text:
Prefix Dr. or Mr./Ms. if I have an MD but not a Ph.D. in medicine?
I am sending in an article to a ScholarOne journal: should I mark my prefix Dr. or Mr./Ms. if I have an M.D. but not a Ph.D.?

Dr. is the style for anyone with a doctorate (excepting JDs).  That goes for PhD, DDiv, MD. DFA, etc.

First, note that the title that you give to a ScholarOne manuscript handling system probably doesn't matter at all --- more than anything else, that is in there to avoid offending you if you are particular about being given your title.  The actual publication of the paper will typically omit titles, so putting in the title just regulates what the system will call you in email.
That said, Dr. is a correct title to use as an M.D.  In fact, many people will argue that opposite, that it is Ph.D.-holders whose use of the title is dubious!

MDs should use "Mr./Mrs./Mx." as in the UK. :-)

@RoboKaren: Surgeons title themselves 'Mr/Mrs', but physicians are 'Doctors'.

I don't always use the prefix, as it has no relevance when I'm, for example, out drinking with friends. But I do sometimes use Dr. with my name, for several reasons. Sometimes it is just fun. Women actually like to call me Dr. Hurst (I could never get a single one to call me Master after I got my MPA). It is just a sign of respect. But sometimes if I am discussing an issue dealing with economics, my Ph.D. field, I will add Dr. to ward off trolls who think they know all about economics and want to educate me about how I'm wrong.
It also made a difference in my work. On one job, my company bought out a competitor and absorbed some of their workers. One supervisor in the modeling department where I worked used to insist that his methodologies were superior to others we were using, which was not true. In order to push his models, he always had to point out that the top modeler on his team had a Ph.D. I kept my mouth shut for a while, until one day in a meeting he made a big issue of it, and my boss said "Well, I have a Ph.D. on my team also, Dr. Hurst." That guy was really embarrassed and shut up and never brought it up again.

Sadly, neither my real doctorate of philosophy nor my fake doctorate of divinity seems to ward off trolls.


text:
What makes someone deserving of a Ph.D.?
Few days back while attending a thesis defense, one Professor was asking the defender why does he think, he deserves the degree. I was wondering since then, is there really any general answer for that? or the answer should be given describing my own work and then emphasis them how it is important for research field?
I asked the question here to know your opinion about it and to list down what could be the possible answers to this question.

Wow, what an awful question to ask during a thesis defense.

@TobiasKildetoft I agree, it may appear awful, but it may just be that the professor wanted to see whether the student can describe the novelty aspects of the thesis' results.

"I fulfilled all of the requirements."

"I don't know, you tell me!"

Eight years or more, working full time, pushing the limits of human knowledge, do you need to validate it any more?

I'm a bit confused by the answers, as I always thought a Msc should already advance human knowledge, though not as visibly as a PhD. Is this a misconception? Or should I ask this as a separate question?

@mafu I think it would make a good question to ask what is the difference in the requirements for a MSc and a PhD.

One of my committee members did this... but he was nice enough to pose the question ("Do you think this merits a PhD?" which truly stumped me, since I figured answering that was the committee's job) a few weeks beforehand, so by the time the defense came I had discussed with my supervisor and wasn't caught flat-footed.

@AustinHenley: I don't think that makes you deserving of a Ph.D., that only means you're going to get a Ph.D. You're assuming the requirements involve deserving the title...

@einpoklum In my mind they are 100% the same.

@Dirk That question is here: http://academia.stackexchange.com/questions/7252/what-are-the-main-differences-between-undergraduate-masters-and-doctoral-thes/7255#7255

Normally such a phrase ("Why do you think this deserves ...") means "Erm... I like you guys and do not want to spoil your celebration, but if you want my opinion, you should be ashamed of what you are doing right here right now." in plain English (or, at least, Russian). Whether it is appropriate to say it in each particular case depends on many factors, but I cannot claim I have never had a temptation ;-).

For a Ph.D., my favorite explanation is this cartoon by Matt Might.
In short: a Ph.D. is a measurable contribution to a sum of human knowledge.
To be able to answer this question, all you need is an idea of how to describe what you have discovered, and how it fits into the context of work by others that has come before.  This is often not easy to answer, but an important thing to think about as one is writing one's thesis in any case.

Had the same thought. The size of the contribution demonstrated in the cartoon is also key to answer the deservingness question: the contribution needs to be measurable but it need not necessarily be large in any absolute sense.

The only thing I disagree with on that cartoon is depicting the human knowledge as a solid circle. As my friend once put it, it rather looks like Serpinski's gasket: there are very long lines in many directions but it is still nowhere dense and a small sidestep in an "orthogonal direction" can bring you to terra incognita right from where you stand at any moment.

@fedja Another interesting view on this a fellow student mentioned is that the sum of human knowledge is not an ever growing connected region, but a hollow disc in which we are constantly scaffolding outwards while forgetting inwards. This is evidenced by how often the idea "All good ideas have already been conceived" is itself reconceived :D

@Tim Indeed, that is true on high levels. Fortunately, one good side effect of human mortality is that we cannot make the new generation reach the outer annulus without maintaining at least some pathways to there from ground zero :-)

Usually the answer to this is formulated in the rules of the institution. In Germany we call this the "Bachelor-/Masterprüfungsordnung" (for BSc and Msc) or "Promotionsordnung" (for a PhD).
The one from my institution contains something like

Die Promotion dient dem Nachweis der Befähigung zu vertiefter selbständiger wissenschaftlicher Arbeit.

which translates roughly to

The PhD degree certifies the ability for in-depth and independent scientific work.

It also says that one needs a written work (called dissertation) and an oral exam. For the dissertation there is

Die Dissertation muss die Befähigung der Verfasserin oder des Verfassers zu vertiefter und selbständiger
  wissenschaftlicher Arbeit nachweisen und einen Beitrag zum Fortschritt der Wissenschaft auf [insert some field] darstellen.

which is roughly

The dissertation has to certify the ability of the writer to do in-depth and independent scientific work, and to contribute to the advancement of science in [insert some field].

There are also some regulations for the oral exam but actually there is not a specific term what constitutes a passed or failed oral exam.

"The PhD degree certifies the ability for in-depth and independent scientific work." Indeed. However, if I were asked to say "I am able of in-depth and independent scientific work" in public, I would either blush from the top of my head to the toes, or collapse in uncontrollable laughter. Such phrases are intended for using on other people and other people only.

Yeah sure, but I thought it would be good to have fact here and the OP asked for a "general answer".

If @Bee decides to "accept" an answer, this one ought to be it. Spot on: the fitness of the research for the award of degree is institutionally defined, and does vary between universities. This is the thinking person's version of Austin Henley's comment to OP: "I fulfilled all of the requirements." Right - what requirements were those again?

These two things are the essentials (1. independent work 2. independent report). To formulate it to fit to a conversation/defense I would say "My thesis shows that I can do scientific work on my own. I have done the research and I written the report independently with the guidance of my Professor (and collaborators)". The last part is the expected acknowledgement which is also essential part of scientific behavior and reporting (be polite and share credit).

Yap I'm pretty sure that is what I remember too : ability to conduct in-depth independent scientific work, nothing about advancing human blahoo or blahaa.

When I arrived to this question, there was (and probably still is) a highly upvoted comment:

"I fulfilled all of the requirements." —  Austin Henley

I think that it's very easy for a new PhD or candidate to have serious doubts about the quality of their work, and to suffer a bit of the impostor syndrome.  After all, they've spent numerous years seeing just how much knowledge is out there, and realizing that despite their new expertise, in the big scheme of things, it's actually a pretty small piece.
I've just completed my PhD, and one of the things that my advisor mentioned to me was very helpful, especially when I was feeling a bit of what I've described above.  At my university, PhD students become candidates when they complete their candidacy, which includes their candidacy proposal, in which the student presents their research proposal to a committee (typically with members of their eventual examining committee) who must approve the proposal.  My advisor reminded me that regardless of my own perspective on my research, the fact of the matter is that three or four years ago, a committee of experienced researchers, professors, etc., (i.e., my candidacy committee) reviewed my proposal and confirmed that the work it describes merits a PhD.
Based on that reminder, I framed by defense slides by beginning with a very quick review of the original candidacy, including a slide with a short problem statement.  At the end of the defense, I pulled up another copy of that slide and addressed each point in the original problem statement, explaining how I'd addressed it.  Then I followed with some "reveal text":

 quod erat demonstrandum

My research involved a fair amount of proof theory and formal logic, so this was especially appropriate, but the point remains: the work that I presented was that "which had to be demonstrated".  The experienced committee said several years ago that the proposed work merits a PhD, and I completed that work.
The point here is that it's not really the candidate's place to determine what merits a PhD.  They haven't, at that time, enough experience to make that determination.  The university and committee does, and has already decided what merits a PhD, and it would be entirely appropriate to respond to the question "What merits a PhD?" with "you, as a committee member, explained that to me some number of years ago, and I've fulfilled those requirements."

This arrangement with proposals and candidacy committees is not universal.

@kundor That's a good point.  I've updated my answer to include a bit more description of the process for context.  In institutions where such arrangements exist, I think that they are beneficial in this situation:  if a student has successfully completed the requirements, there is no retroactive counterargument that the research isn't sufficient;  that argument would have voiced during the candidacy examinations.

