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3

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 ...


21

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 ...


-2

In my experience, you would have to be very unusual to make this jump. Of course it's possible. I have seen it more from chemistry to physics or math to physics for students who knew they just sort of picked wrong to start. Even then the road was not easy. (But consider Lars Onsanger was a chemE bachelors. However, he was also Lars Onsanger!) In ...


0

I can't speak for the UK, which has a different educational system altogether, but in the US, most programs would find a CS graduate "acceptable" for a physics doctorate. This assumes a good record overall, of course, and probably a few physics courses in which you did well. In the US, a CS student probably has a few such courses, though not advanced ones. ...


0

The obvious answer is to shirk teaching and divert time to research. Do it in a stealthy manner of course (just be perceived as efficient, not blowing things off). Use your massive Ph.D. brain to figure out how to do that. (limit graded homework, use established texts and curricula versus trying new ones, etc. etc. use your noggin.) But really, you are ...


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), ...


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 ...


1

Lot of great answers, already. Some different thoughts (not as good, but hopefully additive): You could do it as an avocation. Go and earn a bunch of money elsewhere and then do it on the side. Like Fermat. (US answer) Look at government service, especially the NSA, but also national labs or FFRDCs (quasi government as they have contractors running them)....


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, ...


-1

I will argue that research is the primary job that most salaried professors get paid to do. From Wikipedia: Professor: Professors often conduct original research and commonly teach undergraduate, professional and postgraduate courses in their fields of expertise. Note that "research" is listed first. From an excellent page by Mark Tomforde, ...


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 ...


1

(From comments from the OP) In a very high level, the theorem is on the running time of an algorithm, and I found one instance where the algorithm does not halt. Under mild assumptions on the input it can be shown that the asymptotic running time is the same as what they originally claimed. As someone who works on statistical algorithms, it's my opinion ...


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 ...


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. ...


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 ...


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 ...


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 ...


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. ...


1

I added a PhD minor in computer science to my mathematics PhD. It's helped market me for industry jobs. Every recruiter has mentioned it. One still needs to have the skills (and be able to demonstrate them in the interview) but the minor does seem to get you phone calls.


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 ...


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 ...


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 ...


1

Both for US and outside of US, some maths classes are way more important than those of economics. But that does not certainly mean that you need a maths major, but means that you should absolutely have a notion in maths thinking. Other than that, those majored in engineering or maths can perform better in economics grad school as it relies very much on ...


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 ...


0

My advice is to maximize income and reduce debt. Not do more schooling. You only have so many productive years. Your energy will not be as high at 50 as it is at 35. The only place they really need Ph.D.s is if you want to be a professor. And who would want that. Oh...and many are called but few are chosen. Just look at all the physics postdocs. ...


1

First, taking on a large amount of debt at this point could be a big problem. However, several candidates for president are currently discussing forgiving student debt, a good thing to do in my view. It will be seriously discussed over the next 15 months, at least. It may be that your debt problem will get erased. Whoopie. Second, spending your life doing ...


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."


14

I got my PhD in Germany (Heidelberg) and then did a postdoc in the US. I think that was the right choice: In the US, you will have to spend a couple of years taking classes, satisfying your breadth requirement, and you will likely have to teach alongside your research. There is much to be said about this system -- including that it teaches you to teach, and ...


7

In comparison with someone who is completing a PhD in the US, a candidate who is completing a PhD in Europe will have a few issues to contend with in trying to get a job in the US. Bringing you to campus for an interview will be much more expensive. Many institutions simply won't pay the travel expenses of interview candidates who are outside the US. You ...


6

I think you should choose this based on personal preferences only. I see no career advantage either way. Bonn is a top level university by any standard as is ETH Zurich. You will find no feeling here that they are inferior in any way. Bonn, has, for example, several Nobel Prize and Fields Medal winners. Whenever you do it, you will have to deal with visa ...


8

You should submit your paper to Proceedings. The overview page for Proceedings of the AMS clarifies this: This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. If your article is exactly 15 pages long (or less), then its length does not exceed 15 pages, and so it is suitable ...


2

I don't know if the editors of the two journals have an actual policy for this, but I'll guess two things. First, if you send it to the "wrong" one, you will hear immediately to send it to the other instead. Second, being a bit (i.e. very) pedantic here, your paper probably doesn't completely fill the last page to the very limit, indicating that it is, ...


2

Yes, several people have done that (including myself, though the errors were typos). It is almost always looked upon positively in the academic community. Will the industry look positively upon it? Not sure. On the one hand, it's a positive that you are taking responsibility for what you wrote and correcting the record despite not being required to. On the ...


3

Write the paper, attributing the person in the way you feel most suitable. I would write that the person in question provided an outline/idea of the proof of proposition this and that, and include something to this effect in the acknowledgements, close to the result, and maybe in the introduction if the result is a major one for the paper. Send an email the ...


2

The correct, if not very useful, answer to the title question is no, not absolutely necessary. But philosophy departments aren't likely to advertise very often for mathematicians or computer scientists grounded in computability (an important topic in epistemology). Like any other modern academic field, philosophy has specialization, and some departments ...


4

In most places a citation (ack) would be enough. For a citation, list it as a "private communication". That is normally enough. You avoid plagiarism because you properly credit the idea. There may be a few places, though I can't name them, where it requires specific permission to do this. It isn't needed in the US, but seek local guidance elsewhere. Most ...


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