The article examines the problem of relationships between general, special and creative abilities. We analyzed theoretical views on the problem of general and special abilities and described the discussion between V.A. Krutetskii and S.L. Rubinstein. As the result, it was shown that special abilities are actually reduced to the general ones. The final solution of this problem was suggested by V.D. Shadrikov in his theory of abilities as the properties of the functional systems and special abilities as the general ones that acquired efficiency under the influence of the demands of activities; thus a contradiction is removed and the question of the nature of special abilities is answered. The problem of relationships between general and creative abilities is nowadays the most pressing abroad (B. Sriraman, D. Pitta-Pantazi, M. Kattou, R. Leikin, etc.). In some ways, V.D. Shadrikov problematizes it. He describes abilities at three levels - individual (natural abilities), the subject of activity (special abilities) and personality (including the moral field). Abilities on a personal level are considered as giftedness that can develop into creativity. Further we speak about creative abilities as the ability to develop activity on one’s own initiative, which is the development of the process-activity approach by S.L. Rubinstein. We examine the relationship of different types of abilities by an example of mathematical giftedness. The participants were students and graduates in mathematics (including PhD) from the best Russian universities (n = 83). Creative abilities and giftedness were measured with mathematical material that was developed in the framework of "Creative Field". The results are compared with the intellectual and personal tests. It was shown that the general abilities provide the acquirement of mathematical material. The most important for creativity and giftedness is cognitive attitude, which is expressed in development of activities on one’s own initiative.