@Joshua: While they may be beneficial in this situation, I'm not at all convinced that they're a good idea in general, especially in my field (mathematics). That simply isn't the way I ever did research, before or after my doctorate.

@BrianM.Scott Can you elaborate a bit on your research methodology?  I think we may have missed each other's points a bit, because I have a hard time seeing where it's not a good idea, whether in a formal setting or not, to have other more experienced people in your field at least confirm that "yes, the thing that you're thinking of working on is still an open problem, and it would be useful to work on it." Of course, I recognize that not every significant result can be predicted in such a way, but it seems like a bit of experience helping to avoid some dead-ends would usually be helpful.

@Joshua: I worked on whatever caught my fancy, because it was fun. In the case of my dissertation, a small problem led me to notice a parallel with something more familiar that suggested a host of related problems, many of which I could solve, but it came out of the blue. For the most part I didn’t set out to solve specific problems: I played with neat ideas to see what, if anything, would pop out. (And in my experience most published research simply isn’t very significant.)

The general requirement for getting a PhD degree is to produce novel research results (including of course writing them down in a dissertation and defending it in front of a committee). By this, you should show that you can work as an independent researcher.

one Professor was asking the defender why does he think, he deserves the degree.

If someone asks that during the defense, the answer should point out in which way the results are novel and a contribution to the current knowledge in the thesis' area of research.

"the answer should point out in which way the results are novel and a contribution to the current knowledge in the thesis' area of research."  Agreed, but I also want to point out (and did, in another answer) that the candidacy committee declared however many years ago that the results of the proposed research (if executed successfully) would be novel and a contribution.  The question at this point is only whether it was executed successfully.

For a Masters Degree, you are using existing knowledge and applying it to a new situation.  For a PhD, you are creating new knowledge - you have discovered or invented something that was not known or existed before.  If you can show that you have done this, you deserve a PhD.

Let's look at the abbreviation: PhD. Philosophiae Doctor which literally translates (my translation) as "Teacher of the beloved wisdom". (Doctor from doceo - to teach; philosophia from φιλος - dear, beloved and σοφια - wisdom or knowledge.
To be worthy of a PhD, you must therefore teach - which in the widest sense means add to the body of knowledge that came before. You are no longer learning - you traveled to the edge of the universe of knowledge, and boldly went where no-one had gone before. And - and this is a crucial element - you told stories of what you discovered when you came back.
The question is a good and fair one - and the answer should be obvious:

Through my research I have discovered [X,Y,Z] which I have taught the world through my publications and dissertation.

No need to blush - just state the facts.

Interesting how you mention publications. I know one faculty member who was personally frustrated by the lack of institutional guidance on "how much research is enough research (to justify awarding a PhD)." To address that, he devised his own standard: four published papers; all his students were told his expectations up front. It made sense to me at the time, and I've always marvelled that his idea hasn't gained more traction.

@J.R. - a dissertation is in itself "publication " but the peer review process can add a bit more credibility to the claim of originality; further the act of writing papers helps distill the thought process and it's good practice for a future independent researcher. I agree that some expectation of peer reviewed papers is reasonable.

One thing he liked about papers was how they added a layer of objectivity to the criteria. How much research needs to be put into a dissertation? Those expectations can vary from school to school, from department to department, and even from advisor to advisor. His "four papers" criterion eliminated much of that subjectivity. Since the O.P. is explicitly asking for "possible answers to this [deservedness] question", I thought it was worth highlighting this. (I thought about leaving an answer, but your answer is pretty close).

@J.R. - the "smallest publishable tidbit" can be indeed tiny, depending on your field and your choice of publication... And sometimes one giant contribution could be more than enough (think Brian Josephson http://en.wikipedia.org/wiki/Brian_Josephson - his prediction of the Josephson effect at age 22 got him a Nobel prize, but he didn't get the PhD until he was 24...)

-1 for beginning with the etymological fallacy; +1 for ending up somewhere reasonable nonetheless. Net result: no vote.

@DavidRicherby - would you please explain the "fallacy"? See for example http://academia.stackexchange.com/q/9820/15062 - I believe it is accepted that "Doctor" in this context means "teacher". Whether that is "qualified to teach" or "demonstrating that you have something to teach" may be two different things - but in my mind they are closely related. The use of "philosophy" in the title is indeed a bit harder to explain, but I think that it really is used in its older sense of knowledge, rather than what we generally think of as philosophy today.

@Floris The fallacy is to assume that, because "Doctor of Philosophy" is derived from Latin and Greek words meaning "teacher of the beloved wisdom" (which is, by the way, a beautiful translation), that it must still mean that today.

@DavidRicherby - fair point; I suppose it doesn't mean that it must mean it, only that in the institution where I attained that degree (and where the ceremony for conferring said degree it is still held in Latin, as it has been for the past 800 years) it was considered to still have that meaning. It's possible that newer institutions took the title and forgot its origins. Apologies for being narrow-minded. Thanks for the compliment about the translation!

A couple of years a senior and well-respected scientist that I know personally told me his perspective regarding what the title PhD means to him. I try to take that with me since then, especially at times of self-doubt.
He said the most important message that the title PhD conveys is that the holder has survived a significant period of time (3-5 years depending on where you live/work) in the academic world, battling with self-doubt, uncertainties in work, questionable guidance/project management, and many more challenges.
So, the way I see it; if you have survived until the end of your thesis defence AND fulfilled all criteria set by the university † (including original research), then you damn-well deserve the title and there's nothing anyone can fuss about. :)
Good luck with your work/defence.

† after all it's the university that grants the title, and thus its the institution's responsibility to make sure that the titles they bestow upon candidates is up to the international standard. It's their reputation on the line, as well.

This question is not a check if you are over self-confident or anything the like. Simply provide arguments why your PhD work matches the acceptance criteria that a valid for that institution. Your supervisor should know.
If criteria seem not obvious for some reason, emphasize the scientific novelty (some details you have investigated first ever) and any scientific recognition of the results (accepted papers, attended conferences). Negative results that just disprove the initial work hypothesis may be near equally significant.

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How possible is it to do mathematical research outside academia?
Does anyone know if it is possible for a Ph.D. graduate of mathematics to successfully do research in his/her spare time?
The work environment and conditions in academia seem somewhat deplorable at the moment---no offence intended,  but that simply very much appears to be the case from an outsider's perspective---and it just strikes me that mathematics would surely be the subject most suited to Ph.D. graduates who don't want to go there, but still want to research, as "only pen and paper" are required.
If one were really, truly devoted...how much of a disadvantage would they have compared to someone who chose to stick it out?
Are seminars entirely barred?
Is it impossible to publish?
Collaborate?
How much (more) time would someone who stayed in academia have in a day to spend researching?
Also, what about people who have not got PhDs? I would think it's more or less impossible for them to contribute very much of value if they only have a Bachelor's or a Master's degree, but I really don't know.

What do you mean by "research"?  There are lots of non-academic jobs where your job will be to do research.

Should be moved to Maths SE forum. But still a good question (+1).

@shivams I disagree: I think it is a fine fit for this site.

@shivams I'm from Math.SE. If migrated, this question would be likely to be voted down and closed pretty quick.  It is certainly a much better fit for this site.

"I would think it's more or less impossible for them to contribute very much of value" -- Ramanujan didn't have a degree until 1916, which is after many highly valuable contributions including collaboration with Hardy. But obviously, just because Ramanujan did something doesn't mean it's not more or less impossible.

If you don't have a phd and in not in academia, then no, it will not happen. A person who is brilliant enough to write and publish papers without proper training from an advisor, would without problem also be able to land a permanent position in academia...

Publishing
In mathematics, most people will judge your research on its merits, not based on your credentials or affiliations.  So this is not an issue, if you are able to generate significant results and write them up in a clear way.
Seminars
I have seen many members of the public regularly attend seminars.  I've never heard of them being kicked out.  It's not an issue.
Funding
The primary drawback is that you won't be paid for your research if you are just doing it in your spare time.  Unless you are already independently wealthy, that means you will have relatively little time for research since you need a day job.
It is of course possible to get grants to fund your research without being in academia; there are a number of private entities in the US funded entirely by grants, and many of them include mathematicians.  But you said spare time only.
Collaboration
Another drawback is that you won't be in close contact with other researchers by default.  It wouldn't be impossible to establish that contact, but again you must consider whether you will have the time.  And people won't take you seriously unless you have serious results.
Not getting a PhD
In mathematics, even more than in other fields, it is almost impossible to make a contribution without spending several years learning what is already known.  In principle you could do that without getting a PhD, but why would you?

I totally disagree with your first point. The reviewers of your paper will google your name and they will turn up their noses if you do not have an institutional affiliation.

@Flounderer Some, maybe, but not as a general rule.  I've published papers when I've lacked an institutional affiliation before.  I even asked my advisor, who has served as an editor on several high-ranked journals, if I was doomed from the start doing this, and was assured that I was not.  And that in fact journals both receive and publish papers from authors with no academic affiliation fairly regularly.  A reviewer may have a higher level of scrutiny of your work, but if they reject it simply due to no academic affiliation the editor will ignore them and get a new reviewer.

@Flounderer - I have also had a paper accepted with no affiliation.

