In a recent study, researchers from the University of Cambridge and the Hebrew University explored how ChatGPT-4 solves mathematical problems, specifically an ancient puzzle from Plato‘s dialogue Meno.
The puzzle, known as the “doubling the square” problem, was famously used by Socrates to demonstrate that knowledge could be retrieved from within, rather than just taught. The researchers wanted to see if the AI would simply reproduce a known solution from its training data or if it would “think on the fly” and improvise its own approach.
Key findings and observations in the ChatGPT / Plato study
The study, led by Dr. Nadav Marco and Professor Andreas Stylianides, revealed several surprising behaviors from the AI:
- Improvisation over retrieval: Contrary to expectations, ChatGPT did not immediately regurgitate Socrates’ well-known geometric solution. Instead, it initially chose an algebraic approach, a method that would have been unknown in Plato’s time. This suggested that the AI was not just recalling information but was processing the problem and generating a new solution.
- Human-like errors: When presented with a variation of the problem (doubling a rectangle), ChatGPT made a distinct error, incorrectly claiming that a geometric solution did not exist. The researchers concluded this was more likely an “improvisation” based on the previous conversation rather than an error in its vast knowledge base. This “on the fly” reasoning, including its mistakes, was likened to a “learner-like” behavior.
- Prompting as a teaching tool: The AI only produced the elegant geometric solution after the researchers expressed dissatisfaction with its initial algebraic answer. This interaction highlights that providing guidance and feedback (or “prompting”) can steer the AI toward more sophisticated or desired outcomes, a process the researchers metaphorically called the “Chat’s zone of proximal development” (ZPD).
Educational implications
The findings suggest that generative AI, despite its limitations, can be a valuable tool in education. The authors of the study believe student interactions with the AI tool should be seen as an opportunity for learning rather than as a way to simply be supplied with answers.
By critically evaluating the AI’s responses and prompting it toward better solutions, students can develop key mathematical skills such as proof evaluation and reasoning. This shifts the focus from requesting an answer to a problem to an approach where students can utilize the tool to explore the problem with its assistance.
The study has been published in the International Journal of Mathematical Education in Science and Technology.
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