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Considering a second degree to be a patent bar eligible lawyer--masters or bachelor?
I've always had an interest in math/physics, but ended up pursuing classics instead in undegrad (not remotely related I know). After undergrad I got my J.D., and have spent the last 3 years practicing law. I recently shifted into patent litigation (lawsuits about if someone stole your patent), but in talking with the patent attorneys I am very, very interested in patent prosecution (filing patents) for personal and professional reasons.
However, to prosecute patents you have to be registered before the patent board, which generally means you need a bachelors in a hard science or engineering, though with the right credit distribution a Masters is also fine. Technically you can take the exam without a degree, just the requisite credits, but most firms I've spoken to are not interested in hiring a patent bar certified attorney without a degree they can show to clients, so SOME form of degree would basically be required. However the firms I've spoken to have all indicated that a Masters instead of a Bachelors would be fine.
I'm seriously considering going for a second degree, either a second bachelors or a masters, in order to shift into patent prosecution. However, I'm not sure which would be better to pursue at this point in my life (the Masters would be patent bar eligible as long as I have enough total credits in specific fields... they have a whole guide sheet on this on the USPTO website).
I took through multi-variable calc and gen chem/gen physics in undergrad, so I might be able to get enough classes for admission to a Masters in physics (as much as I love astronautics at this point I'm assuming engineering is out of the question, so Physics seems my best bet). However, I know that programs that take non-science undergrad degrees aren't as common, and probably would be harder to get into. Alternatively I could see about just getting a second undergraduate, though it seems that may take longer, I think?  A shorter or part time is better, obviously, though financially I could take a few years off to chase the degree if needed, esp as studying for it might be hard to do while practicing. Basically I'm not sure which degree direction to start looking.
EDIT: I should add that while this isn't a career in academia immediately, my long term goal is to teach in law, for which one of the common routes is to practice for a while. Probably would get an SJD some time in the future. Law is weird.
Thanks for any insight.

Few MSE programs are ABET accredited so you'll need to take the FE exam anyway. If your end goal is to qualify for the patent bar you'd probably be better off doing a BSE.

I understand you situation from the question, but I think you need to better format it into a question, so that one can know what would qualify as an answer. For instance, what exactly is your goal? Being able to file patents as soon as possible? Figure out which is the easiest admission path into a hard sciences undergrad course? By the way, if you are a lawyer, you might be closer to a Production Engineer than you are to a Physicist. Are you asking for fields that would accommodate you (this is usually considered off topic here)?


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How to study better when underprepared for grad level theory course
I am a 2nd year PhD student in the area of digital communication networks. I am taking an information theory class and we had our midterm last week, which was open book, open notes. I did poorly on it--I got a 68, while the class average was a 90 with a standard deviation of 16. This class is the theoretical foundations of a lot of communication, so obviously I'd like to do well and understand the material. A 68 when the rest of the class did so well means that I'm not understanding essential aspects of the subject.
The grading scheme in this class is weird, in that the midterm score is thrown away if I do better on the final. So I have the chance to redeem myself on the final...problem is given that I actually did study for this exam, I don't know how to do better.
The subject matter is inherently difficult for me. I have all the prerequisites (which is just 1-2 probability classes, I have taken two), but I have always struggled with more theoretical math.
I always go to lecture and do the homework. The homeworks take a long time because they are hard for me. I do each of the problems on my own, and then on the day the assignment is due, I go over my answers with a friend who is also taking the course. For this exam we were provided with 3 practice exams. I spent as much of the weekend studying as I could. We had a homework due on Saturday that I spent all Saturday finishing, and then I studied all Sunday and most of Monday. I managed to complete one and a half practice exams in that time.
My current style of studying worked well for undergrad and master's courses, but clearly my methods are not working here. Arguably I could have started studying for the exam earlier, but I actually spent the week before the exam working hard on the aforementioned homework assignment (at the expense of my own research). I did well on that homework, and I assumed spending time understanding material from the homework would be beneficial for the exam. That did not turn out to be true.
Is it reasonable to try and dedicate more time to the class? My preparation for the exam was already at the expense of doing nearly no research that week. Has anyone had an experience where they did poorly on a class like this at first, but then managed to recover? How did you do it?
Finally, the poor grade has made me feel unmotivated and want to avoid working on the material, which is probably the exact opposite of what I need right now! Any advice on getting over this psychological aversion?