@DavidKetcheson - I agree with your last point.  I.e. if you've done the work necessary to publish (in decent journals), then you've probably done the hard part of getting a PhD.  So you may as well be enrolled on a part time degree and get some credit (and yes, affiliation and access to seminars and a library)

Another obstacle to overcome as a non-affiliated researcher would be lack of access to powerful computers and software, something that can really help speed along research.

To back up @Flounderer point, publishing does depend strongly (if not only) on the affiliation (although many of us would like to think otherwise).

It should be possible, but it will be hard.

Whether seminars are barred to you will depend on your locale. Even if non-students are officially not allowed to attend seminars, you may find a sympathetic professor who may turn a blind eye.
Of course you can publish as an independent researcher. You may come in for some extra scrutiny until you have established a bit of a reputation.
Similarly, nobody will care specifically about whether you have a Ph.D. when you submit a paper, as long as you have a command of the specific specialty you are trying to publish in.
Of course you can collaborate, once you have convinced someone that you have worthwhile ideas. Getting a Ph.D. may be helpful to distinguish you from random cranks in establishing contacts, as well as start you out on building a network.
As to the time you will have to do research, this will vary. If you are at an R1 institution, you will have a lot of time (but of course getting in is hard). If you are at a teaching college or in a research job in industry, you will have more time. If you have a completely unrelated day job, you will need to rely on your spare time. And when you come home after a typical job, you will not be as fresh and as enthusiastic for research as if you started out in the morning, at your desk in a university. (If you ever decide to start a family, expect your spare time for mathematical research to drop to zero immediately.)

Academia still has advantages, for instance:

Your library will likely have subscriptions to the major journals, so you don't need to bombard authors with requests for their papers.
You will likely have at least some budget to attend conferences. If you go the independent researcher route, you will need to pay for these out of your pocket.
If you are not at a university, you may have to pay higher registration fees (which depends on the conference and may be negotiable).
If you hold a day job and want to attend a conference, you will need to use up vacation days for that.
Although you can collaborate as an independent researcher, it will still be easier at a university. There will be seminars right next door, guests, access to students you can mentor and develop into collaborators etc.

I work in a math-heavy research job in industry and have been able to do some more-or-less serious research, mostly on the side. (And I obviously still have affinity for Academia.) It can be done, but it's hard.

If what you want to do is research, do your Ph.D. first (I did). This will give you an idea of what's ahead of you and give you a bit of a network. If afterwards you don't find a job in academia, you can still get a day job and try the research-on-the-side route. (However, your priorities in life may have shifted by that time.)

"nobody will care specifically about whether you have a Ph.D. when you submit a paper" This is true in a literal sense. However, without a PhD, it's hard to pick up the necessary skills to write competent-looking mathematical papers, or to select suitable topics. You'd need to find some other way of acquiring those skills.

If you are at a teaching college or in a research job in industry, you will have more time. Did you actually mean less time (compared to R1)?

@just-learning: "more" time compared to the time at an unrelated day job, but of course less time than "a lot" of time at R1. Sorry, I see how that could have been confusing.

A supplement to other answers: no one seems to have explicitly mentioned what might be biggest "disadvantage": you will probably have a lot less motivation to do "academic" research being outside of academia.  Research is hard, and external motivation (e.g., constantly being around people interested in say pure math research) can make a big difference in your productivity.  Here, where you work and what kind of community you are in and culture you are a part of can play a big role.
My personal impression is that quite a few people in industry positions with a more academic math-heavy culture (like NSA, Microsoft Research, Google, IBM, once upon a time AT&T/Bell Labs, National Labs, etc) do a reasonable amount of academic publishing in their spare time.  But at other kinds of companies, even where you do research, like banks or hedge funds, academic publishing seems to be less common.

In addition to this, it is hard to find the time for research if you have a regular 9 to 5. Research takes chunks of time, not just snippets here and there. It's doable but not easy.

As an academic mathematician, I can assure you that I do about half of my research in my "spare time" (that is, outside of paid hours) and I have done so for over 30 years.  I expect most academics do similarly.  If you are truly devoted, then just do it.  I recommend getting up at 4am or 5am daily so you have a couple of hours before the family awakes.
Regarding access to libraries, seminars, etc: contact a university (probably best near where you live) and ask about an "adjunct" appointment or affiliation that gives you access to facilities.

If you're an academic mathematician, then surely you're salaried, in which case the concept of "paid hours" doesn't apply to you.

@zibadawatimmy contracts usually say you have to work a certain number of hours per week. If you work more than that, you are working unpaid hours.

@Davidmh I would strongly disagree.  You are paid to do your job to a certain minimum specification, but if you go over that's not something that's external to what you're being paid for: it is exactly what you're paid for.  My parents are salaried professionals, and sometimes they work long nights or weeks or even months.  They don't get paid extra, and it's not "unpaid hours": they're doing the job they are specifically salaried to be paid, and sometimes that requires extra time and workload.  That the work can't be easily characterized in work-hours is precisely why you get salaried.

@zibadawatimmy my contract does specify a workload of 39 h a week, but no specific work output (it is very difficult to define, anyway). It doesn't mean I stick to that schedule, but when I work more than that, I am not getting paid for it, hence unpaid hours. Some postdocs here even have contracts for a certain number of hours a year, and they can distribute them as they please.

@Davidmh That's a strange specification.  That sounds like an explicit attempt to classify you as a part-time worker to avoid requirements to give you various benefits and the like.  Looking at your profile confirms what I suspected from that: you're a grad student.  My grad student contracts also involved talk of work hours, in the form of saying I was to work less than 20 hours a week on my TA duties (rarely a problem).  It's mostly a stipulation the university puts in to cover their own butts, and to avoid full-time employee classifications.

@zibadawatimmy It is as mentioned rather difficult to specify output. Research simply does not work like that. Also PhD students in Europe are often (by law or otherwise) full-time employees in case you did not know that.

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Should you state multiple degree titles in your CV next to your name?
If I hold a MSc and a BSc should and I want to show that next to my name in my CV, should I use:

Sosi, MSc, BSc

or simply the highest one:

Sosi, MSc

Related: http://academia.stackexchange.com/questions/55275/do-academic-titles-matter-in-cv

If this is an academic CV (as this site is about Academia), then you should not include your titles next to your name in your CV, but describe them in the "Education" section.

Highest followed by any professional titles, i.e., XXX PhD, PE


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Do professors work through all the homework problems they assign to students?
I'm wondering if this is case especially for time-consuming work like programming problems in computer science spanning several thousand lines of code.
Or when a professor teaches a new course they are not intimately familiar with e.g. did not take it during undergrad.
For professors that don't do this, how (if at all possible) do they address homework concerns during office hours? Is it recommended for professors to know the ins and outs of all problems they assign?

This question seems to be based on a somewhat unrealistic premise, in that it implies professors design tasks that are assigned to students. While it can happen, I doubt this is the rule; in my experience, this is more often than not collaboratively or even completely done by one or more TA, whose task is specifically to design solvable homework tasks and make sure all the organisational details around these tasks run smoothly.

As a graduate TA, I can tell you that the problems that first-year undergraduates work on in my department are so simple to me, with my experience, that I could complete them within a small fraction of the time it takes them (30 minutes instead of 1-3 hours). I imagine that the differences in skill between professors and their students is usually much larger.

Another anecdote: After one exam, a teacher came back and told us that when he tried to solve the problems (four question exam), he realized that the second, third, and fourth were so difficult as to be unsolvable. There was one student who actually made it so far as to also realize this; that student got full credit. The rest of us got varying credit commensurate to how far we got/what we left out from our solutions.

For many professors, undergraduate courses are simple enough that when they go over 1-2 problems, they can grasp them quickly. For others, they go over solution manuals and previous notes to recall and remember how to do them. Some assign office hours to TAs, where the TA deals with students and their homework. Keep in mind that many schools do tell the professors which courses they will teach next semester/year, so they have plenty of time to prepare and develop their notes and slides.
I would be more worried about professors teaching graduate level courses that are not familiar with. It seems that many issues/inconsistencies occur at this level.

Short answer:

Yes and No

All your cases do apply.

Dutiful professors actually work problems before they are assigned as homework problems to students. Such instructors may even go through the trouble to frame their own problems for homework.
There are many who provide a set of problems from standard solutions and web references. They may not have worked out all of them, but rather a small subset of them.
There are, however, some who are fairly (or entirely) new to the subject and are experimenting with questions that are available as exercises in the syllabus with the students. They actually learn along with the students as they teach the topics progressively.

An instructor, in general, would be actually a mix of the above. There may be some topics that are the same as the previous syllabus that the instructor knows well enough to frame own questions, and some others where she/he might prefer to use textbook exercises. There may as well be a few other topics which are new in the updated syllabus which she/he may wish to experiment on.

And another case: No, not the professor, but the (graduate) student tutoring the problem sessions.

I absolutely agree; I just didn't want to repeat the point given before.

