How do you stay in touch with what you learnt?

[u/ada_chai]

Pretty much the title, I guess. I usually don't remember a lot more than a sort of broad theme of a course and a few key results here and there, after a couple of semesters of doing the course. Maybe a bit more of the finer details if I repeatedly use ideas from the course in other courses that I'd take currently. I definitely would not remember any big proof unless the idea of the proof itself is key to the result, and that's being generous.

I understand that its not possible to fully remember everything you'd learn, especially if you're not constantly in touch with the topics, but how would you 'optimize' how much you remember out of a course/self studying a book? Does writing some sort of short notes help? What methods have you tried that helps you in remembering things well? How do you prioritize learning the math that you'd use regularly vs learning things out of your own interest, that you may not particularly visit again in a different course/research work?

[u/Impact21x]

Most guys will say that the key to remember is to teach because you repeatedly use the material and actively engage by answering questions of the students.

For you and me, the srudents, is to review material - check an old book you've used to study from, do a few exercises, if you don't remember the approach, check a few solutions online and study them, and since you knew the material, next exercises will eventually become easier, thus you will recall the material and the useful techniques.

[u/Mobile-You1163 → u/Impact21x]

Tutoring or just offering advice on, say, physicsforums helps, too.

[u/Impact21x → u/Mobile-You1163]

With the assumption that the needed advices will cover the whole course, yes.

Tutoring is the same as teaching because you're running over the whole course unless students come to be tutored on a part of the course they find hard, so again, the assumption that enough students will be tutored or at least one that will be tutored on the whole course would do the trick.

[u/KingKermit007]

I don't for the most part.. The stuff I use frequently or teach stays fresh all the time but for the rest it's more about knowing where to find it when needed

[u/pseudoLit]

After you've put in the work to learn the material, you can keep it fresh using regular flashcard drills, e.g. with Anki. A few months ago, there was someone on this subreddit who claimed to have the entirety of their undergrad degree memorized that way.

[u/likhith-69 → u/pseudoLit]

If that guy is still here, can he please share those anki cards 👀

[u/Haunting-Reindeer610 → u/likhith-69]

I've concerted all of professor Leonard's precalc youtube lectures into Anki flashcards. Now I'm working through the calc sequence. Anki has been phenomenal in keeping all of the methods and concepts in my head long after learning them.

[u/Ok-Woodpecker-8347]

I think it really depends on how you learn. If you’re just memorizing theorems and techniques to apply them in specific examples, it’s easy to forget them later. But if you focus on deeply understanding what’s going on, why something works, not just how, you develop a solid intuition. Then, even if you forget the details of a theorem, you still remember the core ideas. When you need to use it again, you can often reconstruct or guess what it might be, and then quickly check or look it up in a book or online. That way, the knowledge doesn’t just disappear. It becomes something you can access and rebuild when needed, because it’s part of your understanding, not just a memorized fact