LLMs Are Not Intelligent Thinkers: Introducing Mathematical Topic Tree Benchmark for Comprehensive Evaluation of LLMs

TL;DR

This paper introduces the Mathematical Topics Tree (MaTT) benchmark to comprehensively evaluate LLMs' mathematical reasoning across diverse topics, revealing limited accuracy and reasoning capabilities even in advanced models like GPT-4.

Contribution

The paper presents MaTT, a structured, large-scale benchmark for assessing LLMs' mathematical reasoning, highlighting current limitations and discrepancies in model performance.

Findings

GPT-4 achieved 54% accuracy on MaTT

Chain-of-Thought prompting showed limited improvement

Model explanations were only 53.3% complete and correct when answers were correct

Abstract

Large language models (LLMs) demonstrate impressive capabilities in mathematical reasoning. However, despite these achievements, current evaluations are mostly limited to specific mathematical topics, and it remains unclear whether LLMs are genuinely engaging in reasoning. To address these gaps, we present the Mathematical Topics Tree (MaTT) benchmark, a challenging and structured benchmark that offers 1,958 questions across a wide array of mathematical subjects, each paired with a detailed hierarchical chain of topics. Upon assessing different LLMs using the MaTT benchmark, we find that the most advanced model, GPT-4, achieved a mere 54\% accuracy in a multiple-choice scenario. Interestingly, even when employing Chain-of-Thought prompting, we observe mostly no notable improvement. Moreover, LLMs accuracy dramatically reduced by up to 24.2 percentage point when the questions were presented without providing choices. Further detailed analysis of the LLMs' performance across a range of topics showed significant discrepancy even for closely related subtopics within the same general mathematical area. In an effort to pinpoint the reasons behind LLMs performances, we conducted a manual evaluation of the completeness and correctness of the explanations generated by GPT-4 when choices were available. Surprisingly, we find that in only 53.3\% of the instances where the model provided a correct answer, the accompanying explanations were deemed complete and accurate, i.e., the model engaged in genuine reasoning.