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They are just games with symbols. But yes, some moves are scary. The moves that scare me are those whacky out-of-nowhere algebraic additions that lead to a simp
by javajosh 5y ago
They are just games with symbols. But yes, some moves are scary. The moves that scare me are those whacky out-of-nowhere algebraic additions that lead to a simplification later. They are scary because somehow someone anticipated that one addition out of an infinity of possibilities would be useful "down the road" in the computation. (This is done a couple of times in the OP's integral.)
- zwaps 5y agoI think it is interesting that some notions in this thread boil down to the idea that this ain't real math like, say, real analysis. In my limited view, many proofs are easier. Especially easy ones that are (if that makes sense) more sequential in the required thinking. I think there is a lot of cleverness in these integral calculations, a lot of creativity to, as you say, come up with some seemingly nonsensical transformation that down the road turns out useful. Perhaps it's because I am so bad at it, but I find people who does this easily very impressive. I feel the same way for differential equations, where, incidentally, I also suck. I wonder whether anyone ever did a study on the cognitive skill "dimensions" in maths.