Do Large Language Models Truly Grasp Mathematics? An Empirical Exploration From Cognitive Psychology

• URL: http://arxiv.org/abs/2410.14979v5
• Date: Fri, 15 Nov 2024 12:46:30 GMT
• Title: Do Large Language Models Truly Grasp Mathematics? An Empirical Exploration From Cognitive Psychology
• Authors: Wei Xie, Shuoyoucheng Ma, Zhenhua Wang, Enze Wang, Kai Chen, Xiaobing Sun, Baosheng Wang,
• Abstract summary: We show that, even with the use of Chains of Thought prompts, mainstream LLMs have a high error rate when solving modified CRT problems. Specifically, the average accuracy rate dropped by up to 50% compared to the original questions. This finding challenges the belief that LLMs have genuine mathematical reasoning abilities comparable to humans.
• Score: 13.964263002704582
• License:
• Abstract: The cognitive mechanism by which Large Language Models (LLMs) solve mathematical problems remains a widely debated and unresolved issue. Currently, there is little interpretable experimental evidence that connects LLMs' problem-solving with human cognitive psychology.To determine if LLMs possess human-like mathematical reasoning, we modified the problems used in the human Cognitive Reflection Test (CRT). Our results show that, even with the use of Chains of Thought (CoT) prompts, mainstream LLMs, including the latest o1 model (noted for its reasoning capabilities), have a high error rate when solving these modified CRT problems. Specifically, the average accuracy rate dropped by up to 50% compared to the original questions.Further analysis of LLMs' incorrect answers suggests that they primarily rely on pattern matching from their training data, which aligns more with human intuition (System 1 thinking) rather than with human-like reasoning (System 2 thinking). This finding challenges the belief that LLMs have genuine mathematical reasoning abilities comparable to humans. As a result, this work may adjust overly optimistic views on LLMs' progress towards artificial general intelligence.

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