Mathematical Identity

The walls of the Alhambra in Grenada are covered in a cascade of different colours and shapes. But through the mathematician’s glasses there are only 17 different symmetries possible on the palace walls. What does it mean for two totally different images to have identical symmetries? Mathematics is full of different ways of looking at the world where seemingly different objects become identical under the mathematicians microscope. Equations too represent a dialogue between the right and left hand side of the equals side where the mathematics magically transforms one idea into an often seemingly unrelated idea. Yet the logical proof behind the equation reveals an identity between the two concepts.