmarks: AIME 2025-2026, MathArena Apex Shortlist, MathArena Apex 2025, Putnam 2025, IMO 2025, HMMT February 2026, and USAMO 2026. It obtains perfect scores on AIMEs, Putnam, and HMMT, and shows its largest margin on Apex 2025, scoring 93.75% compared with 80.21% by the strongest baseline GPT-5.5. Ablation studies show that the gains arise from the framework's orchestration rather than from model-level diversity since removing key components or substituting in mixed backbones consistently weakens performance. Code is available at https://github.com/Julius-Woo/STAR-PolyaMath.