My question is about how to best read mathematics papers for research.
I just passed the last qualifying exam as a Ph.D. student in mathematics (studying statistics) and I'm reaching the point where I will need to do more research, which involves reading papers. I used to write, in my own words in a journal, pre-reading thoughts (why I'm reading this paper, what I already know, etc.), a summary of the paper's contents while reading, post-reading thoughts (what I think about the ideas, how they connect to others, how this could be useful, opinions, etc.), and a list of potentially interesting bibliography entries for later reading. When reading I would essentially read linearly, making margin notes, highlighting interesting sections, and so on. Reading a single paper could take a day, going through this process.
This did well enough for my undergraduate thesis on a topic in economics. It also worked well for the paper that my adviser and I are wrapping up and submitting to journals. But I get the impression that this is not an optimal way to read papers, especially in subjects as technically intense as mathematics. (My role in the paper I co-authored with my adviser was to do simulation studies for a test statistic he and another co-author developed, which is more computational and programming intensive than mathematically intensive, and paper reading was basically to get background on the subject. This is fine for me as a starting researcher, but I don't think I will get by on this alone for a Ph.D. thesis, let alone in my later career.)
I'm shy about asking my adviser the best way to read papers, so I'd like to hear others' approach. Is my approach to paper reading a good one, or is there a better way?