Large Language Models and Mathematical Reasoning Failures

• URL: http://arxiv.org/abs/2502.11574v1
• Date: Mon, 17 Feb 2025 09:07:32 GMT
• Title: Large Language Models and Mathematical Reasoning Failures
• Authors: Johan Boye, Birger Moell,
• Abstract summary: This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. We rigorously analyze both final answers and solution steps to identify reasoning failures. We find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic.
• Score: 1.6114012813668932
• License:
• Abstract: This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

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