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

Large Language Model for Science: A Study on P vs. NP