Generative AI and accuracy in the history of mathematics
Peter James Rowlett · British Journal for the History of Mathematics · 2024
Generative AI systems designed to produce text do so by drawing on inferences made from training data, which may mean they reproduce factual errors or biases contained in that data.This process is illustrated by querying ChatGPT with questions from a history of mathematics quiz designed to highlight the common occurrence of mathematical results being misattributed.ChatGPT's performance on a set of decades-old common misconceptions is mixed, illustrating the potential for these systems to reproduce and reinforce historical inaccuracies and misconceptions. Misattribution Misattribution is an unfortunately common occurrence in the history of mathematics.There are various reasons for this.Results are sometimes lost and rediscovered later in a different cultural context.Mathematicians don't usually name results or ideas after themselves, others do.This makes it likely that credit will attach to a well-known person who brings a concept to greater attention, rather than the original developer.A particularly clear example of this is Stokes' Theorem.This was named for George Gabriel Stokes because of his tendency to include it on Cambridge examinations, though the first statement of the theorem was by William Thomson (Lord Kelvin) in a letter to Stokes (Rice 2011).Keith Luoma had some fun with this concept in a pair of articles in The Mathematical Gazette in 1996.He offered a quiz of nine questions on 'famous name' mathematics (Luoma 1996b).A follow-up article gave the perhaps surprising answers to these questions, which always indicate that the theorem or result is misnamed (Luoma 1996a). Generative AIChatGPT is a type of Large Language Model (LLM) that uses deep learning techniques for extensive training with tremendous amounts of data, designed as a 'generative AI' to produce 'human-like responses by drawing on its wealth of information