ChatGPT has surprised researchers once again. A new study shows that the AI successfully solved a 2,000-year-old geometric problem, known as the doubling the square puzzle. This ancient challenge, famously discussed by Socrates, asks how to double the area of a square without being told that the new square’s side should match the original diagonal.
In a recent experiment, scientists discovered that ChatGPT’s reasoning process may go beyond simple pattern recall and could resemble something close to learning.
A 2,000-Year-Old Puzzle Put to the Test
Researchers from Cambridge University and the Hebrew University of Jerusalem asked ChatGPT to solve the classic “doubling the square” problem. They intentionally chose a challenge that:
- requires abstract thinking,
- is unlikely to exist directly in the model’s training data,
- and reveals whether an AI can generate original reasoning rather than repeating memorized patterns.
To their surprise, ChatGPT produced a correct explanation of the geometric concept. It recognized that the area of a square doubles when the side equals the length of the diagonal of the original square — a principle rooted in the Pythagorean theorem.
Unexpected Twist: AI Makes a New Error
The real surprise came next.
When researchers asked ChatGPT to double the area of a rectangle, the AI incorrectly claimed that it was geometrically impossible. According to scientist Nadav Marko, this mistake strongly suggests that the model was not recalling a memorized answer. Instead, it appeared to be constructing its own hypothesis based on partial reasoning — a behavior somewhat similar to human learning.
The researchers concluded that ChatGPT was operating in what pedagogy calls the “zone of proximal development” — the space between what a learner already knows and what they can discover with guidance.
Does This Mean AI Can Think? Not Quite
Professor Andreas Stylianides, co-author of the study, warned against overinterpreting the results. AI does not “think” like a person. However, the experiment shows that large language models can exhibit learning-like behaviors, improvising when confronted with unfamiliar problems.
The researchers plan to:
- test newer models on a broader range of mathematical challenges,
- explore whether AI can solve similar geometric puzzles,
- develop interactive systems combining ChatGPT with visual geometry tools to help students learn complex concepts.
Why This Discovery Matters
This experiment highlights a growing field of interest:
Can AI reason about problems it has never seen before?
The study suggests:
- AI may be capable of flexible problem-solving,
- but its reasoning remains inconsistent,
- and combining symbolic tools with language models might boost accuracy dramatically.
For educators and researchers, this opens exciting opportunities for enhanced learning platforms and AI-assisted teaching methods.
