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The answer, of course, is that it varies with each reader and with the specific needs of each reader. For many people, a skim is sufficient for most papers. The question is "does this seem reasonable" and if so, there may be little need to go into the details. This is especially true about proofs. If an overview of the proof suggests that the techniques ...


14

It depends. If I'm just browsing MathSciNet or the arXiv to see what's out there, I'll read a large number of abstracts but few papers. If I find a paper that looks like it might be related to my research area (in a broad sense) then I'll likely read the introduction but nothing more. If I see a paper that looks like it might make use of techniques that ...


9

From personal experience, I read a few papers very carefully and understood the proofs in full detail. For most papers a rough look at the results was sufficient. It depends mainly on the goal of reading the paper. The ones I read very carefully were usually the ones where I wanted to apply the technique to a similar setting for my own research. In order ...


6

Like anyone else, mathematicians by and large read papers selfishly, i.e. to the level needed to advance their own thinking, and no more. So if the result matches my intuition, I may or may not even read past the initial statement in the introduction. If it seems to open up intriguing vistas, or is a bit surprising, I will read enough to understand the ...


3

Talk to the instructor, ask them for advice. Ideally you would have done this before the semester started knowing that you would have this arrangement, but at least the instructor was made aware ahead of time through your supervisor. They are unlikely to be able to offer support that takes a lot of additional effort on their part because this special ...


3

In my opinion, your question contains a false assumption. You say that it is not about correctness, and that one can safely use the results of peer-reviewed papers, but reality shows that still enough papers are published that contain at least in details some flaws, need extra assumptions or similar stuff, and if this happens you are also in the boat! Hence, ...


1

A deliberately blunt answer from someone who started in academia, pivoted, then worked in industry, and has now pivoted fields again and works in a mixture of academia and industry. Suck it up and get your Ph.D. It sounds like you're doing just fine, progressing along. It's not exciting you, but what my trail (listed above) has taught me is that one spends ...


1

You seem to be pretty close to the end. The topic of your dissertation doesn't require that you never study other things. You future is for you to decide. Many people change fields quite drastically after finishing a doctorate. I switched from math to CS because of the job market. I knew nothing of CS, nor even programming until I'd finished the doctorate. ...


1

‘Bloom’s Taxonomy’ is a useful tool for classroom educators. Benjamin Bloom creates the taxonomy, which was later revised by Lorin Anderson. His taxonomy helps educators develop critical thinking and higher order cognitive abilities in students. It provides a framework, or organisation, for classifying classroom lesson objectives. Bloom’s Taxonomy states ...


1

Let me add a long-shot possibility. Some universities have a way to record or even live-stream lectures. If you haven't explored this, you might see if it can be done. There might be a special office, audio-visual, or such. Even audio might be a help to you if you also have lecture slides. Failing that, the professor might be able to record audio and send ...


1

I'd like to add just one point to the fantastic answers already posted. Publish or perish often tends to favour quantity over quality, so a researcher who publishes 5 papers per year in mediocre journals may be seen, on paper, as being more productive than a researcher who produces an actual groundbreaking work once in two years. This is common in places ...


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