58

Only my personal experience, but I hope it will help you a little bit: I am almost in the exact situation you describe in your question. I finished my PhD in Algebra (coding theory, lot's of linear algebra and representation theory) and am now working as a software developer. As a fun fact, this wasn't always planned. When I started my PhD, I was still ...


49

In the US, 99% of long-term positions that involve being paid to do research in pure math are tenure track faculty positions, colloquially known as professorships (in the US, they follow the progression Assistant Professor -> Associate Professor -> Professor). A professor is paid to teach, do research, and to a lesser extent, to do a variety of other vaguely ...


38

I have not been in such situation. However, I do not see what is the problem for you to write a paper complementing or correcting the previous paper? Isn't this how science works? In my opinion, it is very toxic culture in academia to consider such thing as inappropriate. Those previous auathors are humans. Assuming good faith, that was what they knew and ...


20

Yes, an editor can review a manuscript themselves, but you cannot infer an editor is reviewing themselves when a manuscript has been with "a journal [for] one month...and the status is 'with editor' up to now."


19

Edited: OP mentioned that the paper has been published in conference (not just on ArXiv as was implied by phrasing). This can be tricky. The main thing is that you get due credit, and that the scientific community is aware of the mistake. If the mistake is in a key theorem that is the basis for the entire paper, then the authors should retract the paper. ...


19

Well, it's been more than a couple years for me since grad school, but I can add my personal experience to what is appreciably a rather subjective question. Of my group of students at a pure math department, with a few world renowned old timers, I would not say algebra was considered the harder path. On the contrary geometry and analysis students, such as ...


15

This is also something that is very true in statistics as well (applied vs theoretical). A theoretical math PhD is (obviously) extremely difficult and most of the topics in it tend not be directly beneficial towards future employment in anything but more work in abstract theoretical math. While many people think this is what they want to do at the ...


11

Since everyone here seems to scratch their heads about what might be going on, my first reaction is that there is a breakdown of communication between you and your adviser. It clearly doesn't make sense to do 100-page long computations on paper if they can be done by a computer. So the reaction of your adviser doesn't seem to make any sense -- but what ...


10

The current top answer is simplistic and US-centric. First, it glosses over the obvious. Tons of PhD students and postdocs are paid to do research and nothing else. It is difficult (and not really desirable, or usually possible) to be a postdoc forever, but this is certainly doable for many years, even more than a decade if you count PhD+postdoc. Second, ...


8

The editor may simply not have had the time to look at your manuscript and find a suitable reviewer. Or he may have contacted one or more potential reviewers, but they may not have accepted yet, in which case the editorial system may still show the manuscript as "with editor". Also, of course, editors do look at manuscripts themselves. They typically don't ...


8

First, I’ll describe what happens at my department (engineering, high ranking, UK). It might be useful to understand the mindset. We were recently hiring for teaching only position at my school (teaching fellow). The idea behind it was to get someone to teach in a specific area. The job is open-ended, the same salary as other faculty (Lecturer/assist prof), ...


8

The editor and publisher will have no special insight into the contents of the paper. The publisher doesn't even have any particular mathematical expertise at all. It is a waste of time to contact either of them. You speak about "the detail" as if you think that a more detailed version of the proof is out there somewhere, and if you ask the right person ...


7

First, it is not accurate to use "algebra" to refer to broad swaths of mathematics, any more than it is accurate to refer to "pure math", in fact. One immediate objection is already partly related to the issue of the question, namely, these are labels very often used by outsiders to refer to "not what they themselves do", and/or reflections of their own lack ...


6

If you think that you have found the proof of a paper, or you can (with evidence) notify the community of the wrong/improper/incomplete proof, you can itself publish it as a research article. For example, look at the following comment (to be) published in IEEE Trans. on Wireless Communication: Comments on “Coverage Analysis of Multiuser Visible Light ...


6

I believe that paul garrett is pretty much correct here, but here's a way you can incorporate this into your paper: Smith and Jones (1995) found that the area under the rhomboid apparatus was upper-bounded by the third order discriminant. While their final result is valid, a minor flaw was found in their proof. We provide a corrected proof in Appendix A. ...