I suggested a more general title that I hope will help you get more attention and more answers.  If you don't like it you can roll it back.  Let me know if you need help doing that.

I would prefer underprepared be removed from the title, as that implies that I don't already do the basics, like go to lecture, do practice exams, do the homework, work with friends, seek help when stuck, etc.
Using a phrase like 'effectively' or 'more efficiently' would be good instead, because at this point it is more about my quality of study than the quantity. My goal is making the 20+hours a week I already spend more effective. Thank you for asking!

It's great that you have a study partner.  What you could add is some regular visits to office hours (TA and instructor if there are both).
As for sacrificing research work at crunch times, this is something you should discuss with your research supervisor.
Edit (responding to comment)
Thoughts about how to benefit from visiting office hours:

Go over portions of the lecture notes you're not solid about.
You may have some gaps in your background knowledge and skills, which you can work on with one-on-one guidance.
You can bring a draft of your homework:

Check your reasoning.  Your instructor or TA can point out places where you make a leap of faith in a proof, where you could consolidate some steps, or ask if you've considered such-and-so other approach, e.g. indirect proof.
Get unstuck on a problem.
Better understand the relationship between an example worked in class and the problem posed in the homework.

Get additional practice with certain key types of problems.
Learn tricks for working more quickly -- which can be extremely valuable in an exam setting.
Practice explaining a topic.  At a key juncture your instructor/TA can ask you to be more precise if necessary.  Getting feedback about which of your ideas are correct and well put in itself can help you gain more confidence.
Request a practice exam, and have it evaluated.

In short, in office hours you can receive tutoring at the source!  (Always being sensitive to the instructor's or TA's need to balance your needs with those of the other students.)

I do go to office hours when I have a question on the homework or material that isn't answered by our class forum, which ends up being about once a week. But If I don't have a question, what would I do? There's about 6 hours of office hours a week, and I'm usually there for 15-20 minutes a week.

@CAJ - added some thoughts.

Taking your account of the events at face value, it certainly sounds like you are making every attempt at performing well in the course. So, my suggested course of action for you:
A key first step is to get to the bottom of the mistakes you made on the exam. Have you done this?
The test was successful at exposing a deficiency in your approach to the course material, so the best way to adapt and do better in this particular course with this particular instructor is to understand your mistakes on the exam, and correct those, from simple mistakes to those that pertain to understanding a particular topic at a deeper level -- you want to really challenge your understanding of each mistake you made.
Moving forward, you'll have a better idea of the particular twists that your instructor is going for, and, given enough time to process those (while successfully balancing your research obligations, etc.), you may boost your exam performance.
Good luck.

I have browsed the solutions, but the exams haven't been handed back yet (scores were just posted online). Definitely planning to look it over though!

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Moving from chemistry to oceanography as a current chemistry PhD student?
I am currently working my way towards a PhD in chemistry in a very good EU university. Things are running smooth and I expect to graduate within 1 to 2 years. But there is one big problem: the time spent in the lab made me realise that this is not the life I want. Although my passion for science is still intact after all those years, I have to admit that the lab work, the dreadful academic and private job market and the unexciting prospect of "parallel careers" have finally dented my motivation to pursue such a path.
I do, however, have a second passion in life: the ocean. I simply love earth, climate and ocean science about as much as I love chemistry, and seriously considered going for such studies instead. Since I started college, I have continuously taken classes in related subjects (biological oceanography, biogeochemistry, atmospheric physics...), and have enjoyed every bit of it. The only reasons why I picked chemistry for grad school were that I considered the outcome of the research I would do as more valuable for society (I specialise in cancer biochemistry) and the illusion that surely, I would get my own lab some day. But with the current physical sciences job market being grimmer than ever in both academia and private research, I have to accept the possibility of doing no research at all after graduating as the likeliest scenario. And the mere thought of ending up in careers such as consulting, no matter how lucrative, makes me want to off myself straight away.
On the other hand, the job prospects in marine and earth sciences appear somewhat more decent (please correct me if I am wrong here) - at least in the sense that you have better chances of working as a scientist in the end, although not necessarily in a tenure-track position or in an elite institution. This, coupled with my very strong interest in the field, has led me to consider quitting traditional chemistry for a field such as chemical oceanology and the likes. To do so, several branching pathways seem not entirely absurd:
1) Finishing my PhD in chemistry, and then jump into oceanography via post-doc training: this would be the easiest and safest option IF permanently moving from chemistry to oceanography is realistically doable. (It seems to me that the fine understanding of the physical and chemical processes common in living systems and natural milieus deriving from a PhD in basic chemistry could be a plus in that prospect).
If 1) was to be an impossible/unrealistic course of action, I guess my options would then be:
2) Finishing my PhD in chemistry, and then do a second PhD in oceanography: I am honestly not a huge fan of this idea, as it would considerably extend the duration of my studies. I have also read quite often that already holding a PhD will basically disqualify you from being admitted in any serious graduate programme (committees would understandably see you as a degree chaser, an eternally indecisive student or a pisstaker). I would however gladly follow that path, provided that it is actually possible to go for the second PhD route and if it was my only option.
3) Dropping out of my current PhD and start another one in oceanography as soon as possible: This would be the Mad Max card. I am obviously very, very reluctant to this idea, but would consider it if everything else was to fail.
In the end, my question(s) would be: which one of these scenarios appears the more realistic? Is 1) a plausible option, and do I have to consider the other, riskier courses of action?
I would welcome any insight from people experienced in the related fields or who have heard of similar situations.

