In this article I referred to the psychopedagogical aspects of identifying intellectual giftedness for the mathematical discipline. The student is not born with talents and skills, but they take shape within the instructiveeducational process, over a long period of time, through sustained efforts, that is, in activity. The presence in the class of some students with these qualitatively and quantitatively superior results acquired in a short period of time, shows, indisputably, the existence of the aptitude. For the mathematical discipline, exceptional intellectual endowment represents a particular category of intellectual superendowment, which cannot be definitely separated from it. Mathematical aptitude is shown earlier than other scientific aptitudes and presents some characteristics such as: memory, working capacity. Students with a talent for mathematics creatively transfer working algorithms from one category of problems to another, they quickly understand the requirements of the problems, they are not overwhelmed either by the polyvalence of data or by its quantity. School practice shows that students with aptitude for mathematics are distinguished by special characteristics of thinking, the ease with which they solve exercises and problems, self-confidence. The teaching staff who teach mathematics use tests in the form of graded exercises, but also resort to new methods and work procedures, stimulating for the formation of genuine interests or even passions for the fields of mathematics.