What kind of memory support do proofs want?

If I’m studying a math textbook, and I want to avoid the problem of People seem to forget most of what they read, and they mostly don’t notice by using a Spaced repetition memory system, it’s pretty clear how to do that for some details. For instance, in linear algebra, the text might introduce the concept of singularity and discuss some of its implications. I want to remember those details, and to be able to classify examples, and it’s easy to write prompts which achieve that. But how should I treat proofs discussed in the text?

The appropriate answer here seems to depend a lot on my stance towards the text, and my interest in this particular proof. Some things I might want:

To remember the theorem itself
To remember the theorem’s implications—why it’s interesting or useful
To remember interesting details about the theorem itself: its domain, why it only applies to that domain, how it relates to other theorems, etc
To remember the proof’s critical insight (see e.g. MN’s essay)
To remember any interesting “moves” done in the proof
To ensure I can reproduce the proof in its entirety in the future

And if the proof is part of a problem set, rather than being discussed in the text (Active learning insights need memory support too), I might want:

To remember how I stumbled upon the key insights
To remember what didn’t work and why
If I failed to spot an important “move”, give me more different proofs in the future which require an analogous move, until I reliably notice when it applies

References

Last updated 2024-04-16.