I teach at a small all-undergrad department. No TAs here, so yeah, if I'm not using some kind of on-line homework system (which I have only ever done in service classes, and I'm trying to give it up) then I have to do all the problems at some point to produce a key.
Now, that doesn't mean that I've worked them out in fine detail, nor that I have done them before I assign them. In my upper division classes I just chose a few that look like they go to my learning goals and might be interesting. If several students complain that problem X is too hard I look again and then maybe post some hints to the LMS or give them a less ambitious goal for the problem; or maybe not: tackling the occasional hard problem is a skill that they should be exercising.
As for how I help students when I haven't done the homework first myself, well, mostly it's a cakewalk. For one thing I never work the problem for the students: I just keep asking them related questions and suggesting concepts they might try to apply. For another, I've been doing this subject for longer than a "traditional" student (i.e. 18-24ish years old with little real-world experience between the end of secondary school and the start of college) has been alive. I choose problems on the basis of the concepts they exercise and I can usually tell that at a cursory reading, which means I can decide on a strategy (or several strategies) that will work when the student shows me the problem that has them stuck.

Do professors work through all the homework problems they assign to
  students?

No, not all the time. Dealing with your secondary issues in reverse order:
Re: Recommend knowing all the ins and outs? Perhaps in an ideal world, but I would recommend prioritizing other things first. When prepping a new class, my protocol looks like: (1) Folders, (2) Schedule, (3) Syllabus, (4) Tests, (5) Homework, (6) Slideshows, (7) Handouts. (In addition, there are clerical duties like: export PDFs, set up Blackboard, submit duplications to office services, make attendance sheet, make backups, etc.) Keep in mind that sometimes we are assigned a course only a few weeks, or even a few days, beforehand. In those situations an instructor would not have any time to do more than select a list of promising-looking exercises on the topic from the book. In later semesters perhaps I will go back and work individual exercises to be completely comprehensive, and refine the assignments (but likely some colleagues would consider that obsessive, and think the time better spent on service or research, etc.).
Re: How do they address concerns? The thing is, the whole point to real knowledge is to have an abstracted higher-level framework in which the minute details fade to unimportance. I can look at an exercise set and say, "these are all really the same piece of work". This is frequently the case if you look at a text explanation written next to a series of mathematical manipulations; the line-by-line English descriptions may be totally identical for a given exercise set (even if, say, the numbers and variables are all different). In this sense, a professor working out the details of individual exercises may be entirely redundant, whereas for a student they're constructing a new perspective on the topic (what initially looks different gives way to awareness of commonality). That said, it may be good to check and see if there are details or complications unfamiliar to students, so that can at least be mentioned ahead of time in class. But: If one truly understands the subject in general, then any exercise or detail should be easily addressed on the fly.
Re: Professor not taking undergraduate course? It should be pretty unlikely for a professor to be teaching a course they didn't take as an undergraduate; undergraduate curricula are usually pretty standardized, and a PhD holder has taken all those classes and much more.

"It should be pretty unlikely for a professor to be teaching a course they didn't take as an undergraduate" - maybe customs differ between places and fields, but I know plenty of CS professors who themselves never studied CS, but who actually studied physics, or something else. Moreover, I have seen basic classes change considerably over the course of only a few years, and whole undergrad curricula getting redesigned every few years. It strikes me as extremely unlikely that anything in an undergrad class will still be the same now as at the time when the professor was an undergrad student.

Computer science's reputation for rapid change is deeply exaggerated, especially in introductory classes. Sure, programming languages and tools change every decade or so, but the underlying tasks used to teach programming don't change as quickly. The algorithms classes I teach now are nearly identical to the class I failed 30 years ago as an undergraduate.

I disagree with this statement as well.  I've taught undergraduate courses in number theory, dynamical systems, cryptology, and the differential geometry of curves and surfaces, and I didn't take courses covering any of these subjects as either an undergraduate or as a graduate student

Maybe the last little paragraph in this answer is needlessly literal about coursework as the  sole way to learn something. Even so, as @JeffE observes, from a somewhat higher level, things don't really change as much as a more superficial appraisal might suggest. I'd claim that a more figurative version of that last paragraph would fit better with the earlier parts of it, namely, that years or decades of experience in a subject can/should profoundly change the way a person interacts with a subject, and most undergrad standardized coursework becomes more transparent than a student might think.

@JeffE: I agree some of the underlying problems remain the same, but that is about the only constant. The concrete challenges even in basic tasks such as "implement a binary tree with traversal operations" vary considerably depending on whether the language/framework used supports garbage collection, whether it is typesafe, etc. With this background, I see introductory classes being completely redesigned every 4 to 5 years, especially the practical parts such as programming-related homework problems. This different experience might explain why we perceive rapid change in CS differently.

I was teaching an ODE class for the first time in Spring 1997, and in the section on exact equations one of the problems I assigned wound up being unexpectedly tricky. If you know the topic, then you know that these tend to be rather mechanical. But not this problem. A student stopped briefly at my office (on the way to another class) and asked me to look at #25, because several students in the class thought there might be a mistake in the problem statement, as what was supposed to happen didn't.

(continuation) When I (finally!) figured out what to do, I made it into a handout for a neat example that I passed out to students in subsequent years.

@DaveLRenfro: I've run into that too, and partly I'm glad that there can be surprises like that from time to time. But my point is that they're sufficiently rare, I would not recommend prioritizing time looking for such, when so many other tasks are needed to get a class prepared.

When I was an undergrad, there would not have been a school in the country teaching any of the undergraduate courses that teach.

In most courses I was a Teaching Assistant in, the answer was: "No, the Professors let the Teaching Assistants do that, and they report back any issues they find." (And sometimes we would handle coming up with and checking HW assignment problems all on our own - when there were several TAs in the same course, anyway.)
I'm not saying this just to relate my personal experience - it is literally something a Professor can be assisted with. If you are a Professor and you want to give homework, try to pressure your department to assign you a part-time TA - even if only for this work specifically.

A lot of professors do solve their problems first. Among other things, it's always a good idea to check the problem to make sure it's solvable with the techniques the students know so you don't have egg on your face later.
Many people teach the same class over and over, it's common to prepare the problem once at the beginning and then reuse them. They can create extra problems and rotate them each semester to avoid students memorizing solutions from past courses.
Relatedly, common textbooks often have teacher's only problem banks. The answer book isn't really that hard to get, but many students don't bother.
Some have TAs handle the questions. Since it's tedious, boring work, it's great for getting the TA to do it. Often TAs solve the problems in problem sessions anyway.
Some profs just don't care and give problems without checking. When someone complains after they discover an impossible problem (eg. angles of a triangle add up to 190 degrees) they say "oops" and carry on. Students get upset but when's the last time a professor got fired for making a mistake in his homework problems?
So your answer is: Yes, some do.
However, it sounds like you're just shocked at how long you took with your assignment, so are assuming it can be done faster. It's always possible that there's a faster way to do it than you don't know. Also, repeatedly doing the same problems quickly makes you very efficient at it: Even students can, just by solving problems throughout a single course, get good enough to get an A. Imagine how good the professor must be: They are probably smarter than the average student, know more techniques and methodology, and have taught the class multiple times.

This will vary tremendously based on the professor - I'm not sure you'll get any answer other than "sometimes".
In my own experience...the answer is sometimes.
I've had professors where it's very clear they've only had their TAs do their assignments, or where the level of testing hasn't even gotten that far. On the other hand, a professor I worked with used to sit down every week for a meeting with his TAs, work through the problems, suggest extensions that the group presenting the homework that week could do, etc. That was a tremendous amount of effort, and likely wouldn't be repeated in later years once the problem sets were fine-tuned.

This might be just my experience, but I've been now almost 4 years at a UK university, and all (with one exception) of my main lecturers would know their coursework by heart. Furthermore, for most of the math classes I took, the lecturers would actually work through the coursework problems after all coursework has been submitted/returned.
And for project-like coursework, e.g. writing a not-so-small computer program, or performing such-and-such experiment, many of the course leaders would maintain either a thick booklet with a lot of guidelines/examples/marking schemes/etc, or libraries of work done by students from previous years. And these materials are usually passed to the new course leader, when course leaders change.
In summary -- yes, in my experience at a UK university, professors work through all the coursework problems they assign to students.


text:
What is a brief announcement?
What is a brief announcement in terms of accepted conference papers?
For an example, see here

It is a short conference paper (maybe 2 pages) + a short talk (maybe 5–10 minutes).
Cf. a normal conference paper (maybe 10 pages) + a normal conference talk (maybe 20–25 minutes).
Brief announcements do not usually count as a publication, so you can use them to advertise work published elsewhere, or you can later submit a full version of your work to another conference.
In some conferences, you submit a normal paper, but if it is not quite sufficiently interesting to be accepted as a normal paper, it may be accepted as a brief announcement. In some conferences, brief announcements are a separate track — you directly submit a brief announcement. Some conferences combine both approaches: some of the brief announcements that they accept are "downgraded normal papers", while some of them have been directly submitted as brief announcements.

In particular, the conference linked by the OP says: "A submission for a brief announcement must be no longer than 3 single-column pages on letter-size paper using at least 11-point font, including title, authors' names and affiliations, and references. Such submissions may describe work in progress or work presented elsewhere. (...) brief announcements will be included in the conference proceedings. (...) brief announcements receive up to 2 letter-size pages."


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Number of recommendation letters while applying through Mathjobs
I am applying for postdoc positions in math. In MathJobs, I can add 5 recommendation letters (4 for research and 1 for teaching) for any position even if the position specifically asks for 4 letters. Is it advisable to send all the recommendation letters in such a scenario?

Follow the instructions for each job.
Consider five letters instead of four only if you know that all five are very strong and cover different areas of your strengths. And then explain briefly in your cover letter why you are asking the hiring committee to read more than they asked for.

