Large Language Models (LLMs) have shown remarkable success on 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, models frequently proceed as if the problem is well-posed, producing incorrect answers or falling into overthinking and verbose self-correction. 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 problem statements. Based on extensive experiments covering 19 LLMs, we find that even state-of-the-art general models like GPT-4o struggle on UMP. While reasoning models such as DeepSeek-R1 demonstrate a higher sensitivity to unreasonable inputs, this 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, making them practical solutions in this challenging setting.