I would be very surprised if doing oceanography offer better career chances (esp if you think non-tenured job / average institutes are an option) than biochemistry, esp if you come from a respectable grad school.

Chemistry and oceanography are quite closely related, with a lot of people who explicitly overlap the two.  A nice example that I happen to be familiar with is Chris Reddy at Woods Hole, who works on marine chemistry, especially in the area of oil spills.  There are lots more like him, so I think that a transition via postdoc is entirely feasible to attempt.
Whether you stay in biochemistry or shift to oceanography, however, I think that you may wish to consider the broader scientific ecosystem of research opportunities.  Your view of the biochemistry world is probably somewhat distorted by an environment dominated by highly competitive "big PIs" with large labs.  There's a lot more to the research world than that, even in medical biochemistry.

Thank you for letting me know of Chris Reddy, jadebeal. His profile is indeed very interesting, and I might start looking for postdoc opportunities in similar research groups right now. About the job market, I know for a fact that a crushing majority of chemistry graduates end up doing something else entirely because of the scarcity of academic positions and the growing outsourcing of chem/pharma R&D divisions to Asia and Africa. This problem seems less blatant in ocean and earth sciences, as the academic market looks less cluttered and plenty of foundations and NGOs are hiring in the field.

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What non-research activities are most valuable when applying for faculty positions in mathematics?
I am asking this question for two reasons: first to work on activities to strengthen my CV for the future, and second to write a plan for professional development activities as part of a grant proposal.
What non-research related activities are most valuable to have on a CV when applying to permanent faculty positions at research-focused universities? For example, how valuable is it to have experience working with graduate students, organizing conferences/seminars, etc.?
I am a pure mathematician, hoping for advice that can apply to both European and American jobs. I currently am working on my second postdoc, although my first one was only six months long.  I had to take some adjunct teaching positions here and there as well, so I have a decent amount of undergraduate teaching experience. I have a limited publication record however (one thing I know I need to work on).

What is valued around here is to show independent work (not just papers with your advisor, have your own research grants). Show involvement with the relevant community (organize conferences, attend conferences, get invited to talk about your work).

I decided to focus on the following:

More (high quality) publications
Assist in supervising students
Participate in organizing conferences
Build on my programming/computational skills
Focus on international collaborations

I figure this mostly covers all of my bases.

Research production is BY FAR the most important for R1 universities.  They figure you can figure out the teaching.  But they don't think a teacher is going to figure out how to be Einstein.  And (despite, I would argue it is a fallacy for the interests of undergrads who actually want to learn, not do research), having Einsteins is helpful to premier school.
If you can show some evidence of moving to a PI status (e.g. getting a grant, leading a conference session, etc.) that might be a positive.

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Can open science project be performed/published by non-scientists?
In other words, can anybody publish an open science project, or does the author need to have some specific title or at least study the subject in order to receive some positive feedback from the community?
Or is it simply evaluated based on the quality of the published data and its positive feedback/output?