This is an interesting suggestion, which implicitly assumes that an applicant knows the content of the recommendation letters. Personally, I never share this information with applicants for whom I write letters.

@MoisheKohan Yes, the exception  works only if the OP knows (essentially) what's in the letters. Practice varies: I always show applicants what I plan to write.

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text:
Marie-Sklodowska-Curie actions: publish a part of the proposal just after the deadline?
I am applying for the Marie-Sklodowska-Curie Actions Fellowship (MSCA) in physics this year. The proposal includes developing a novel theoretical method, applying it to various models, and making a framework that translates the parameters of these models to the impact on some observables.
The point is that I have developed a prototype of this method and am going to submit a paper to arXiv. My naive plan was to submit it right after the MCSA deadline. On the one hand, the prototype is a kind of proof of principle, i.e., it cannot be applied to most of the models from the box and just demonstrates that it is, in principle, possible to achieve the basic requirements outlined in the proposal. On the other hand, it implements some of the fundamental features I mentioned in the proposal and includes some simple case studies.
My question is whether this may severely affect the chance of my proposal being approved. Namely, when searching for papers similar to my proposal, referees will find my own paper, decide that some part of the project has already been done, and then reject the project.
I am wondering whether I should mention the forthcoming paper in the proposal, or just drop it completely. Also, how should I write the paper's abstract in order to avoid some issues if the paper is found.
What do you think?
Edit
Can the scenario of not mentioning this paper and then being discovered by the referees be positive? They will see that the prototype demonstrates the principal possibility of developing the method discussed in the proposal, which may reveal some risks.

My situation ditto. But, I am mentioning in my proposal about my pilot study and also providing my results in brief to give the reviewers a bit of confidence jn my research ideas.

@Coder : good idea, I will probably proceed in a similar fashion.

My question is whether this may severely affect the chance of my proposal being approved. Namely, when searching for papers similar to my proposal, referees will find my own paper, decide that some part of the project has already been done.

This seems like a plausible concern. If you are saying in the proposal "I am going to do X" and you have already done X at the time when the proposal is being evaluated, it would indeed be quite reasonable for the reviewer to not recommend your proposal for funding. If I were the reviewer I would ask myself why you are asking for money to do something that you've already done, and why I should recommend to the funding agency to give you that money.
However, much would depend on how you frame your description of your plans, and what else you say you will do aside from X. For example, let's imagine that instead of saying "I am going to do X", you write: "I am going to do X, and then proceed with follow-up work Y and Z. In fact, I am close to finishing a paper where I do X. This sets the ground for achieving the [much more important] goals Y and Z." Suddenly the fact that you are about to finish X appears to be a positive rather than a negative. It makes your proposal seem more suitable for funding: you are pursuing important goals Y and Z, and you are making yourself look like you are well positioned to pursue them -- better positioned in fact than someone who is just proposing to do Y and Z without X, or than someone who is proposing to do X, Y and Z and hasn't yet made any progress on any of those goals. (This is assuming that there is some relevant conceptual relationship between X, Y, Z, e.g., that X is some natural first step on the path towards Y and Z.)

I am wondering whether I should mention the forthcoming paper in the proposal, or just drop it completely.

See above. Again, things depend a lot on the details of what you are proposing so I can't give a definite answer. But I would say that a good research proposal will do a good job of communicating where you are at the moment with your work on the topic of the research, and where you plan to go from there. So if you are about to publish a paper, that could be a good thing to mention, as it shows you are already fairly advanced in your thinking on the topic and have a good foundation to build on for continued work; but this rule of thumb assumes the premise that the main thing you are proposing is that continued work (the "Y and Z" from my discussion above) rather than the things you will do in the forthcoming paper. If the paper is not the beginning of something bigger but rather the end of a research project, then it might be better to not mention it and focus the proposal on the other things you are planning to do.

Also, how should I write the paper's abstract in order to avoid some issues if the paper is found.

Just write the abstract as you would if you were not submitting a proposal. The existence of the proposal is simply irrelevant for writing the abstract -- most people reading the abstract will not even know about your proposal, let alone read it. However, the existence of the paper is not irrelevant for writing the proposal: you need to carefully think about the paper's relationship to the research you are proposing, and mention it (or possibly not mention it) in a way that optimizes the overall impression your proposal will make on the reviewers.

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Second round of applications at CERN
I have applied for a CERN postdoc theory fellowship. After the 21st, I got no response (unlike many other places, CERN sends an email even in case of rejecting the application) and decided to ask a person from the theory department what my status was. I got the reply stating that at the 1st round, they can't offer me a position. Probably (correct me if I am wrong), it means that there may be a chance for me if someone from the first round declines the offer later (before the 15th of February). Then, I asked about my position in the queue for the second round but did not get an answer (yet).
Does anyone know about these rounds, in particular, if there is such a thing as a "queue" for each subsequent round?

They might think it improper to give "position in the queue" information. And, any queue might not be cast in stone with reevaluations possible, though I don't know CERN's policies.

The answer shouldn't change your next steps, which involve applying for other positions and waiting.

@BryanKrause : I have to inform my current place whether I want to extend my current postdoc with an extra year. On the other hand, CERN is a preferable place for me. It is therefore very important to me to know this detail.

Knowing where you are in the queue won't tell you if you're hired or not until you are, so you need a contingency either way.

@BryanKrause : I know that 2-3 people reject the offer every year, so if I were 1st-2nd, there is a chance, while if 3rd-4th, it would be hopeless. So knowing the order is very important to make a realistic plan.

If the average is 2-3 that reject, you can be sure that the confidence interval includes 0.

@JohnTaylor Just because the information is important to you does not mean that you can obtain it.


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What to do when someone is doing the same subtopic (originally brought up by me) of our group project as me and not willing to collaborate
Basically, we are in group of four working on a larger project in a graduate seminar. I brought up an idea to approach a subtopic X (abbreviated as X for convenience, but if you are familiar with graphics, it's about making a 3D scene generator multispectral, currently, the generated scene only supports RGB values) within this large project, constantly in front of class, the professor, and in front of the group. I told my idea to my professor, he told me to not do this because he doesn't believe that I'll finish the idea in time (we have one month in total), instead he asked me to do something easier, but I only spent 5 days and finished the thing he brought up (which he expected would take around >2 weeks). I think this shows that I would have been more capable of finishing the task than he expected.
So I thought I could go back to topic X now. Then I found out that a team member was already working on my idea, and his approach was incredibly similar to how I explained idea X to the class (verbally, I didn't write down the approach), and he said that it was his original approach! I chose to believe him (maybe he zoned out when I was explaining my approach to the class) and told him that his approach X1 is actually kind of problematic. I explained to him why it's problematic, then in our presentation slide I added a variation of idea X, called it X2, and planned to start on idea X2 soon. The next morning he came up to me and told me that X2 is actually just X1 and so it's his idea! However, in the presentation slide, it was incredibly clear that X1 uses Machine Learning while X2 doesn't use Machine Learning at all, and I told him that X1 is problematic so why the heck would I do anything similar to X1!
Not to my surprise, I found out that he is also working on X2 now. He refuses to inform me his progress or his approach, which basically means collaborating isn't a choice. He doesn't want to communicate his thoughts/progress with me. I hesitate to communicate my thoughts to him as well, as I'm afraid that he would claim they are his ideas again. I feel this is very unfair. It was MY idea initially, I expressed strong interest throughout, and even if he might just happen to have similar approach (which I doubt it). Why can't he acknowledge that I talked about this approach in class first? If we both work on X2 separately, it will be ugly and we both might look like clowns during project demo presentations (such failure in communication, within the group!).
Should I just let him do X2 while I find something else to do? Or should I just go ahead and work on the same topic without communication (at least for the project demo presentation soon)? What should I do in this case? I would really appreciate your insights and thoughts, thank you!

could you clarify a few information: the professor told you to not work on X, but the team member got the authorisation? Or did they never asked? You say you work in a group in a larger project, is there interaction in between the work you are doing and the one your team member are doing (like different module that are expected to be working together)?

Regardless of those answer, have you tried bringing the issue with the professor? From my understanding, you are working in a group project supervised by this professor, and there's clearly some troubled communicating in between you and another group member. A supervisor will be able to mediate the discussion, and helps you resolve the issue. You probably want to explain properly to the professor why you think you are able to work on X (despite them telling you not to) and try to explain in an unbiased ways the situation

I would advice bringing to the professor who is supervising you. The biggest issue in group project, at every level, is communication. There is clearly some issue when trying to have a discussion with your team member and possibly the professor.
I can't say why your team member is behaving like this. I don't know what they think, and it obviously seems they are not cooperating or not acknowledging your ideas. But I have to remind you that people don't think the same way. You only know of what they said and your own assumptions. Even if you presented it in class, it doesn't mean they didn't think of it by themselves before, or even didn't start working on it before.
What is for sure is that there is issue discussing in between both of you, when trying to claim ownership about the idea.
I would advice getting someone else, preferably someone who has responsibility within this project, to mediate before both of you. This could be the professor who is supervising you.
If you can't have proper communications, bringing all your points and explaining them, as well as listening to your group member / professor arguments about why they are doing it or why you shouldn't do it, then you should seek alternative solution towards the person responsible for the seminar/course at large.
As a small point, even if it doesn't sounds fun, if it is a group project and you have assigned task by your professor, if they tell you to do A, and not B, even if B sounds really good and you try to convince them, they may still say no and you have to accept it. This can sometimes sounds unfair, especially if someone else get to work on B.


