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 = 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.
@article{arxiv.2309.05689,
title = {Large Language Model for Science: A Study on P vs. NP},
author = {Qingxiu Dong and Li Dong and Ke Xu and Guangyan Zhou and Yaru Hao and Zhifang Sui and Furu Wei},
journal= {arXiv preprint arXiv:2309.05689},
year = {2023}
}