The Illusion of Reason: LLMs and Mathematical Fragility

Fundamental limitations of Large Language Models (LLMs) in mathematical reasoning, highlighting a critical dichotomy between their linguistic fluency and mathematical fragility. It explains how LLMs, despite their advanced text generation abilities, often "hallucinate" incorrect mathematical results due to their probabilistic, token-based architecture and the nature of their training data.

The text then discusses current mitigation strategies like Chain-of-Thought (CoT), which simulates step-by-step reasoning, and Program-of-Thought (PoT), which offloads computation to external tools, revealing PoT's superiority.

Finally, it contrasts LLM mechanisms with human mathematical cognition, emphasizing the absence of true metacognition in AI, and proposes future directions such as neuro-symbolic architectures and formal verification to achieve more robust and verifiable AI mathematical intelligence.