Yes, of course anyone can publish an open science project. As many of us in the scientific community wish would happen, the project should be judged on merit, not who initiated it, where they studied, or what their background or education is.
These principles are enshrined in the San Francisco Declaration on Research Assessment (DORA), which have been widely circulated and many (unfortunately not a majority, yet) organisations quick to sign up to.

Yes.
I'm not a scientist. However, let's say that for a project I do research on the genome of a fruit fly. I upload my data to GenBank, submit my pre-print to arXiv, and make sure that my pre-print, data, and overall project satisfy the criteria for an open science project, as given in What criteria does a research project need to match to be called open science?.
While I am not a scientist, I have still performed open science.

Some might argue that if you have done all that then you are, by definition, a scientist ;-)

@SimonW Groan. Semantics.

No specific training or credential is required to make a meaningful intellectual or technical contribution to an open science project. Training, credentials, where/how research outputs are published, how much those outputs get cited, and so on are primarily concerns of career economics—that is, how does one get, keep, and advance in a scientific career. For those interested in a scientific career, these considerations are important. But ideally there should be nothing stopping someone without scientific career aspirations from contributing to an open science project.


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Does publishing a paper with a non-edu email influence the review process?
I saw many good papers on good journals (by Springer, Elsevier, IEEE, etc.) with a Gmail as a corresponding email.
I'm about to submit a paper and since I don't have (yet) an academic email, I would like to know how bad is it to publish a paper with a Gmail account. Does it have influence on the author's reputation or the reviewing process?

Related: http://academia.stackexchange.com/questions/2872/e-mail-address-to-use-in-publications

Standard caveats apply: don't use an obnoxious or questionable username, and you will be fine

I would argue that Gmail looks much better than yahoo or hotmail in the paper.

@seteropere I don't see why, though. Probably just because it's "in" now? (Seems to be in, with the 4 comment upvotes...)

If you're genuinely concerned just get your own domain, only costs $10/year.

Note that .edu domains only concerns US institutions.

Going back 10 years, hotmail and yahoo was very limited and only used by people that could not get a "real" email account.   They were also used by spammer to create many fake email accounts.
There days, that has all changed, but memory lives for along time.

None. Outside/commercial email addresses are more likely to be permanent than academic ones, since people change jobs all the time. I think that a Gmail or Yahoo address is fine, and I rarely look at them when reviewing. Some venues use double-blind reviewing, so the reviewers won't know your email address or affiliation anyway.

+1 This is the reason I put my Gmail address on all my papers. If I hadn't I might already be missing correspondence directed to my previous affiliation's email.

Speaking as somebody who publishes using a .com address, I absolutely concur.

@Miguel Would an affiliated institution not look down on that though? A sign that you're perhaps not intending stay, or that you're distancing yourself?

@OllieFord, I would hope that such institutions (and presumably we really only mean tenure committees, here), wouldn't be so petty or try to read such "signs". You're going to put down your institutional affiliation directly above or below your email address (or in a footnote, or whatever). I wouldn't sweat the fact that someone might look down on you for using a personal or commercial email address. If they want you to commit, they can offer you tenure.

BillBarth Hell yeah, offer me tenure and I'll be sending errata around just to get the email addresses changed. @OllieFord I've never had a complaint, usually institutions are happy to be mentioned in the normal way (usually below my name) and funding agencies in the acknowledgments.

@Martin I disagree. Some older people might even have trouble using email (or just don't read email, it happened recently to me). As someone in my late 20s I have grown up and am familiar using the internet, yet I sometimes have trouble finding a working email address for someone who has a ton of institutional webpages each with a different email. Some people are very hard to track on the internet.

@Martin Again I disagree, not everybody who does not want their info all over the internet is not willing to receive correspondence regarding their research.


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Use of "we have a large backlog" euphemism by journal editors when rejecting articles without sending them out for review
Several times now I've had desk rejections from journals in pure mathematics that are variations on the theme of 'we have a large backlog of very good articles, so unfortunately we won't even be sending your paper to a referee even though we might ordinarily do so'. I suspect this is just euphemism for 'we aren't interested in your paper/your paper is not good enough/go away', as claiming a large backlog seems to me to be more objectively defendable than making an editorial decision (ie 'not significant enough') and standing by it on its own terms. Alternatively, it may be phrased this way to soften the blow in claiming to not make an explicit judgement call on paper quality.
Is this common practice among editors and/or journals? I haven't in my admittedly limited experience heard similar wording in rejections from, say, experimental sciences journals. More controversially, am I correct in my reading, that it is just euphemism? (If so, I do not appreciate it, in the interest of academic honesty over lawyer-approved weasel words.)
Ideally answers would come from people who are editors and/or those with extensive experience in publishing. A bonus would be answers that can detail whether this sort of thing is on the rise, coming from people who have decades of experience.

