Proof Schemes Used and Owned by Artificial Intelligence Chatbots

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Chinese explanation / 中文解读

中文解读待补充：本站会优先为大语言模型、生成式AI、ChatGPT相关技术、计算机视觉、深度学习等高价值论文补充中文说明。

Original abstract

People possess proof schemes. These schemes reveal the cognitive characteristics of the proof process, that is, the persuasion process. Investigating the cognitive features of artificial intelligence (AI) that imitate human intelligence is an issue that needs to be addressed urgently. This research aims to identify the proof schemes used and owned by AI chatbots (AICs) (ChatGPT, Claude, Copilot, Gemini, Grok, Le Chat, and Perplexity). The first aim is to identify the proof schemes that AICs use to convince elementary, middle school, high school, and university students of the truth of some mathematical formulas. The second aim is to identify how AICs convince themselves of the truth of these formulas, that is, the proof schemes they own. For this, two similar mathematical formulas related to consecutive numbers were used. The reason for using two similar formulas is to investigate the internal consistency of AICs. The data was obtained from the results of prompts entered into AICs. This data was analyzed using descriptive analysis. Harel and Sowder’s (1998) proof schemes are used for the codes. According to the results of the research, as a teaching tool, chatbots are able to use proof schemes appropriate to the cognitive levels of students at all educational levels. As an AI, chatbots have analytical proof schemes. But interestingly, some chatbots also have perceptual proof schemes. Also, chatbots have internal consistency. These results are a cornerstone for “AI in mathematics education” and “mathematical development of AI” and are hoped to guide future studies.

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