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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 ...


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 ...


6

Yes, some 225 journals do operate under such a model, called Registered Reports. As you suggest, the approach has a lot of advantages. The tagline is: Registered Reports: Peer review before results are known to align scientific values and practices. Clearly, this is not yet a majority view, but as a methodology it is in the ascendant. The umbrella term ...


6

Welcome to the club of being a miserable postdoc! I was and am in quite a similar situation. I had the benefit of my first postdoc being with a horrible boss and lab, and my second being with an amazing boss and lab, so it has been easy to figure out which aspects of postdocing are me sucking and which aspects are the environment sucking. During the ...


5

What makes this question challenging to answer is that it’s addressing the wrong level of generality: you’re asking about a very specific situation (publishing a simpler proof of a known result) but your questions suggest you’re missing basic facts about publishing of math research in general (how to “address an editor”, how to select a journal to send your ...


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

If you've had to go through ethics approval process, you are bound by the protocols that you come up with them. We've carried out interviews with other academics and are bound by ethics, and when I have been interviewed by other academics, I have gone through the ethics process. I would be skeptical if somebody was carrying out a research interview with me ...


3

Principles of academic freedom usually leave it up to the individual researcher to decide what to study (within ethical limits). They may certainly be judged (for promotion, tenure, raises, etc) based on whether their research is successful, but there's no "prior restraint" as it were. So an institution usually won't require this sort of pre-review. It is ...


3

That depends on the journal. Some do put accepted articles onto their websites. In most cases, however, the article must first go through some kind of editorial process where the style of the manuscript is adjusted to the requirements of the journal -- for example, many manuscripts are submitted double-spaced, with figures at the end of the manuscript, and ...


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, ...


3

When you were an undergraduate, studying (I assume) math, the advice you got was good. Read a lot of papers, somewhat superficially, to get an idea of what it is possible to do and how to go about it generally. But now that you are in a graduate research program you need to do more. The basis you get from textbooks isn't enough to get you to the research ...


2

If you have questions then ask them. Otherwise a simple Thank You note would be appropriate. But just asking questions in an attempt to pad your application probably won't do any good. But thank him now and ask questions later if they arise. How long it takes is variable and up to them. But they need all required information before they make any decisions. ...


2

In my experience (in the field of statistics - but I suspect it is of wider application) you need to switch between two modes. Sometimes, all you need is to skim a paper for its main ideas. But sometimes you will never understand a paper unless you try to reproduce its results. The reason for that is that published papers tend to be highly compressed, ...


2

New proofs are valued in mathematics if they open new doors. But the proof probably needs to be something that has value in its own right, though there are exceptions. A short proof of the four color theorem that doesn't rely on computers would be interesting, even without the "new doors" aspects. (I hope that is still the case. I haven't looked at it in a ...


1

"A direct proof of Cockatoo's equation." "An elementary approach to Shrokensveny and Ljubovitch's inequalities" "Deriving the circumferent super-Galois hyperextension of Williamson spaces from basic topological axioms" Simplified proofs are amongst the most valuables contributions to mathematics if they convey either new perspectives, or clarity or ...


1

You sound like a thoughtful and honest person. Being into Menotring, service and teaching is a great reason to want to be and academic, because it is 90% of the job as fa faculty member. I can't speak for your field, but in my field it would be not be unusual for a postdoc to produce little in the first 5 months. So its possible you are doing better than ...


1

Although I haven't seen this format in particular (and I'm a neuroscientist, maybe I should be paying more attention!) it looks like Open Peer Commentary is also a phrase used by other journals, so searching based on that phrase may help you find journals in other fields relevant to your interests. A less-formal approach that is somewhat similar is "post ...


1

Some publishers will put things online and others will not. For an individual case you need to consult the publisher. Some suggest, or even require, that the author publish to a repository. Some publishers will even forbid it. Ask an editor or consult the publisher's website.


1

Textbooks and problem sets are the specialized tools to teach you technical abilities. Research papers may describe a technique, but they're often more focused on proving that the technique is sound, or a promising direction for research. Teaching you how to use the technique is not their primary aim. That's probably why your professors told you not to get ...


1

is a journal publication possible for...a methodology? Yes, assuming the ability to add functionality to a tool - from data generated by the tool - is useful to others, and assuming outcomes can be (relatively easily) manually derived from the aforementioned data. Added functionality is presumably useful, so the former assumption can be dropped. (Some ...


1

It depends. A good student who is very self motivated can rise above. That means you would need to be doing a lot of work in addition to the work assigned in class. If you can do that, consistently for your entire degree, you can come out knowing as much as you would in a "tough" school. It's a two-fold challenge. First, there is doing it and keeping it ...


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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