Large Language Models Struggle with Unreasonability in Math Problems

Large Language Models (LLMs) have shown remarkable success across a wide range of math and reasoning benchmarks. However, we observe that they often struggle when faced with unreasonable math problems. Instead of recognizing these issues, the models frequently proceed as if the problems are well posed, producing incorrect answers or overthinking and producing verbose self-corrections. To systematically investigate this overlooked vulnerability, we propose the Unreasonable Math Problems (UMP) benchmark, designed to evaluate LLMs’ ability to detect and respond to unreasonable math problems. Based on extensive experiments covering 19 LLMs, we find that even state-of-the-art general models such as GPT-4o struggle on UMP. Reasoning models such as DeepSeek-R1 demonstrate higher sensitivity to unreasonable inputs; however, this sensitivity often comes at the cost of generating overly long and meaningless responses that fail to converge. We further find that prompting and fine-tuning enhance the detection of unreasonable inputs with minor and acceptable trade-offs that make them practical solutions in this challenging setting.