In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P $\neq$ NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.

翻译：本研究利用大型语言模型（LLMs）来增强并加速对P与NP问题的研究——这是理论计算机科学和数学领域最重要且尚未解决的问题之一。具体而言，我们提出了苏格拉底式推理（Socratic reasoning）框架，这是一种通过LLMs促进复杂问题深度思考的通用方法。该框架鼓励LLMs递归式地发现、求解和整合问题，同时支持自我评估与优化。针对P与NP问题的初步实验表明，GPT-4成功生成了一个证明方案，并在97轮对话中保持了严密的推理过程，最终得出“P ≠ NP”的结论，这与Xu和Zhou（2023）的研究结果一致。本研究揭示了LLMs在广阔解空间中的新颖洞见，为“LLM驱动科学”领域提供了启示。