Researchers were stunned when ChatGPT-4 solved Plato’s ancient geometry puzzle of doubling a square’s area not by replicating the known geometric method, but by independently constructing a novel algebraic solution, suggesting a capacity for reasoning beyond simple data recall.
In a remarkable fusion of ancient philosophy and modern artificial intelligence, OpenAI’s ChatGPT-4 has astounded academics by solving a 2,400-year-old mathematical puzzle from Plato using an unexpected method. The discovery suggests AI may be capable of genuine reasoning rather than simply recalling information from its training data.
Researchers Nadav Marco of Hebrew University and Andreas Stylianides revisited Plato’s dialogue “Meno,” in which Socrates guides an uneducated slave boy to understand how to double the area of a square. The classic text uses this demonstration to argue that knowledge is innate and can be drawn out through questioning.
When the team posed the same puzzle to ChatGPT-4, the AI did not default to the well-known geometric solution documented by Plato. Instead, it employed algebra—a mathematical system invented centuries after Plato’s death. Even more notably, the AI later demonstrated it knew the geometric method, indicating it had constructed a new solution pathway rather than retrieving a pre-existing one.
The AI also displayed robust critical thinking. The researchers attempted to mislead it into making the same initial error as Plato’s slave, who thought doubling the sides would double the area. ChatGPT refused, carefully explaining that doubling the sides actually quadruples the area.
This event has ignited fresh debate about the nature of AI cognition. The ability to generate a novel and valid solution to a millennia-old problem indicates a move beyond pattern recognition toward a form of logical reasoning, challenging our understanding of what artificial intelligence can achieve.