This article explores how contradictions, as framed by activity theory (Engeström, 1987), can explain first-year undergraduate students' experiences of learning advanced mathematics. Analysing qualitative interview and observational data of students and lecturers based in one university mathematics department, we argue that contradictions between the school and university activity systems, as well as those within the latter, help explain some of the difficulties, including the conflict in cognition and identity, students can experience when they encounter advanced mathematics at university. This helps us to adopt a critical stance towards the systems students are expected to learn in, and points to system developments that might better support student learning.