Examples of Admissible Simplification of Mathematical Theories

TL;DR

This paper presents examples of simplifying complex mathematical theories to make them accessible to children while maintaining their intellectual and aesthetic value, enabling feasible problem sets for school students.

Contribution

It introduces specific methods of simplifying mathematical models without losing core concepts, making advanced mathematics more approachable for educational purposes.

Findings

Simplified models retain essential mathematical properties.

Simplifications enable problem-solving by school students.

Preservation of aesthetic and intellectual value in models.

Abstract

"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.