Answer by Qiaochu Yuan:
I graduated from MIT with a GPA of 4.8 (out of 5.0) in mathematics. I had two non-As, both of which were non-math classes.
That doesn't imply that I have good study methods, but anyway, here's how I studied at MIT. My main study method as an undergraduate, for math classes, was knowing a sizable chunk of the material in advance.
This isn't a method that will work for everybody. I did a lot of mathematics outside of the classroom both in high school and at MIT, and I often saw a substantial portion of the material in a given class before I took it. I can't emphasize enough how much easier this makes a class, and not just for the reasons you might expect: one of the most valuable things you get out of knowing a lot of the material already is just not being intimidated by it. (And you can get this benefit even if you've only seen some of the material before and possibly forgotten some of it too.) You're much more relaxed, and that makes it easier to process the part of the material that you don't know.
What that translates to in terms of practical advice is this:
- cultivate a sense of curiosity,
- don't restrict your learning to the classroom,
- only take classes that actually seem really interesting to you, and
- try to learn something related to those classes the semester before.
None of this is advice for studying for a class you're taking now, but it's advice for reducing the extent to which you will need to study for classes you'll take in the future.