ChatGPT stumbles like a student facing a 2,400-year-old mathematical puzzle.

The artificial intelligence assistant ChatGPT thought on its feet, improvised, and made mistakes, just like a student would, while trying to solve a mathematical challenge (the quadrature problem) that is more than 2.4 billion years old.

Educational researchers at the University of Cambridge experimented with this artificial intelligence tool to see if it could solve the problem of doubling the square (the quadrature problem), a lesson described by Plato around 385 BC. They published the results of their work today in the International Journal of Mathematics Education in Science and Technology.

The researchers wanted to know whether it would solve Plato's problem by using existing knowledge or adaptively developing its own solutions. They saw how this artificial intelligence tool improvised its approach and ultimately made a "distinctly human" error, opting for an algebraic approach that was unknown in Plato's time.

Like other 'Large Language Models' , ChatGPT is trained on massive collections of text and generates answers by predicting word sequences learned during training, so the researchers expected it to solve the ancient Greek math challenge by returning its prior knowledge and providing the solution proposed by Socrates.

But that wasn't the case, and the researchers who conducted the experiment concluded that this artificial intelligence tool behaved "like an apprentice," even though it did demonstrate a deep understanding of Plato's work.

The authors have compared the behavior of this artificial intelligence with the educational concept of the "zone of proximal development," understood as the gap between what a student already knows and what they could eventually know with support and guidance.

And they have suggested, in light of the results, that working with ChatGPT in the so-called "zone of proximal development" can help turn its limitations into learning opportunities, since by prompting, questioning, and testing their answers, students will not only navigate the limits of Chat, but could also develop critical evidence-evaluation and reasoning skills that lie at the heart of mathematical thinking.