Examples of Admissible Simplification of Mathematical Theories

"Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding, and you would not do it without some strong urge." [D. Ruelle]. We shall give some examples from our experience, when we were able to simplify some serious mathematical models to make them understandable by children, preserving both aesthetic and intellectual value. The latter is in particularly measured by whether a given simplification allows setting a sufficient list of problems feasible for school students.