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Stuctured vs Individual German doctoral program
I am looking for a Ph.D. in a German-speaking country in Europe.
I am looking at some possible institutes for applying on Ph.D. program.
Some offer "individual" and some "structured" doctoral programs, and some offer both.
My situation is that I do not come from academic environment, which means that I don't have contact with any potential supervisor. I guess that if you go directly from Master to Phd (in academic environment), you should have thesis subject, which means you apply for Individual doctorate.
Instead, I am coming from industrial environment, and I don't have yet thesis subject. I completed my Masters 2 years ago, and left academic circles.
My question is: why choose one of "structured" or "individual" over the other?
I believe that structured is "easier" if you don't have potential supervisor or thesis subject, but I would appreciate guidance from those who know this system better.

I agree with @jakebeal.  I didn't downvote, but I'd guess the downvotes are because the question is difficult to understand.  I can guess what individual vs. structured might mean (I'm thinking of a German-style Ph.D. vs. an American-style Ph.D.), but I might be wrong and in any case I'm puzzled as to what it would mean for the same institute to offer both.  I doubt you'll get any useful answers without clarifying.

Thank you for the clarification; I have edited the question further to try to reorganize it for best chance of good answers, and nominated it to be reopened.  Please feel free to re-edit if you feel that I have not preserved the sense of your question in any particular.

I think there are some basic misunderstandings here to clear up.

You do not necessarily have to have a pre-conceived thesis topic to do a PhD with an individual faculty member at an academic institution in Germany, particularly if you're in the sciences or engineering. This can actually be counterproductive, since usually the faculty member will have funding for a student to work on project X. If you're not interested in working on project X, you're not going to be a good fit for the project, whether or not you had a topic in advance or not.
Having a pre-existing relationship with a potential advisor is useful, but not necessary for a project. Often times, they will be looking for the best individual candidate if no "internal" candidate is available.

The primary difference between "structured" and "individual" programs is that the structured programs tend to be a cluster of related PhD projects with a similar infrastructure holding things together, and potentially a different funding mechanism than traditional individual projects. There may also be some differences in the required duties outside of research (for example, there may be reduced teaching requirements, or even none at all). However, in terms of the long-range benefits, there is essentially no difference, except for listing a special program in addition to the faculty where your PhD was awarded. From a functional standpoint, the degree you'll get will be essentially identical.

So, what would be correct / optimal path to apply for Individual PhD? Find position and then apply?

@user24258: Basically, yes.

@user24258 You can often find open positions on academic-oriented job sites like jobvector or on the individual institution's page. However not all positions are advertised. If you find a researcher you'd really like to work with, it's worth  contacting them even if they don't have an open position on their site.


text:
Reasons for a request for reference being ignored
What are the reasons that emails for a request for reference might be ignored or delayed in response, a long time after the deadline by an intimate academic advisor?

Your email arrived in the spam box. You mis-typed their email address so they never got it. etcetera...

i don't think close associates' emails will arrive in spam folders, will they

@feynman Sometimes yes.  Or they may not even arrive there if a mis-configured malware blocker decides to trash your email entirely.  Email has no delivery guarantees.

@jakebeal This failure of arriving at their mail box never happened when advisor and advisee actually worked together. Failing to receive emails after both sides stop meeting each other is hard to believe

It is easy for the IT dept to "adjust" email spam filters which causes issues... And yes had it happen to me, Thanks IT...

Granted the large websites that curate this process now, I've had account problems in the past that prevented me from submitting references in the required window.

Professors and other researchers are typically busy people receiving a constant flood of emails in their inbox, a great many of which are time-sensitive and important.  Yours is only one of many.
The most likely reason for somebody's failure to respond promptly to an email, then, are just the typical ones for any busy person: getting lost in their inbox, technical failures (overactive spam filter, address mixups, dodgy forwarding systems), and falling through the cracks in an overcrowded schedule.
It might also be, however, that the professor is wasn't actually as strong a reference as you thought and just didn't feel comfortable saying no.  Did you ever have a non-email conversation about the references? And if they aren't responding to email, pick up the phone and call!
Finally, since this is not an uncommon occurrence, I also recommend that for important but asynchronous interactions like references, if possible one should give 1-2 more than required.


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Should I abandon an open math problem, if it hasn't been actively studied since the mid-1980s?
There is an open math problem that I am interested in. There was a lot of progress in fully working out the problem in low-dimensions and progress towards sub-problems of the main question up until the 1980s, but it seems that the research activity has mostly stopped since then.  Newer papers just essentially reiterate previous results.
A pretty well-known professor in my department also published a few papers on this problem in the mid-80s, so I reached out to him and told him that my thesis adviser and I are currently studying this problem.  He confirms that his work on the problem is very old, so I'm guessing he hasn't done anything newer with the problem since his last papers.
The problem itself is known to be quickly intractable for higher dimensions, say, for n>5.
I'm taking his words as an indication that there is not much interest in this problem, and that I should probably abandon it and find another problem to work on, for my master's thesis.
Am I making the correct interpretation of this professor's remark?
Should I still stick with the problem, even though it might be true that it is not currently being actively studied?

Rather than asking us how to interpret the professor's words, a perfectly reasonable thing would be to send a quick follow-up mail where you ask more explicitly whether he thinks there's still interest in the problem.

There was a lot of progress in fully working out the problem in low-dimensions and progress towards sub-problems of the main question up until the 1980s, but it seems that the research activity has mostly stopped since then — Uh-oh.  Sounds like we're working on the same problem.

Until you have tenure, and the respite from professional pressure that comes with it, you should probably always be working on something with a reasonable probability of producing usable results in a near-term timeframe.  Absent a compelling and convincing new insight, working on old, open, unsolved problems should probably be side-projects that you're fine spending time on and getting nothing tangible done with...because there's a strong probability that this is exactly the outcome you will end up with.

Unsolved problems from the 1980's are likely either very uninteresting or very difficult.

@gnasher: Somewhat likely, yes.  But that's a bit of a defeatist attitude.  The highlight of my postdoctoral career was when I answered an unsolved question from the 1950's (from a paper written by two very famous mathematicians).  Long story short: it turned out to be neither very uninteresting nor very difficult.  I might not have the tenured position that I do now if I hadn't given it a try.

and it was a highlight because it was so unusual.  No one is telling you not to do this.  The recommendation is that unless directed to do so, it would be better to place your primary focus elsewhere.  If you continue to find this problem interesting, then by all means work the problem, but your employer will probably want some results/progress in the weeks - months time frame and not the years - never time frame.

On the other hand, I worked on a moribund field of study that was moribund for a reason. It can be a career killer.

If you are using new techniques and will find interesting new directions by solving this problem then by all means solve it. But if you are doing the n+1 step after n was done in the 1980s and your solution won't help with step n+2 or have interesting new insight, then please find a new problem!! Such a thesis has led to many an academic death for talented people before!

@TK That assumes he has his heart set on a professorship.  If he ends up in finance, the subject of his thesis may not matter as much.

@gnasher729 There are shifts in focus as well.  For example, there was a lot of research into topology in the 1970s, that was to some extent crowded out by number theory in the 1980s due to usefulness of the latter suddenly increasing with the massive increase in importance of computer science.

To my mind, there are two critical questions to ask here:

Do you and/or your advisor have any ideas for making progress and/or any new results on the problem?
In general, what does your advisor advise?

Regarding (2): In mathematics, the single most important role a thesis advisor can play is helping a student choose a good problem.  Problems are good because of a combination of interest on the part of the student and the advisor, community interest, potential or actual applications, and perceived difficulty level (i.e., tractable but not trivial).  Asking a bunch of random internet academics whether to attack this problem seems a bit weird to me: what does your advisor think?
Interregnum: I would like to respectfully disagree with @Wolfang Bangerth's answer.  A problem which was studied in the past and on which many papers obtaining partial results were written is a problem of interest to the mathematical community.  In my circles at least, solving longstanding open problems is at least as good as solving problems that were posed last year, because the older problems have a higher level of demonstrable difficulty.  If the papers in question had been written, say, 80 years ago, then one might have some concern that no living mathematician cares about it (still, you can make us care by doing something sufficiently nice), but problems from 30 years ago that are still being mentioned in contemporary papers are likely to be viewed as having a strong pedigree.
Regarding (1): if you have some traction on this old, unsolved problem, it sounds like a great thing to work on...at least for a while, to see what happens.  Conversely, if you have no ideas....tell me again why you and your advisor started studying this problem?  Or rather: ask your advisor again.

solving longstanding open problems is at least as good as solving problems that were posed last year - in fact, usually better than

Thanks so much for your answer, Professor Clark.  I agree that it is a bit weird to ask this question.  I assumed that I would get some very quick answers that say something like, "yes, you are mistaken, if you choose to work on problems that haven't been actively worked on since the 1980s, and you should focus on what's current".  I didn't expect much more dialogue.  Instead, I got way more detailed, well-thought-out answers that advocate for both abandoning the problem or trying to work on the problem.  This was surprising :)  Thanks also for your awesome comment to Wolfgang's answer.

