Spaced proof review routine
Here are the basic steps I take for spaced proof review.
For each proof/exercise:
- Do the proof for the first time. This isn't any different from what people normally do when solving exercises out of a book, or when reading a proof in a book. You just read it or do it on a piece of paper.
- Decide if it's interesting enough to keep reviewing. If it is, continue to the next step. Otherwise, stop here.
- Write up the proof as an Anki card, adding it to the "Math problems (only for new cards)" deck. It's important to add the complete proof on proof cards to reduce friction when reviewing. If you couldn't solve the problem and looked up the solution, you should still add the partial progress you made and give your guesses about why that's a useful step to take (e.g. any heuristics/pattern matching that you used); these kinds of "motivation" for certain steps are typically lacking from solutions you can find, and so will be especially helpful to include for your future self (who may forget these things when re-doing the problem).
- Do an empty review of proof cards immediately after adding to prevent backlog (increase the "new cards per day" deck option to force the new card to be visible if you've already maxed out your new cards for the day). (This also helps because now all the cards in the main math problems deck will be not-new, which means burying them will work as expected. In the past, I've experienced weird issues when burying new cards, where they get sent to the very end of the new cards queue or something like that.)
- After reviewing, move the cards to the main math problems deck.
Some of these steps are needlessly complicated due to the way Anki works. In the future there may be a system that can automatically deal with proof cards, but at the moment I am not aware of any such system.
Each day:
- Review all cards that are due (sometimes, if there are too many due cards, I will try to do some of them and leave the rest to the following day. There's a lot of variance in number of due cards per day because of the way Anki works.) When reviewing, I use actual paper and pencil, and write down the proof on paper. I use scratch paper that I throw away when I'm done reviewing. (Any new insight I get when reviewing should be added to the back side of the card or in some other long-term notes) When scoring, I usually only use "Again" and "Good" (i.e. no "Easy" or "Hard").
- If a proof I write down when reviewing is not the proof that's on the card, I take a moment to reflect on whether the new proof is correct. If it is, I write it up and add it to the back side of the card. (See spaced proof review as a way to invent novel proofs)
