Overview

• University of Cambridge researchers used Socratic-style questioning to probe ChatGPT-4 on Plato’s 2,400-year-old doubling-the-square lesson and related variants.
• The model favored an algebraic route, resisted geometric steering, and produced the diagonal-based construction only after the researchers expressed disappointment with its earlier answer.
• When asked to double a rectangle while preserving proportions, it incorrectly asserted that no geometric solution existed, which the authors interpret as an improvised claim.
• On a triangle version it again began with algebra but, after further prompting, produced a correct geometric method, consistent with weaknesses tied to text-only training rather than diagrammatic reasoning.
• The study, published in the International Journal of Mathematical Education in Science and Technology (DOI: 10.1080/0020739X.2025.2543817), urges collaborative prompting in classrooms and cautions against inferring internal mechanisms the authors could not inspect.