Maybe answers should also discuss what kinds of factors usually warrant desk rejection. My impression was that desk rejections occur indeed upon very objectively defendable (and accordingly easily verifiable) issues with a manuscript, such as violating the minimum or maximum page count, being obviously off-topic, not being a paper at all (e.g. a few pages only comprising of graphics, ...). While editors might evaluate significance of findings, this sounds more like something that the actual referees would look into first, to reduce the workload for editors and because significance is ...

... a somewhat fuzzy factor that is sometimes subjectively seen (or recognized) differently, so it seems reasonable to leave evaluation of that to actual referees.

Great question. Euphemisms in general are a despicable thing, and way overused in Anglo-Saxon culture.

I should add that the paper has been described by a referee as being very good, certainly not rejected for being obviously out of scope or inappropriate.

@O.R.Mapper -- there's a time investment involved in finding reviewers and sending something out to them. There's also a major time investment involved in reviewing a paper. I see nothing wrong in rejecting a paper without review if I can see in ten minutes that that paper isn't going to go anywhere.

@WolfgangBangerth: it would be interesting, though, to test and calibrate one's intuition that a paper isn't going to go anywhere. Perhaps send out one such paper to a reviewer or two, see what comes back - reviewers may have a very different impression. As a reviewer, I have recommended rejection-and-summary-burning for quite a few papers that I hope never went anywhere but that cleared the editor's threshold (unless he was calibrating with me), and conversely, a few papers of mine have been desk-rejected as "not going anywhere" that did indeed later go somewhere.

@DavidRoberts: "the paper has been described by a referee as being very good". If the paper actually is very good, then the simpler explanation in your case surely is that the editor is telling the truth, not that the editor is both wrong about the quality of the paper and also lying/euphemising about the reason for rejection?

Wow.  First I've heard of this.  Sounds like a field in death throes to me,

"Too long a backlog" is always to some extent an excuse.  If you proved the Riemann Hypothesis, any journal would move heaven and earth to accept your paper, no matter what the backlog is.  At the other end, as long as your paper is in scope, somewhat interesting and not wrong, a journal needing papers will be happy to publish it.  Editors adjust their standards every month based on what their backlog is, so what the editor is telling you is that, given the current state of the backlog and the competing papers in the pipeline, they don't think it's worth publishing for them.

@ScottSeidman  I've heard of humanities fields where almost all journals have had an acceptance rate in the single digits for decades.  Pure mathematics is comparatively much better off.

@AlexanderWoo  rejection without review is different from a low acceptance rate.  When a field can't review it's own body of work, that's a sign of ill health IMO

There are NIH institutes with pay lines lower than 10%, but every vetted grant application is vetted by consensus of multiple reviewers who have carefully read it.

An NIH study session is a very different process than a journal, because reviewers explicitly compare competing proposals against each other.  When an acceptance rate is low, a reviewer cannot provide any useful information to an editor because he or she doesn't have a sense of the competing papers.  When it comes to evaluating the importance or potential impact of a paper, the reviewer's slightly greater specific expertise is far outweighed by the editor's broader understanding of the competition.  (This is not so true when it comes to checking the correctness - that's why there's review.)

in plain words this says "it is not a proof of Riemann conjecture; moreover, you are not my buddy, not even a buddy of my buddy, and as a publication in out hot-shit journal ticks one on the list of tenure requirements in many places, my backlog consists of papers by pupils of my buddies who are lined up for jobs"...

@Dima sadly that's probably true. I could even name a journal I strongly suspect has such a policy.

