In a novel experiment that bridges ancient philosophy with modern artificial intelligence, researchers from the University of Cambridge presented ChatGPT with a geometry problem first posed in Plato's dialogue 'Meno' over 2,000 years ago [3][5]. The AI's initial failure to solve the puzzle was expected, but what happened next surprised the team. By adopting the questioning style of the Greek philosopher Socrates, the scientists guided the AI to correct its own mistakes and arrive at the right answer, revealing a dynamic reasoning ability that challenges common perceptions of how large language models (LLMs) operate [1][2].
The Ancient Problem: A Test from Plato's 'Meno'
The mathematical challenge originates from a famous philosophical text where Socrates engages in a dialogue with an uneducated slave boy [2]. The goal is to demonstrate that knowledge is innate and can be surfaced through guided questioning, a concept known as anamnesis, or recollection. Socrates asks the boy to determine how to double the area of a given square [1]. He never provides the answer directly but instead uses a series of simple questions to lead the boy away from his incorrect assumptions and toward the correct geometrical solution: constructing a new square using the diagonal of the original one [5]. This Socratic method became the blueprint for the Cambridge researchers' interaction with ChatGPT.
ChatGPT's Human-Like Stumble
When first presented with the problem, ChatGPT made the same intuitive error as the boy in Plato's dialogue [1]. The AI's initial suggestion was to simply double the length of the square's sides. This is a logical first guess but is mathematically incorrect, as it would quadruple the square's area, not double it. This initial failure was significant because it suggested the AI was not merely retrieving a known solution to a famous problem from its vast training data. Instead, it appeared to be attempting to solve the problem from scratch, mirroring the flawed, step-by-step reasoning of a human learner [5].
A Socratic Dialogue with an AI
Led by doctoral candidate E. M. Pila, the Cambridge classics and computer science researchers then shifted their approach [5]. Instead of correcting the AI directly, they began to prompt it with Socratic-style questions. They asked ChatGPT to check its own work and reconsider its logic, much as Socrates did with the boy [2][3]. Under this line of questioning, the AI began to self-correct.
- Initial Error: ChatGPT first suggested doubling the side lengths to double the area.
- Socratic Prompting: Researchers questioned the outcome of this action, guiding the AI to calculate the resulting area.
- Self-Correction: The AI recognized its error—that doubling the sides quadrupled the area—and acknowledged its initial answer was wrong.
- Guided Discovery: Through further prompts that broke the problem down, ChatGPT eventually reasoned its way to the correct answer involving the square's diagonal [1][5].
This interaction demonstrated that the AI was not just a "stochastic parrot" mindlessly repeating patterns [1]. It was able to engage in a dynamic, corrective dialogue and seemed to "think on the fly" to solve a problem it initially got wrong [5].
Beyond Rote Memorization: Implications for AI
The results of this experiment carry significant implications for our understanding of artificial intelligence and its potential applications, particularly in education. The study suggests that the way we interact with LLMs can unlock different levels of capability. While they can provide direct answers, engaging them in a Socratic dialogue may reveal a deeper, more flexible reasoning process.
- Challenging Perceptions: The findings challenge the view that LLMs are incapable of genuine problem-solving or are limited to regurgitating information.
- Educational Potential: This method could be used to develop AI-powered tutors that don't just give students answers but guide them toward discovering solutions on their own, fostering critical thinking skills [3][5].
- Future of AI Interaction: The research highlights the importance of prompt engineering and interactive dialogue in harnessing the full potential of advanced AI systems.
In conclusion, by tasking ChatGPT with a 2,400-year-old math puzzle, Cambridge scientists did more than test its computational ability; they probed the nature of its reasoning. The AI's Socratic journey from error to correctness suggests that these models may possess a latent, human-like capacity for learning and self-correction that can be unlocked with the right kind of conversation, opening a new chapter in human-AI collaboration [1][2].