Linked list proof card
Linked list proof card is a method of memorizing proofs using Anki. In linked list proof cards, each card asks for the next step in a proof so the cards together form a linked list data structure for the proof.
I don't actually like the name "linked list proof card" because it makes it sound like each card is a linked list, rather than that the collection of cards forms a linked list. Maybe "linked list proof method" or something is better?
I think cards that basically try to string together the proof are not a good idea. it always takes time to refresh the context for the proof before you can answer what the next step is, and i feel it isn't that helpful to answer some random step when you can just write the whole proof as part of a "big" card. (of course, when you get stuck when writing the proof, you can make a "small" card that answers a specific question). — maybe another way to state this is that you don't need random access for proof steps. what you need is to be able to start at the beginning and flow through till the end; you need the ability to tell the story of the proof from start to finish. and to gain the ability for the latter, doing the former is a painful way to go about it. (a story teller doesn't need to be able to start at arbitrary points in the story). This forum post expresses a similar sentiment: "And don't try to convince me that you can chop up a single problem in its intermediate steps because IMO that's bollocks. Solving a maths problem is a holistic thing, it's about the procedure from beginning to end. Your mind needs to see where you're coming from and where you're going. You can't solve half an integral..."
A problem with step-by-step proof cards (where you break down a proof into many cards): there are often many "next steps" that are possible, so it's annoying when i don't remember the exact next step, but i can give a plausible next step that is different from the one i wrote down in the card.
One thing I've been frustrated about recently is that when I add cards about different parts of proofs, I often can't quickly recall the statement/context of the proof, so then I'm stuck going "uhh..." or maybe I can quickly answer the card without recalling details of the proof (which is concerning in itself). It's like, these proof cards are too costly to recall and yet I'd like to know about them. Maybe one problem is that some of the proofs don't have names (e.g. one of them in Peter Smith's Goedel book is an incompleteness result that doesn't have a name, or the one from Stillwell's reverse math book about infinite binary trees). If I had a name for proofs, then I might be able to use that as a "central node" that can go off to all the other cards (including a statement of the proof).
Another thing I've noticed, which is related to the above, is that I often have these cards that just strengthen one particular association. But what I need to do is to continue making cards so that the graph becomes denser and denser.