Can LLMs Master Math? Investigating Large Language Models on Math Stack Exchange

TL;DR

This study evaluates the mathematical problem-solving abilities of large language models, especially GPT-4, on Math Stack Exchange questions, revealing strengths and limitations in their accuracy and reasoning capabilities.

Contribution

The paper introduces a systematic evaluation of LLMs on real-world math questions and provides detailed analysis of GPT-4's performance and shortcomings in mathematical reasoning.

Findings

GPT-4 outperforms other LLMs on math benchmarks

GPT-4 achieves a P@10 of 0.37 on Math Stack Exchange questions

Limitations in GPT-4's accuracy highlight challenges in complex mathematical reasoning

Abstract

Large Language Models (LLMs) have demonstrated exceptional capabilities in various natural language tasks, often achieving performances that surpass those of humans. Despite these advancements, the domain of mathematics presents a distinctive challenge, primarily due to its specialized structure and the precision it demands. In this study, we adopted a two-step approach for investigating the proficiency of LLMs in answering mathematical questions. First, we employ the most effective LLMs, as identified by their performance on math question-answer benchmarks, to generate answers to 78 questions from the Math Stack Exchange (MSE). Second, a case analysis is conducted on the LLM that showed the highest performance, focusing on the quality and accuracy of its answers through manual evaluation. We found that GPT-4 performs best (nDCG of 0.48 and P@10 of 0.37) amongst existing LLMs fine-tuned for answering mathematics questions and outperforms the current best approach on ArqMATH3 Task1, considering P@10. Our Case analysis indicates that while the GPT-4 can generate relevant responses in certain instances, it does not consistently answer all questions accurately. This paper explores the current limitations of LLMs in navigating complex mathematical problem-solving. Through case analysis, we shed light on the gaps in LLM capabilities within mathematics, thereby setting the stage for future research and advancements in AI-driven mathematical reasoning. We make our code and findings publicly available for research: \url{https://github.com/gipplab/LLM-Investig-MathStackExchange}