## LESSWRONGLW

You're right on both accounts. Maybe I should've discussed this in my original post... At least for me, Anki serves different purposes at different stages of learning.

Key definitions tend to be useful in the early stages, especially if I'm learning something on and off, as a way to prevent myself from having to constantly refer back and make it easier to think about what they actually mean when I'm away from the source. E.g., I've been exploring alternate interpretations of d-separation in my head during my commute and it helps that I remember the precise conditions in addition to having a visual picture.

Once I've mastered something, I agree that the "concepts and competencies" ("mental moves" is my preferred term) become more important to retain. E.g., I remember the spectral theorem but wish I remembered the sketch of what it looks like to develop the spectral theorem from scratch. Unfortunately, I'm less clear/experienced on using Anki to do this effectively. I think Michael Nielsen's blog post on seeing through a piece of mathematics is a good first step. Deeply internalizing core proofs from an area presumably should help for retaining the core mental moves involved in being effective in that area. But, this is quite time intensive and also prioritizes breadth over depth.

I actually did mention two things that I think may help with retaining concepts and competencies - Anki-izing the same concepts in different ways (often visually) and Anki-izing examples of concepts. I haven't experienced this yet, but I'm hopeful that remembering alternative visual versions of definitions, analogies to them, and examples of them may help with the types of problems where you can see the solution at a glance if you have the right mental model (more common in some areas than others). For example, I remember feeling (usually after agonizing over a problem for a while) like Linear Algebra Done Right had a lot of exercises where the right geometric intuition or representative example would allow you to see the solution relatively quickly and then just have to convert it to words.

Another idea for how to Anki-ize concepts and competencies better that I haven't tried (yet) but will share anyway is succinctly capturing strategies pop up again and again in similar forms. To use another Linear Algebra Done Right example, there are a lot of exercises with solutions of the form "construct some arbitrary linear map that does what we want" and show it... does what we want. I remember this technique but worry that my pattern matching machinery for the types of problems to which it tends to apply has decayed. On the other hand, if I had an Anki card that just listed short descriptions of a few exercises and asked me which technique was core to their solutions, maybe I'd retain that competency better.