The transition from school to university mathematics is a challenging process for many students, which is reflected in high dropout rates during the first year at university. Using mediation analysis, we want to shed light on the role of students' attitudes towards mathematics--especially their interest in mathematics and their mathematical self-concept--for early dropout and investigate the underlying mechanisms for the relations between attitudes and dropout. Informed by frameworks of person-environment-fit and results from educational psychology, we consider satisfaction with one's studies and achievement as potential mediators, influencing the relations between attitudes and early dropout. Our results within a sample of 274 first-year students, enrolled in a pure mathematics or a teacher education program at a German university, show that interest in university mathematics and mathematical self-concept are associated with less risk to drop out. In the case of interest, this relation is mediated by students' satisfaction, and in the case of self-concept, this relation is mediated by satisfaction and achievement. Based on these results, we discuss how to support students during the transition from school to university mathematics in order to prevent early dropout.