In this talk, I explore the tension between mathematical rigor and perfectionism, particularly how the fear of failure can hinder their engagement with rigorous mathematical thinking. Drawing on Imre Lakatos’ book Proofs and Refutations, which describes a dialectical process of conjecture, proof, and refutation, I argue that just as historical developments in mathematics emerge through a cycle of failure and refinement, our students develop their own rigorous thinking through their experiences of failure. As a result, a large barrier to developing mathematical cognition stems from a rise in maladaptive perfectionism. I will discuss pedagogical strategies, including course structure and historically motivated problems, to help students navigate the discomfort of not knowing and cultivate genuine mathematical rigor.