In my own notes, my general approach for summarizing a paper is the following:

 - I copy the abstract verbatim, aside from correcting blatant typoes. (Every so often there's an exception here for papers with ridiculously long abstracts - which sort of defeats the point of an abstract, after all!)

 - I generally don't copy definitions exactly; instead I just record the *term(s) introduced*, the *type(s) of object(s)*, and the *intended role*. (That said, particularly snappy/amazing definitions do also get stated in full.)

 - I copy the main results verbatim, again aside from correcting blatant typoes. I use my own judgment as to what constitutes a "main theorem" here, and that doesn't always coincide with the authors' although they usually do.

 - I never copy proofs in their entirety, but I don't fully omit them either: for each theorem I mention I include a *summary in 1-10 sentences* of its proof. This summary may only be limited to a description of the major obstacles; I err on the side of brevity. This is often quite hard, but is a super useful exercise.

*(In each case above I also record the page number(s) of course.)*

 - Finally, I also record some information about the background of the article. I write a summary of the bibliography (or at least part of it), recording how the various sources are relevant. I'll also record the general gist of each paper, even if it goes beyond how it's used at the moment: if Paper 1 just needs one lemma from Paper 2, I'll still give a very brief summary of Paper 2 itself as well as mentioning the lemma. This summary is again on the order of a few sentences, usually taken from the abstract or introduction (I don't need to read Paper 2 itself for this). Finally, I'll make a list of a small number of *very relevant sources* from the bibliography. This list could change over time as I understand the topic better, and often is pretty meaningless initially.

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This is quite a bit of work in general, but note that the only step which requires deeply engaging with the article is the proof-summary bit; the rest can be done fairly mechanically or instinctively. The result is usually a 1-3 page document. A **huge** amount of information is generally lost by doing this, of course, but I find the whole process extremely useful and the result is still quite helpful in recalling the paper much later.