Artificial intelligence (AI) has demonstrated impressive progress in mathematical reasoning, yet its integration into the practice of mathematical research remains limited. In this study, we investigate how the AI Mathematician (AIM) system can operate as a research partner rather than a mere problem solver. Focusing on a challenging problem in homogenization theory, we analyze the autonomous reasoning trajectories of AIM and incorporate targeted human interventions to structure the discovery process. Through iterative decomposition of the problem into tractable subgoals, selection of appropriate analytical methods, and validation of intermediate results, we reveal how human intuition and machine computation can complement one another. This collaborative paradigm enhances the reliability, transparency, and interpretability of the resulting proofs, while retaining human oversight for formal rigor and correctness. The approach leads to a complete and verifiable proof, and more broadly, demonstrates how systematic human-AI co-reasoning can advance the frontier of mathematical discovery.

翻译：人工智能在数学推理领域已展现出显著进展，但其在数学研究实践中的整合应用仍较为有限。本研究探讨了AI数学家系统如何作为研究合作伙伴而非单纯的问题求解工具发挥作用。聚焦于均匀化理论中的一个挑战性问题，我们分析了AIM的自主推理轨迹，并通过针对性的人工干预来结构化发现过程。通过将问题迭代分解为可处理的子目标、选择适当的分析方法以及验证中间结果，我们揭示了人类直觉与机器计算如何相互补充。这种协作范式增强了所得证明的可靠性、透明度和可解释性，同时保留了人类对形式严谨性与正确性的监督。该方法最终产生了一个完整且可验证的证明，并在更广泛层面展示了系统化的人机协同推理如何推动数学发现的前沿发展。