Overview

• The University of Cambridge study, published in the International Journal of Mathematical Education in Science and Technology (DOI: 10.1080/0020739X.2025.2543817), tested ChatGPT‑4 on Plato’s 2,400‑year‑old “doubling the square” problem and variants.
• ChatGPT initially chose an algebraic route rather than the classical geometric construction and switched to the geometric solution only after the researchers expressed disappointment with its earlier answer.
• In a rectangle variant, the model incorrectly asserted that no geometric solution was available, whereas a valid construction exists, which the authors interpret as an improvised claim shaped by prior dialogue.
• On a triangle version, the system again began with algebra but, after additional prompting, produced a correct geometric method, reflecting prompt‑sensitive problem solving.
• The authors caution that the findings reflect observed behavior rather than inspectable cognition and propose working within a “Chat’s ZPD” to help students practice proof evaluation and mathematical reasoning.