Right, there's a big distiction to be made here.

Knowledge that is primarily conceptual (like almost all of math) generally does not benefit from spaced repetition. The learning involved is understanding -- a new concept may be hard to understand in the first place, but once you get it, you don't really forget it. Or you just need a super-quick refresher if you haven't touched it for a few months.

While knowledge that is primarily arbitrary-factual is the perfect candidate for spaced repetition -- mainly things like vocabulary, medical terms, and so forth. Just associating a largely arbitrary name for something. And indeed they are mostly useful for learning for exams. E.g. I used it to learn Chinese characters and could never have passed Chinese class otherwise. But on the other hand when I actually lived in another country that speaks a different language, spaced repetition isn't much of a help -- you learn vocab just by absorbing it day-to-day, like a kid does.

I've been working on https://github.com/trane-project/trane for the past year or so, mostly to get around these limitations. I tried to find a way to use Anki or another existing software to aid my music practice, but I couldn't get it to work.

Some ways in which it's different:

- Dependencies are core to the system. For example, if I am learning a music piece, I want to start by learning small sections and only move on to larger sections when I am good enough at the small stuff, eventually ending with a final exercise that tests my performance of the whole piece. A lot of knowledge/skills follow that pattern, but I couldn't find a way to make Anki or SuperMemo understand this.

- It's meant for both memorizing stuff and practicing exercises. I have tested it with your exact example (math problems from textbooks). It works fairly well, but it's at a very early stage (you can look around at https://github.com/trane-project/trane-math, but it still needs a readme). So it's doing the same thing as the students you mentioned. The difference is that the scheduling is done automatically. Review of existing problems and addition of new ones happen without requiring planning or tracking from the student.

- There's an emphasis on generating the flashcards as text files, so they can be shared. I don't understand why people insist of remaking their own flascards every time. If someone wishes to learn guitar, for example, it's my hope they just download some courses and start learning without spending any time redoing flashcards. This design choice probably makes it harder to write the flascards, but it balances out once the flashcards are done and can be passed around.

I've found the sweet spot.for Anki is the things that I need only occasionally but not never.

Things I use frequently I already pick up through repeated use, things that I never use eventually falls out.

But things that are somewhat relevant about that I find myself googling more than twice is a good candidate to Anki.

Sure, even for the task that it was designed for, learning Japanese, I mostly pursued a method of just writing stuff in a notebook over and over when I was getting that degree. But the specifics of Anki itself are less important an observation than the main one: despite the widespread conviction that rote learning is pointless it is actually extremely helpful to a wide number of fields of endeavor.

> Several excellent physics and math students I worked with have never used spaced repetition software, but were excellent at their studies because they consistently solved textbook problems.

Isn't it the case that only minority of students uses this software or flashcards in general anyway? I mean, of course it is possible to succeed without it, because overwhelming majority of students/learners are not using it.

> (though I moved to SuperMemo about a year back)

What pushed you to make the switch? Was it Incremental Reading, or some other feature/reason?

You're right that retrieval practice isn't optimal for all types of knowledge. But not all spaced repetition systems are flashcard systems.

Just under a month ago, I read about 'math academy' here on HN. One thing it does is sort of what it sounds like you envisage: surfacing exercises relating to concepts you might be about to forget.

I agree. I believe that it’s one of the things that sets apart great books. Lately I see this more often and think “Neat, they make me practice this old idea and make me build this new thing”. It makes an appreciate the work and thought that went into writhing the text much more.

> I learned mathematics more effectively by focusing primarily on textbook problems (reviewing older material through new problems)

As a caveat, sometimes it can be hard to do this. If I randomly pick textbook problems, I have no guarantee that the new material will review the old.

I had the same experience. I tried Anki for 2 years to learn to crack programming interviews, and failed. Then I started doing leetcode problems regularly on the site and that helped me to get past my block.