Explanatory Proofs and Grounding in Mathematics: A Reply to Maarefi

Abstract

Do explanatory proofs of theorems in mathematics derive their explanatory power by virtue of providing information about the grounds of the theorems they explain? I have argued that they do not (Lange 2019), and I have offered my own account of what makes certain mathematical proofs but not others able to explain why some theorem holds (Lange 2017). Recently, Maarefi (2025) has critiqued both these arguments and that account in support of a grounding-based conception of explanatory proofs. Here I respond to some of his critiques.

Keywords

• explanation in mathematics
• ground
• mathematical coincidence
• mathematical practice
• proof