A sidetrack but are there any good resources on using Anki for learning mathematics? Google brings up a lot of varied and conflicting info. I know nothing is a substitute for working through proofs yourself but surely flashcards can help with memorization of proofs and theorems?
Anki is peerless for learning large numbers of very small facts. I found it very unsuited for learning relatively small numbers of large facts like entire proofs. The best way I found to use it was to select one or two key, short, intuitive (informal) milestones within each proof, and use Anki to associate the theorem statement with those milestones. Any larger unit of memorisation just didn't work for me - took too long to learn, made it a miserable slog to get through the repetitions, and so on. Convert things to lists, where each element of the list is small, and you have a much better chance. I did once try and learn a proof of the three Sylow theorems by means of a 50-card Anki deck, assembling a linked list of the stages of the proof; but even a single sentence of proof can be more mathematically dense than really lends itself to Anki, and I would probably redo it with fewer cards and more intuitive steps (relying on my mathematical ability to fill in the gaps dynamically).
If you want to learn long formulae, I got some success out of setting them to music. I learned the various differential operators in polar coordinates this way, to avoid having to rederive them every time I needed them. (As an aside, I learned Hard 'n Phirm's "Pi" song almost by accident, which got me nearly 150 digits of pi.)
It's exactly as you say. Small, quick to review facts. Anything else makes reviews unbearable.
In a somewhat related experiment I'm trying to use it to learn codebases. Important classes, outline of code paths etc. It's challenging. It sort of works and sort of doesn't. I'm finding a similar thing to how you mention learning milestones in a proof. Kind of memorizing hints that can help you rather than full sequences of things.