You don't necessarily start from the top and go to the bottom. Good proofs will do some really clever things like set up a good one-two punch. The Galois proof I talked about earlier is like this.
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When I took Real Analysis at RPI I finished with a C, partly because it was my last semester and once I got a passing grade I stopped going. When I re-took the class at UVa, I had much more maturity and a finer grasp of proof-based math and got an A+.
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Some top mathemeticians do ground-breaking work early, though, yes? (Not said dismissively of your own learning process.) I was always jealous of my math PhD colleagues, whose dissertations were often short papers where they worked out theorems. So different than humanities!
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This is a common myth that is largely a product of western academic structures. But it is true that math PhDs can be (much) shorter.
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