INC-Math: Integrating Natural Language and Code for Enhanced Mathematical Reasoning in Large Language Models

Large Language Models (LLMs) are commonly used to generate solutions for mathematical reasoning problems in the following formats: natural language, code, or a combination of both. In this paper, we explore fundamental questions related to solving mathematical reasoning problems using natural language and code with state-of-the-art LLMs, including GPT-4o-mini and LLama-3.1-8b-Turbo. Our findings show that LLMs are better at reasoning in natural language compared to code. Additionally, although natural language and code serve as complementary forms of reasoning, they can affect each other in a negative way in certain scenarios. These insights motivate our development of a new prompting method, INC-Math, which leverages an LLM to dynamically select the most appropriate reasoning form, resulting in improved performance over comparable baselines with GPT-4o-mini.