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What a bummer. When I discovered that the best way to get an A in my math theory classes was to memorize proofs, I pretty much guaranteed that I wasn't going to get good at math. Before I discovered this, I did the homework and learned from it, and I tried to figure out proofs in the moment during exams. One of my proudest moments was on an advanced linear algebra test, where I proved a theorem in a way that was not anticipated by the professor. He wrote a nice note next to my proof. But I missed more than I got, and I received a B+ in the class. Later, I figured out that most professors rarely present completely new theorems on undergraduate exams, so I copied everything down and especially attended the pre-exam review sessions. I learned everything by heart. If you asked me how to prove anything that the prof had reviewed, I could bounce it to you immediately. I think my abstract algebra teacher had been doing some of it on the spot, because when I regurgitated one of his proofs back to him on an exam, he wrote a nice note next to it as well. It didn't feel nearly as great it had when it was really my own creativity, I remember thinking, "don't you realize you did this in class?" Now, of course you can't learn it by rote. It's impossible to learn something as complicated as a proof, even a short one, without understanding it. So my advice about learning the proofs by heart is to make sure you completely understand them. I found that I still did get stuck, and I came up with little memory tricks - not mathematical things, the kind of tricks you'd use to remember people's names. There was a rare breed of student who didn't memorize the proofs, and only sometimes came to class. They'd get the questions right on the exams anyway. The professors loved them. I doubt I'm smart enough, but I do feel that I might have eliminated my chance of become one of these students by making sure I was an A student who memorized proofs rather than a B student, for a while, who understood the underpinnings and used logic and deduction (gasp! mathematical reasoning). The best solution, I'd say, is to go ahead and memorize those proofs, since grades do matter an you aren't getting into a top grad school with mainly B's (and if you're doing this for engineering or something, I guess to some extent it's just something to get through). But if you care about math theory and want to be good at it, make sure you spend a lot of time working independently on problems that don't have an answer you can memorize. |