5

I am an editor at a mathematics journal which uses a (IMHO) pretty crappy online editorial system. When a paper is assigned to me, I find it much easier to work with referees "off the grid" rather than using the infernal editorial system. (For example, the system insists that I input in an entire page of details before sending a referee request to someone ...


5

I have asked my adviser, if we can use software to do this computations and he refused without giving any reason why other than being embarrassed(I did not ask why.). He said it would damage his reputation. Not sure if he was joking or not. He also mentioned that, he had use software during his dissertation and have now forgotten how to use it ...


4

Don’t trust the US News grad school subfield rankings at all. They’re based entirely on surveys and most people don’t actually know a lot about things outside their speciality and their university. So you infamously end up with high ranking places that actually don’t have anyone in the subfield. If you want to know how good a school is in a subfield you’...


4

A few that come to mind, and are probably valid in other fields also -- Learn how to give good talks. Learn how to describe your research informally. Say you meet someone at a conference, and they ask you "What do you work on?" Can you convince them that what you work on is interesting? Learn how to come up with interesting questions that you don't know ...


4

Let me start by saying that while I have never been involved in graduate admissions (my college does not offer a graduate program in mathematics), I'm an assistant professor of mathematics at a well regarded liberal arts college whose graduates regularly go on to attend top graduate programs. As you acknowledge in your question, the reality of the ...


3

This funding comes from two main sources: Employment, e.g. by getting a professorship somewhere. This means a steady salary. Note professorships aren't just teaching duties - professors are also expected to output research, mentor PhD students who output research, and so on (see this recent question for what happens to "unproductive" professors). Grant ...


3

How can a student in the US honestly hope to learn enough math to be on an equal footing with a student who has worked 50% longer hours, and begun their mathematics education years earlier (if we're also not looking at particular cases of geniuses emerging at a young age in either country, but rather the average intelligent student)? Your question contains ...


2

2) Say something like ... "the results are based off the ideas by author X" but don't give as much of a "these are author X's results" flavor. Author Y then after mentioning author X, proves the theorem themselves. You’re missing the forest for the trees here. The result is author X’s result. A small mistake that anyone can correct cannot reasonably be said ...


2

Hmmm. Muddle. Try. Fail. Muddle. Repeat. Repeat. Try. Succeed (partially). Muddle. Refine. Muddle. Succeed (maybe). To paraphrase a bit of wisdom from another field: Posing good questions comes from Experience. Experience comes from posing bad questions. There isn't a plan in mathematical research (or in most other fields) that will guarantee success. ...


2

Understanding the research process and how to overcome hurdles and frustrations. Some of these points have already been addressed in other answers, but I think an explicit list of things around this is good. This means: Knowing how to find interesting research questions. Knowing how to get started on the research process. Understanding what it means to put ...


2

It sounds like the research mathematicians are at the same campus. If so, even if not in the same building, you can cultivate collegiate relationships: Go to the seminars held by the research group Be a co-supervisor for PhD students in the research group If you spend some time finding out peoples' interests, then you could potentially write a grant ...


2

It's very dependent on where you are. I'm from Europe and here it's extremely competitive. In some developing countries though, it's less competitive because there is a great need for university-level teachers, but research is far from the priority in these jobs (according to some of my friends who took them). It all depends on what you're looking for. If ...


2

I doubt that your advisors motives can be learned except from him. There are too many options, but I doubt that simply stalling you is one of them. No one gains from that, I suspect. I can only speculate on why this is happening. Perhaps the advisor is simply distrustful of computer programming for this sort of thing. An error in coding can throw you off ...


2

First of all: you should really be asking your advisor this, not strangers who don’t know your circumstances. In any case: if you have a result that you feel is ready to be shown to others, why not write it up and put it on ArXiv yourself? That way no one could do this to you.


2

Hmmm. Are apples better or are oranges better? Hmmm. It is difficult to compare educational systems with such a narrow focus as is done in the question. Where do we study Linear Algebra? Ultimately there are more important questions. These questions are attempted to be answered through a somewhat ill formed national educational set of objectives that may ...


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