Sep 18, 2025 01:50 AM
https://www.eurekalert.org/news-releases/1098246
INTRO: The Artificial Intelligence chatbot, ChatGPT, appeared to improvise ideas and make mistakes like a student in a study that rebooted a 2,400-year-old mathematical challenge.
The experiment, by two education researchers, asked the chatbot to solve a version of the “doubling the square” problem – a lesson described by Plato in about 385 BCE and, the paper suggests, “perhaps the earliest documented experiment in mathematics education”. The puzzle sparked centuries of debate about whether knowledge is latent within us, waiting to be ‘retrieved’, or something that we ‘generate’ through lived experience and encounters.
The new study explored a similar question about ChatGPT’s mathematical ‘knowledge’ – as that can be perceived by its users. The researchers wanted to know whether it would solve Plato’s problem using knowledge it already ‘held’, or by adaptively developing its own solutions.
Plato describes Socrates teaching an uneducated boy how to double the area of a square. At first, the boy mistakenly suggests doubling the length of each side, but Socrates eventually leads him to understand that the new square’s sides should be the same length as the diagonal of the original.
The researchers put this problem to ChatGPT-4, at first imitating Socrates’ questions, and then deliberately introducing errors, queries and new variants of the problem.
Like other Large Language Models (LLMs), ChatGPT is trained on vast collections of text and generates responses by predicting sequences of words learned during its training. The researchers expected it to handle their Ancient Greek maths challenge by regurgitating its pre-existing ‘knowledge’ of Socrates’ famous solution. Instead, however, it seemed to improvise its approach and, at one point, also made a distinctly human-like error.
The study was conducted by Dr Nadav Marco, a visiting scholar at the University of Cambridge, and Andreas Stylianides, Professor of Mathematics Education at Cambridge. Marco is permanently based at the Hebrew University and David Yellin College of Education, Jerusalem.
While they are cautious about the results, stressing that LLMs do not think like humans or ‘work things out’, Marco did characterise ChatGPT’s behaviour as “learner-like”... (MORE - details, no ads)
INTRO: The Artificial Intelligence chatbot, ChatGPT, appeared to improvise ideas and make mistakes like a student in a study that rebooted a 2,400-year-old mathematical challenge.
The experiment, by two education researchers, asked the chatbot to solve a version of the “doubling the square” problem – a lesson described by Plato in about 385 BCE and, the paper suggests, “perhaps the earliest documented experiment in mathematics education”. The puzzle sparked centuries of debate about whether knowledge is latent within us, waiting to be ‘retrieved’, or something that we ‘generate’ through lived experience and encounters.
The new study explored a similar question about ChatGPT’s mathematical ‘knowledge’ – as that can be perceived by its users. The researchers wanted to know whether it would solve Plato’s problem using knowledge it already ‘held’, or by adaptively developing its own solutions.
Plato describes Socrates teaching an uneducated boy how to double the area of a square. At first, the boy mistakenly suggests doubling the length of each side, but Socrates eventually leads him to understand that the new square’s sides should be the same length as the diagonal of the original.
The researchers put this problem to ChatGPT-4, at first imitating Socrates’ questions, and then deliberately introducing errors, queries and new variants of the problem.
Like other Large Language Models (LLMs), ChatGPT is trained on vast collections of text and generates responses by predicting sequences of words learned during its training. The researchers expected it to handle their Ancient Greek maths challenge by regurgitating its pre-existing ‘knowledge’ of Socrates’ famous solution. Instead, however, it seemed to improvise its approach and, at one point, also made a distinctly human-like error.
The study was conducted by Dr Nadav Marco, a visiting scholar at the University of Cambridge, and Andreas Stylianides, Professor of Mathematics Education at Cambridge. Marco is permanently based at the Hebrew University and David Yellin College of Education, Jerusalem.
While they are cautious about the results, stressing that LLMs do not think like humans or ‘work things out’, Marco did characterise ChatGPT’s behaviour as “learner-like”... (MORE - details, no ads)
