" ... This is a major theme in mathematics: things are what you want them to be. You have endless choices; there is no reality to get in your way.

On the other hand, once you have made your choices then your new creations do what they do, whether you like it or not. This is the amazing thing about making imaginary patterns: they talk back! "

― Paul Lockhart , A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form