Am I making the correct interpretation of this professor's remark?

All you've told us about the professor's remark is "He confirms that his work on the problem is very old, so I'm guessing he hasn't done anything newer with the problem since his last papers." And what you said about your interpretation of his remark is "I'm taking his words as an indication that there is not much interest in this problem". While this may very well be a correct interpretation, there are certainly other possible interpretations. For example, I worked on problems 15 years ago that I no longer have any interest in. If a student came to ask me about them I would probably shrug and not show much enthusiasm, but those problems are still very interesting to many other people.
In other words, your description of the professor's remark (and possibly also the remark itself) is too vague to be able for anyone here to be able to meaningfully say whether the problem is still of interest to anyone or not. You and advisor might want to get a second opinion from another person who is knowledgeable on the subject.

Should I still stick with the problem, even though it might be true that it is not currently being actively studied?

I'm currently writing a paper on a problem from the 1960's that has been the subject of only very few papers since then, the last of them being from the early 1990's. I don't know for sure how the world will react to my paper, but I think I've made very nice progress on the subject and have hopes that my new results will excite new interest in the problem, which is intrinsically very appealing. I am also a tenured professor and can easily afford to risk the scenario where this doesn't happen. Nonetheless, I am of the opinion that pure math research shouldn't be about following fashions or fads (which math is very much susceptible to, much like other areas of academia) but should be driven by an innate desire to understand a structure one is interested in and finds beauty in. See also Pete L. Clark's comment on Wolfgang Bangerth's answer for examples where working on an unpopular or archaic subject paid off bigtime.
With that said, a lot of people prefer working on popular topics and think that working on such topics is a safer route to success in math, especially for someone who is just starting out. I don't have a strong opinion that that's false -- it's simply not my style -- and I completely respect someone who makes their decisions based on such a belief. So keep in mind that working on a subject no one else is working on is a somewhat lonely pursuit with a very uncertain payoff. But if that where your heart tells you to go, you should know that it is certainly possible to find success working on unpopular subjects.

Thanks so much for this awesome answer, Professor Romik, and best of luck to you with your upcoming paper! :)

This is my favorite answer.  If your math has intrinsic beauty, people will notice.

Being a researcher is, like anything else, a job. It's a great job, and (I assume from context that you're in mathematics) academia is literally the only place where you can work on nontrivial pure math. Unfortunately, in order to eventually get the awesome post as a university professor, you need to jump through the various hoops beforehand: publish a ton of papers, get prestigious postdocs, publish a second ton of papers, etc. If you don't do so, then you'll be stuck deciding working in insurance or finance. (Not that there's anything wrong with either, but I assume from the fact that you're doing a PhD in math that you'd rather be doing academic math research.) If you have what you think is a promising approach, go ahead and take the time to work on the project; resurrecting a moribund field and solving a problem that was thought to be intractable is a great feather in your cap. On the other hand, if you simply think that the problem is interesting but don't have a specific plan of attack, I'd suggest you work on something else instead.
Of course math and research are supposed fun and interesting, and they are. It's irresponsible, though, to suggest that you should simply work on whatever project you find most interesting. Being a grad student is a job like any other; your task is to churn out awesome papers. If you don't do that, then you won't be allowed to be a mathematician, and you won't have an opportunity to work on math at all. I'm not saying that grad school, post-docs, etc. should be a joyless slog; I am saying that you always need to keep in mind that this is just the preliminary stage of your nascent career, and that you need to consider that the ultimate goal is to move up the ladder. You need to show results. If this new project isn't generating results, dump it and get another.

This is certainly a valid point of view, but your answer assumes the premise that the problem in the supposedly inactive, abandoned area is in fact a less fertile ground for discovering exciting, groundbreaking research. The point that I was trying to make, and I think the point Pete L. Clark was trying to make in his comment and answer, is that it is far from obvious that that premise is correct. There are hidden diamonds lying buried and waiting to be discovered in long-abandoned areas, and someone who goes digging for them may find them, and has the distinct advantage that ...

... he/she is the only one looking. By contrast, when you work in a very active, "hot" field you have tons of competition, which could end up making it that much more difficult to be the first to discover those diamonds. So, there are pros and cons to both approaches. With that said, I completely agree that a student early in his career needs to be very mindful of the effect of research choices he/she makes on their career. But working on an old, abandoned problem can in certain cases be good for someone's career, and in that case honestly I don't see a problem.

@Dan: What you say about my comments is correct.  (And I agree with what you wrote.)

@DanRomik: There's also the unavoidable fact that certain fields are sexier or in higher demand than others. If you're publishing great results in a field no one cares about, it's possible that no one will still care about it. Universities build up subfields in departments, and professors like people they've worked with.

There are two possible interpretations:

It may be that the problem is really just that hard that with the knowledge we have today, no progress can be made, and consequently no progress has been made in the last 25 years. If this is the case, it's probably a bad problem for you to work on as it seems rather unlikely that you will be able to squeeze useful results out of the general area (either for your personal satisfaction, for writing a thesis, or to build a research career on).
Or, it may be that simply nobody cares about the research area any more. There are many areas of the sciences that have been abandoned over the decades and centuries, simply because the circus moved on. There can be many reasons for this. In pure math (it sounds like this is your area), a possibility is that in the 80s people thought that working on question Q would open a way to prove open problem X in a certain way, but then someone found a completely separate approach to prove X, and so question Q has now lost its previous status and people don't care about it any more. Of course, if this is the case, you may be able to squeeze some results out of problem Q for a thesis, but it's again not a good problem to work on because nobody cares about it any more.

Upshot: If an area is dead, let it rest in peace.

"Upshot: If an area is dead, let it rest in peace." Hmm.  If Robinson had followed this advice (calculus with infinitesimals), we would not have nonstandard analysis.  If Mumford had followed this advice (classical invariant theory), we would not have geometric invariant theory.  If Bhargava had followed this advice, he would have neither his Annals papers on counting number fields (Gauss composition) nor on average ranks of elliptic curves (geometry of numbers) hence probably not his Fields Medal.  A student of math history can cite many such "fruitful resurrections."

@PeteL.Clark -- come on, you surely know better. The fact that there may be successful alternatives to the rule doesn't make the rule any less valid. We may all be able to cite fruitful resurrections, but any student of math history will also point out equally many, or probably more, areas that are solidly dead, rightfully so, and for the better.

"[C]ome on, you surely know better." No. "The fact that there may be successful alternatives to the rule doesn't make the rule any less valid." That is literally the least scientific statement I have ever heard.  Falsification is exactly what makes a proposed rule less valid!  "[B]ut any student of math history will also point out equally many, or probably more, areas that are solidly dead, rightfully so, and for the better." I am a (part time) student of math history, and I am having trouble thinking of any good examples: especially of "for the better".

What you are saying now is based on a strange fallacy for which you surely know better.  Even after I mentioned one of the most recent Fields Medalists got his Fields Medal by not following your advice, you still want to regard that as an exception to be discounted.  That doesn't make any sense: if some of our contemporaries are building amazing careers by not letting things "rest in peace," then obviously you should not always let dead areas rest in peace.  It does not follow that you should never do it either: why do you have to give a categorical answer?  You don't: that's a fallacy.

@PeteL.Clark I take your point, but I share some of the POV of this answer. There is an unfortunate possibility that people get inspired by stories of beating the odds, or of extremely talented people taking risks which pay off, and completely misjudge the likelihood of fruitful outcomes. (For instance, I would love to see an answer to the "contractible Banach algebra" problem or the "invariant subspace problem", but I would strongly caution any early career researcher that these are almost certainly not the best way for them to spend their time)

@Yemon: Yes, I didn't say anything about beating the odds, taking big risks etc.  In my answer, I recommend that the OP work on this old problem for a little while, if he and/or his advisor have any ideas.  Otherwise not.  I also hit pretty hard that it is an advisor's job to help their student work on problems with the right level of ambition and difficulty: students working alone would have a lot of trouble with this, and it is probably the thing that young-but-post-PhD math researchers struggle with the most.

@PeteL.Clark -- my answer of letting it rest in peace was written to a masters student. My assumption in writing this is that the student is talented and gifted, but not at the level of Robinson, Mumford, Bhargava -- statistically a sound assumption we probably agree.

@PeteL.Clark -- on providing counter examples: we don't use the textbooks from 50 or 80 years ago any more, because they are full of things that we don't think are important any more. They contain quaternions and octonions, and methods to construct classical solutions to PDEs for academic cases of $C^\infty$ domains and right hand sides. They contain vast chapters on special functions and long discussions of round-off errors/backward error analysis for limited precision arithmetic. All of which have largely disappeared from the important places they had in our curricula 50 years ago.

@PeteL.Clark -- my examples are largely from applied math, since that's the area I know best. If I open journals from 50 years ago in applied math, a very very small number of papers are about topics people still care about today. But I'm sure you can also enumerate the pure math colleagues over 60 in your department who are still doing what they did as grad students, are now having difficulty getting their papers published, and are generally considered to be doing things nobody cares about any more.

@Wolfgang: Your initial examples are of mathematical exposition rather than mathematical research. We don't even explain freshman calculus the same way today as we did 50 or 80 years ago...but the subject as viewed by a research mathematician has not changed at all. Quaternions and octonions are highly studied in contemporary mathematics. I regularly read and cite papers that are 50-80 years old. This week I read a paper from 1967 and one from 1935: the latter has a theorem that I will prove again in a paper I'm writing. So your comments really do not ring true to me. I'll end there.

