Representation theory

Representation theory is a way of studying shapes with math. Say for example, you want to study a square. It has four corners, four sides, and its shape is always the same. To study it with math you can create numbers (like 1,2,3...) to represent the four corners, sides, and the fact that the shape remains the same. This way, you can make calculations and predictions about the square without having to use a ruler or drawing it out. Representation theory is a way of using numbers to study shapes, patterns and other things.