Large Language Model for Science: A Study on P vs. NP
This is an incremental approach for theoretical computer science researchers, using LLMs to augment reasoning on a foundational open problem.
The authors tackled the P versus NP problem by using large language models (LLMs) with a Socratic reasoning framework, resulting in GPT-4 producing a proof schema concluding 'P ≠ NP' over 97 dialogue turns, aligning with prior work.
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.