Great article! I've always thought that having math education focusing on formulas is having poetry and literature focus on grammar and spelling -- the painting

Great article! I've always thought that having math education focusing on formulas is having poetry and literature focus on grammar and spelling -- the painting and music analogies are dead-on. But that's exactly what happens: Formulas and equations (grammar) are one way to express a beautiful idea. Unfortunately we end up focusing on the syntax and not the semantics, the underlying meaning. Shameless plug, but I try to do my part to make math intuitive at betterexplained.com. What a great essay.