ISTANBUL 

ChatGPT, the AI chatbot, appeared to improvise and make human-like mistakes when tackling a 2,400-year-old math problem, according to a new study by researchers at the University of Cambridge and Hebrew University.

The experiment focused on the famous “doubling the square” problem from Plato’s Meno, in which Socrates guides an uneducated boy to double the area of a square by using its diagonal, rather than simply doubling the length of its sides.

Researchers aimed to see whether ChatGPT would recall Plato’s classical solution or develop its own approach.

Instead of immediately providing the geometric answer, ChatGPT initially approached the problem algebraically and made errors along the way. Only after repeated prompting did it provide the traditional solution.

Variations of the problem — such as doubling the area of rectangles or triangles — showed similar patterns. The chatbot defaulted to algebraic methods, occasionally made mistakes, but eventually produced correct geometric answers.

The researchers observed that ChatGPT’s responses resembled the reasoning process of a learner generating hypotheses, rather than simply retrieving pre-existing knowledge.

They likened its responses to a “zone of proximal development,” describing the gap between what a learner can do alone and what they can achieve with guidance. They said interacting with AI in this exploratory way could help students develop critical reasoning skills, encouraging them to think through problems rather than relying solely on automated answers.