Tertiary transition in mathematics appears to be an insurmountable struggle for many students, including for high achievers in secondary school. The high dropout rates in many Western Countries represent a big issue from an individual and social point of view. It appears particularly significant to analyse this phenomenon in the context of the degree course in Mathematics, studying students' cognitive and affective reactions to the (often unexpected and severe) difficulties encountered in the tertiary transition. With this aim, we developed a narrative study in a specific context in Italy--that involves "excellent" students from secondary school--to investigate how "successful" and "dropout" students describe their experience in transition. Implications for the educational practice are discussed.