  Disagreements that resist rational resolution, often termed ``deep
disagreements'', have been the focus of much work in epistemology and informal
logic. In this paper, I argue that they also deserve the attention of
philosophers of mathematics. I link the question of whether there can be deep
disagreements in mathematics to a more familiar debate over whether there can
be revolutions in mathematics. I propose an affirmative answer to both
questions, using the controversy over Shinichi Mochizuki's work on the abc
conjecture as a potential example of both phenomena. I conclude by
investigating the prospects for the resolution of mathematical deep
disagreements in virtue-theoretic approaches to informal logic and mathematical
practice.