@PeteL.Clark -- I guess we'll have to chalk it up to the different cultures in applied and pure maths then.

authors: Кристина Дегтярёва


text:
Citing newspaper articles (primary vs secondary? no references)
I have come across a few infamous newspaper articles and I'd like to cite them to support some of my ideas and to take a few thoughts from them. However, I cannot seem to distinguish whether such articles are primary or secondary. What worsens things further is the fact that the authors do not cite their words and, usually, reference lists do not exist.
Do I treat a newspaper article like a primary source and cite it as such? If not, how can I track back the information given the fact that there are no references?

Whether a newspaper article is good to cite or not depends on the purpose for which you are citing it.

If you are writing about a factual topic, then newspaper articles are highly unreliable secondary sources, with a well-known tendency to be blatantly incorrect.
If you are writing about newspaper articles, however, then the newspaper is a primary source and can be cited directly.

So what should you do if you find a really juicy fact in a newspaper article with no reference?  The same thing that you do if you hear something with no reference anywhere else: spend some quality time searching the literature and other sources to see if you can track down an actually reliable reference.  And if you can't find one?  Then you should reluctantly conclude that this "fact" is probably made up, whether intenationally or by accident.

I see, thanks for the new insight. However, if I have cited some newspaper articles in the past (for factual purposes, for example) as one would do for a typical newspaper article citation style in Harvard, regardless of how much the information is reliable, is it considered as plagiarism? In a sense that I am citing someone who is just mentioning information without sources... (I don't want to commit plagiarism by citing a secondary source as a primary source which I've done before; the reason why I've asked this)

@R.AS. If you are clearly citing your sources, then you are not committing plagiarism.  You may, however, have committed an act of poor scholarship by citing a source that you should not have trusted.

Wherever I cited newspaper articles, they were part of a homework, presentation or an essay, not a major research. My question, according to your answer, is: what if I cited someone as (in-text: Blake 2010, 'Apple', para. 2) and then at the end: Blake, J. 2010, xxxx, The News, available from.... However, the information which I got from Blake turned out to be secondary and not primary or new data, shouldn't it be something like (someone cited in Blake 2010)? I worry that I could have unintentionally plagiarized by giving credit to a secondary source in a primary source style. Got me?

@R.AS. Again, I wouldn't worry about anybody taking it for plagiarism rather than sloppy scholarship: the connection between your text and your source is clear.


text:
Why would the editor in chief add a new reviewer after the first round of revision?
I have a manuscript submitted in a journal, and there is a newly-added reviewer after the first round of revision, which is surprising for me. The three other reviewers remain the same in the second round (this round) and agree with acceptance of the manuscript.
I don't know what reason is behind adding a new reviewer. Any thoughts?

While this is rare, it's not necessarily bad, and probably reflects more on the associate editor or the reviewers than you.
One of the jobs of an editor is to ensure that reviewers are sufficiently well qualified, objective, and thorough in their evaluation of a manuscript. Likewise, an editor-in-chief needs to ensure the handling editor is doing their job well as well.
It's hard to say without more details, but my guess on the most likely cause of this situation is that there was some issue with the original set of reviewers, such as:

Too many were your recommended reviewers
There was a critical missing perspective
One or more of the reviewers turned in a low-quality review (which the editor might have forced them to improve before it got to you)
The journal usually requires more than three reviews

This could be caused by bad choices by the handling editor or by having more than three reviewers originally assigned but some failing to return reviews.
Whatever the case may be, I would recommend not worrying about it too much. You can inquire with the editor if you wish, but don't be surprised if you don't get a particularly informative response (especially if the reason is a mistake they might feel embarrassed by).
Bottom line: it's not so strange, and your paper is probably still in good shape, though its fate is never certain until accepted.

It is surprising to me because the comments of this newly-added reviewer are way too much general and unspecific.

@Baghererfanian Maybe the journal just prefers to have four reviewers, then.

@Baghererfanian This could also simply mean that the editor's plan didn't work out because the reviewer "underperformed".

There are two possibilities

a reviewer dropped and needed to be replaced.
the editor needed to get someone with specific content or methodological expertise.

Those are the two most common reasons on why you see a change of reviewers. Sometimes you use a method and all three reviewers say they are not comfortable reviewing it.
Jaret

Or the editor just didn't find someone's review helpful enough.

All reviewers remain in the second round. Unfortunately, the comments of the new reviewer show that he is unfamiliar with our work :(

There're many possibilities. Here are some:

One of the original reviewers declined to review the revision, and the editor decided he needed an expert to check your response.
The editor received confidential comments from a reviewer saying he should invite a reviewer with [expertise], and decided to do that in the second round of review.
Or possibly the editor had already invited reviewers with [expertise], but they declined. Since there are already three reviews, he opted to let you revise first and then invite reviewers with [expertise] after revision.
The journal's standard policy is to require a certain (>3) number of reviewers. Again, since the editor already has three reviews, he opted to let you revise first and then invite the remaining reviewers after revision.
The handling editor (not the editor-in-chief) invited three reviewers and was happy, but the editor-in-chief has a close friend who also works in your field and he thought, "I'm sure my friend will be interested in this, let's ask him".

Overall it's not something to worry about; just wait and let the process run its course.

It's definitely unusual.  We could speculate all kinds of reasons (innocent or nefarious).  But you should be capable of brainstorming the same.
You should send an email to the editor asking for an explanation.


text:
How to indicate obscurity in a translated quotation?
I'm writing a historical work about a German philosopher, in which I use some of his unpublished notes.
One quotation contains an almost untranslatable, hardly intelligible expression - it's not essential to the point I'm making with the citation (which is perfectly clear), but by cutting it out using [...] I mangle the quotation even more.
Can I translate it literally (which turns into nonsense) and write [sic] behind it? After all, it's not what was actually written but my translation, so I feel like this isn't really an option. Or should I chose one of the different possible interpretations that make some sense of it, but thereby pushing some particular reading, even though I don't need that to make my point?

Make a choice that you can reasonably justify and explain that choice/justificaiton to the reader.

Yeah that's what I decided to do. Added the original text in a footnote and explained that it's not crucial to the point. Thanks!

OP: consider accepting one of the answers posted below

@user2768 "Make a choice that you can reasonably justify and explain that choice/justificaiton to the reader." And then follow that up with a separate few pages paper, perhaps published elsewhere, on the conundrum, and several solutions you considered in the process!

Are you quoting the original wording as well?

Are you sure it would be an improvement to include a hardly intelligible and irrelevant expression (translated or not) above simply leaving it as ...?

How sure are you of your transcription? Are you sure you can read the word, or could it be saying something else?

@Davidmh I am very sure of it. Firstly, it's a printed collection, so somebody else transcribed it, I only translated it. Secondly,  I'm a native German speaker---the expression is suggestive but makes no proper sense because of a grammatical ambiguity that allows at least three different readings.

After all, it's not what was actually written but my translation, so I feel like this isn't really an option.

You seem to have unconsciously ruled out what I would consider the best option: leave the phrase in question untranslated with a footnote which gives the literal translation and says that the phrase's meaning is unclear but irrelevant.

This is the best answer. It leaves the option there for the reader to try to make some sense out of the quotation, if they can.

In language-related papers, it is common to do all of these options:

give the untranslated version
give the literal translation
give the semantically closest translation in English

Of course it depends how important this particular sentence is to your work. But if you want to mention it, you should at least give the original sentence and a translation in my opinion.

Give the loose translation in brackets. For instance, if the original says "This happens once in a blue moon", then give the translation as "This happens [very infrequently]". If you want to be complete, give a footnote with the original German and literal translation.

So-and-so says "this happens [very infrequently][1]".[1]"alle Jubeljahre", literally "once in a blue moon", an idiom expressing extremely low frequency

(Obviously, this answer is pretending, for the sake of an example, that "alle Jubeljahre" is German idiom that literally translates to "once in a blue moon" but means "infrequently", and is not asserting that this is the case in reality.)

"alle Jubeljahre" literally does not translate to "once in a blue moon"

Make a judgement call and explain the basis for that call to the reader.

Please expand this into a full answer.

Explain how one might do this or give an example.

@jakebeal You want me to explain how to make a choice? That seems rather fundamental. Let me side-step the issue and rephrase to avoid the notion of choice.

The question is asking for advice on how to make this judgement call, so I don't see what your answer adds.

@DavidRicherby The question actually asks whether to translate it literally or to chose one of the different possible interpretations. I suggest making a judgement call and explaining the basis for that call. That answers the question...

@user2768 The question is "Which of these things should I do?" and your answer is that "Choose one of them." Really, that doesn't say anything.

@DavidRicherby My answer is not choose one of them, my answer is choose one of them AND explain why, which is rather different.

OK, so your answer is "Whatever option you go for, justify it." That still doesn't answer the question, which is which option to take. Including justification is probably good advice and might be a sensible comment, but it's not an answer.

@DavidRicherby Well, as it stands, the OP has adopted my answer, https://academia.stackexchange.com/questions/124908/how-to-indicate-obscurity-in-a-translated-quotation/124910?noredirect=1#comment332200_124908 So, it is surely reasonable to considered it an answer.