Intuition and Insightfulness in AI-assisted Proofs
Katia Parshina

Abstract:
In this work, I analyze how AI was implemented by Davies et al. (2021) in a mathematical proof. The authors claim that they used AI to guide mathematical intuition. First, I analyze the existing accounts of mathematical intuition and mathematical insight and distinguish these two notions. Then, I discuss the way Davies et al. implemented AI into their work and compare it to the classical, non-AI-based computer assistants. Finally, I discuss whether the notions of mathematical intuition and mathematical insight can be used to describe the work AI performs in the discussed proofs. As a main result, I conclude that the discussed AI cannot, as suggested by Davies et al., guide mathematical intuition, and the role it plays can only be described as assisting a mathematician in obtaining mathematical insight.