Some remarks on creating mathematical concepts

The author tries to show some causes of failures in the creation of mathematical concepts. One of them is stiffening of concept cores. It makes impossible identification of untypical exemplars of a given concept and solving untypical problems. Moreover, it causes a hiatus between two distinct concept systems — a natural system of everyday concepts and a system of categorial concepts. The last ones are verbalized in a special pseudo-scientific language and used only in school situations. The hiatus makes impossible mathematization of everyday examples as well as interpretation and understanding of mathematical concepts.