So [in mathematics] we get to play and imagine whatever we want and make patterns and ask questions about them. But how do we answer these questions? It’s not at all like science. There’s no experiment I can do ... The only way to get at the truth about our imaginations is to use our imaginations, and that is hard work.
Paul  Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form
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