I took my first real analysis course last semester, and I made flashcards with pen and paper for every single non trivial definition, theorem, lemma, and corollary that we covered in lecture.

Analysis definitions and theorems get really complicated with intricate and difficult to follow logical chains, and there are a lot to remember.

These definitions and results don’t mean much on their own without exploring their neighbourhoods by proving relevant things, and I could have learned these definitions and results by just doing proofs. But being absolutely sure I could recite every theorem and definition definitely helped me on the final exam.

I think if you’re learning algorithms (like find the area under a curve) in a calculus course for example, flashcards might have more limited value, as in that case problems are relatively short and you’re better off just running through your set of algorithms a ton of times by doing problems.

I also took a group theory course last semester and I memorized every definition and result from lecture via flashcard, but didn’t practice using them enough by writing proofs. I ended up with like 2 or 3 out of 10 complete proofs and the rest half finished on the final exam because I had the right starting points, but not enough practice using what I knew in unexpected ways. Still passed somehow.

It is a bit more challenging, but it is workable.

Same caveat as in the article: Spaced repetition is just one (minor) part of learning math/physics. It alone won't get you anywhere.

For math - particularly higher level math, the most obvious use case is definitions. There are so many!

You can put theorems in there, but it is a bit challenging on how to phrase it. A single theorem could result in several smaller flash cards.

I think what works better is taking a theorem, finding a representative problem that is solved via that theorem, and make the problem statement the question. The downside of this approach is each card takes longer to process as this is not just plain recall, but actively solving a problem. For this reason, I keep such cards in a separate deck and review them only when I have time I can dedicate (e.g. spending well over a minute per card).

Depends on how you use the flashcards. You can use them to memorize definitions and equalities, and you can also use them as quiz questions which excercise your reason and not simply your memory. For example, you make a flashcard for each excercise question in your textbook. Once you identify what you're struggling with, make more flashcards of that same problem type to avoid remembering the solutions. This will take you from a shaky understanding to much firmer ground pretty quickly.

Honestly just making the flashcards and elaborating on/modifying problems you're struggling with will take you a very long way.

Yeah most of the advance assumes you have the data ready at hand and just need to phrase the cards right, get the number of words right. Whereas for conceptual domains the biggest problem is: how do I encode this as question-answer pairs at all? What I want to read more of is people sitting down and writing in the first-person perspective how they go about it, like Michael Nielsen does here: https://cognitivemedium.com/srs-mathematics

I wrote a bit more about this problem here: https://borretti.me/article/the-applicability-of-spaced-repe...

Perhaps "Using spaced repetition systems to see through a piece of mathematics " [1] might be of interest for you. I have read author's "Augmenting Long-term Memory" [2] and have incorporated a lot of his advice into my Anki practice.

For me, it's quick access recipes (breakfast pancakes for kids), what was the name of the glacier that we hiked to last year, behavioral prompts etc.

1: https://cognitivemedium.com/srs-mathematics

2: https://augmentingcognition.com/ltm.html

Just put every definition, theorem, and exercise in a textbook into a card in an anki deck.

There are no "rules" for how flashcards should work.

I actually tend to keep my cards super concise. I treat Anki as a way to practice fundamentals, like memorizing certain formulas. Anytime I try to add conceptual stuff to cards I feel like I'm only memorizing one specialized version of the thing and it doesn't feel super useful.

I kinda feel like using memorization techniques for things that require deeper understanding probably isn't the most efficient way to learn.

IMO you want to be actively trying to map the new concepts to things you already understand, and constantly working to update your mental model.