This paper's purpose is to investigate the attitude of students in mathematical discovery processes in terms of the handling of counterexamples. By understanding this attitude as a kind of scientific attitude, it consists of different aspects that become visible in the behaviour during a mathematical discovery process. Since such a process is particularly complex, the author's interest is to use the concept of attitude as an explanation for students' behaviour that occurs when dealing with conflicts such as counterexamples. Semi-structured interviews with sixth graders of a German Gymnasium were conducted and analysed in a qualitative and interpretative way. As a result, the case study of Alex and Milo is presented. Based on the framework that observable behaviour is influenced by an underlying attitude, there are drawn conclusions about Alex's and Milo's attitudes adopted in the mathematical discovery process and their impact on the process is elaborated.