An exploration into the nature of ChatGPT’s mathematical knowledge

Abstract

In this article, we investigate, from the perspective of a user's digital experiences, the nature of mathematical knowledge of a Large Language Model (LLM), ChatGPT-4. As a context for our investigation, we use Plato's slave-boy experiment in ‘Meno,’ where Socrates demonstrated his thesis that knowledge is innate, which sparked a philosophical debate about the nature of knowledge as a recollection from memory versus knowledge as ongoingly generated from experiences. Focusing on the Doubling the Square geometry problem from the ‘Meno’ and conducting a ‘conversation’ with the Chat according to specific underpinning guidelines, we show that the Chat's responses reflected both types of knowledge. Also, our underpinning guidelines enabled us to allocate what we call the ‘Chat’s ZPD,’ that is, problems that the Chat cannot solve by itself but can solve with some prompting from a suitably knowledgeable user. We suggest implications of our findings for users’ digital interactions with LLMs and for future research.