Evaluating the Reasoning Abilities of LLMs on Underrepresented Mathematics Competition Problems

TL;DR

This study assesses the reasoning abilities of three leading LLMs on underrepresented mathematics competition problems, revealing strengths in calculus and weaknesses in geometry, with distinct error patterns across models.

Contribution

It introduces an evaluation of LLM performance on underrepresented math problems, highlighting specific error types and model differences in reasoning and accuracy.

Findings

DeepSeek-V3 outperforms other models across categories.

All models show weak performance in Geometry.

Different models exhibit distinct error patterns.

Abstract

Understanding the limitations of Large Language Models, or LLMs, in mathematical reasoning has been the focus of several recent studies. However, the majority of these studies use the same datasets for benchmarking, which limits the generalizability of their findings and may not fully capture the diverse challenges present in mathematical tasks. The purpose of the present study is to analyze the performance of LLMs on underrepresented mathematics competition problems. We prompted three leading LLMs, namely GPT-4o-mini, Gemini-2.0-Flash, and DeepSeek-V3, with the Missouri Collegiate Mathematics Competition problems in the areas of Calculus, Analytic Geometry, and Discrete Mathematics. The LLMs responses were then compared to the known correct solutions in order to determine the accuracy of the LLM for each problem domain. We also analyzed the LLMs reasoning to explore patterns in errors across problem types and models. DeepSeek-V3 has the best performance in all three categories of Calculus, Analytic Geometry, and Discrete Mathematics, both in reasoning and correct final answers. All three LLMs exhibited notably weak performance in Geometry. The majority of errors made by DeepSeek-V3 were attributed to computational and logical mistakes, whereas GPT-4o-mini frequently exhibited logical and approach-related errors. Gemini, on the other hand, tended to struggle with incomplete reasoning and drawing rushed conclusions. In conclusion, evaluating LLMs on underrepresented mathematics competition datasets can provide deeper insights into their distinct error patterns and highlight ongoing challenges in structured reasoning, particularly within the domain of Geometry.