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.<p>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.<p>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?"<p>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.<p>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.<p>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).<p>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.