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.

Large Language Models (LLMs) have gradually become the gateway for people to acquire new knowledge. However, attackers can break the model's security protection ("jail") to access restricted information, which is called "jailbreaking." Previous studies have shown the weakness of current LLMs when confronted with such jailbreaking attacks. Nevertheless, comprehension of the intrinsic decision-making mechanism within the LLMs upon receipt of jailbreak prompts is noticeably lacking. Our research provides a psychological explanation of the jailbreak prompts. Drawing on cognitive consistency theory, we argue that the key to jailbreak is guiding the LLM to achieve cognitive coordination in an erroneous direction. Further, we propose an automatic black-box jailbreaking method based on the Foot-in-the-Door (FITD) technique. This method progressively induces the model to answer harmful questions via multi-step incremental prompts. We instantiated a prototype system to evaluate the jailbreaking effectiveness on 8 advanced LLMs, yielding an average success rate of 83.9%. This study builds a psychological perspective on the explanatory insights into the intrinsic decision-making logic of LLMs.