ChatGPT and the Philosopher: A Modern Take on Plato’s Math Lesson

How AI interprets an past puzzle from Plato. Credit: Greek Reporter

In a caller study, researchers from the University of Cambridge and the Hebrew University explored however ChatGPT-4 solves mathematical problems, specifically an past puzzle from Plato‘s dialog Meno.

The puzzle, known arsenic the “doubling the square” problem, was famously utilized by Socrates to show that cognition could beryllium retrieved from within, alternatively than conscionable taught. The researchers wanted to spot if the AI would simply reproduce a known solution from its grooming information oregon if it would “think connected the fly” and improvise its ain approach.

Key findings and observations

The study, led by Dr. Nadav Marco and Professor Andreas Stylianides, revealed respective astonishing behaviors from the AI:

Improvisation Over Retrieval: Contrary to expectations, ChatGPT did not instantly regurgitate Socrates’ well-known geometric solution. Instead, it initially chose an algebraic approach, a method that would person been chartless successful Plato’s time. This suggested that the AI was not conscionable recalling accusation but was processing the occupation and generating a caller solution.

Human-Like Errors: When presented with a saltation of the occupation (doubling a rectangle), ChatGPT made a chiseled error, incorrectly claiming that a geometric solution did not exist. The researchers concluded this was much apt an “improvisation” based connected the erstwhile speech alternatively than an mistake successful its immense cognition base. This “on the fly” reasoning, including its mistakes, was likened to a “learner-like” behavior.

Prompting arsenic a Teaching Tool: The AI lone produced the elegant geometric solution aft the researchers expressed dissatisfaction with its archetypal algebraic answer. This enactment highlights that providing guidance and feedback (or “prompting”) tin steer the AI toward much blase oregon desired outcomes, a process the researchers metaphorically called the “Chat’s portion of proximal development” (ZPD).

Educational implications

The findings suggest that generative AI, contempt its limitations, tin beryllium a invaluable instrumentality successful education. The study’s authors suggest that a student’s enactment with the AI should beryllium seen arsenic an accidental for learning, not conscionable a mode to get answers.

By critically evaluating the AI’s responses and prompting it toward amended solutions, students tin make cardinal mathematical skills similar impervious valuation and reasoning. This shifts the absorption from asking “Tell maine the answer” to “Let’s research this occupation together.”

The probe is published successful the International Journal of Mathematical Education successful Science and Technology