The article discusses the risks involved in identifying gifted students in mathematics in the school environment. Although the theory of gifted students is widespread and available today, school practice shows many cases of gifted students who have not been identified in the school environment. The reasons for this are various. The article will present the theory related to this topic. The research was conducted as two case studies using qualitative research methods. Semi-structured interviews with parents and pupils were used, and the pupils were observed for a long time by the researcher. In the first case, it was a mathematically gifted pupil with dyslexia, and in the second case, it was a mathematically gifted pupil with an extremely high IQ. The result of the study was to find out in which moments the school did not provide support to the pupil in the two cases mentioned and what kind of help the pupil would appreciate at school. Both pupils were involved in a 1-year intervention in which the intention was to cultivate their mathematical thinking and expressions with the help of appropriately chosen tasks. The stated findings are important for practice and discussion about the training of future mathematics teachers, for which consistent professional training focusing, among other things, also on the education of gifted students is essential. Both case studies are part of long-term research dealing with the identification of gifted students.