... 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
About This Quote

The idea of mathematics is to make an imaginary pattern that's like reality. If you make a pattern, it will keep on telling you, "This is how it works." Your choice of the model will determine the properties of the things that result. (For instance, your choice of model determines whether you see a spiral or a circle.) Yet once you've made your choice, then it can't be changed. This is what makes mathematics so difficult. It should be easy; it's not!

Source: A Mathematicians Lament: How School Cheats Us Out Of Our Most Fascinating And Imaginative Art Form

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