This is a real phenomenon, which I've had to deal with in practice as an editor.  It's by no means universal, and it's probably a cop-out to some extent, but in at least some cases it genuinely indicates that standards are temporarily higher than normal while the journal deals with a backlog.
My impression is that it is caused by several factors:

A publisher that targets a certain number of pages per year and will not substantially exceed this target (on the grounds that it will cost more without raising subscription revenue correspondingly), regardless of how many papers the editors accept.  If there are too many accepted papers, then they will be published gradually over time.
A decentralized editorial board in which individual editors recommend papers for acceptance without having to justify their decisions in terms of the publication rate of the journal.
A sufficiently large backlog that authors start to get upset about how many years they have to wait to see their paper in print.

All of these factors can contribute, but they are not all necessary.  For example, Journal of the AMS has had backlog issues in the past, despite having an editorial board that makes decisions jointly.
Typically what happens is that the publisher or the editor in chief starts to get worried about the high backlog (since it can hurt the journal's reputation) and pressures the other editors to accept fewer papers until the backlog starts to decrease.  During this period, it can be tricky to coordinate with referees on the new standards, so editors typically desk reject papers they aren't excited about, even if those papers might plausibly have been accepted normally.
Each year the AMS publishes backlog estimates for mathematics journals (here is the 2015 version).  If you see a particularly high backlog listed there, then the stated reasons are probably real.  If you don't, then the editor might be trying to soften the blow of rejection, or it's possible that the AMS's backlog estimate is not right.
It's worth noting that a small backlog is good, since it evens out the random fluctuations in the acceptance rate and keeps the publisher happy.  It's only a problem to the extent that it starts to upset the authors, and it has been less of a problem in recent decades (since the AMS started publicizing the backlogs).

I haven't in my admittedly limited experience heard similar wording in rejections from, say, experimental sciences journals.

Yes, this phenomenon does not seem to exist in most other fields.  In mathematics, formal publication is not the primary mode of communication (rather, it's for permanent archiving), so nobody is too horrified by backlogs, and this lets things get out of hand occasionally.  In the experimental sciences, authors demand rapid publication, so there is no concept of accepting more papers than you have space to publish and developing a serious backlog.

A small backlog also allows the editor to pick and choose what will be published in the next issue, in case you want to strike a balance between an issue's articles in some way.

"A sufficiently large backlog that authors start to get upset about how many years they have to wait to see their paper in print." -- I strongly support electronic-only journals for this very reason. If people need paper copies for archiving, if they want paper copies for themselves, there are ways to do this, without the journal worrying about thickness of volumes and subsequent costs.

@DavidRoberts That solves exactly nothing. The journals are not going to increase the volume of published papers. They have gone up by some percentage during the creation of the backlog, but that's it. You can argue that you'd like to see your paper get a DOI and stuff sooner; there are other solutions to this (for instance, e-first).

@yo' why couldn't an electronic journal set a quality bar and publish everything above it, regardless how many accepted papers that represents?

@BenoîtKloeckner Because it costs money. The most money-efficient way is to keep a steady flow of issues/pages, and a reasonable backlog to make the flow really steady. Also, note that by indexing the articles in future issues, the bibliometrics are improved (possibly, not all of them, and this can't work forever).

@yo' : if the journal charges APC, it gets money for each article published so I don't quite see the issue. A journal can also do basically no typesetting in fields where authors use LaTeX, and then the costs are more with handled papers than with published ones. And hacking the impact factor can probably be done in any number of ways.

@BenoîtKloeckner That's a big over-simplification. The publishers get a lot of money from the library subscriptions, it's much more than what they get for pay-to-open-access or pay-to-publish.

@yo' This is not the place for such a long discussion, but I cannot help stressing that not all journal use subscriptions for funding. Never heard of Open Access?

I can confirm that I have never heard the 'we have a large backlog' thing when submitting to science journals and have only heard it in pure mathematics.

Although I've not been "an editor", I've been involved-enough with refereeing in "pure math" for almost 40 years now that I can observe some patterns:
First, the last several decades were very productive in the sense that many, many people got PhD's in math from pretty darn good places, and were focused on research. Second, the advent of TeX + internet (as opposed to paper mail) has effectively decreased the "friction" of submission so that the volume of submissions is insanely higher than 30 years ago. Maybe 100 times that rate? Meanwhile, the number of reasonably-substantive-status mathematics journals has not at all increased, and the refereeing system (pro bono, in people's spare time) has not changed. I hesitate to suggest that referees should be paid (jeez, for one thing, this starts to create conflicts of interest worse than those already present...), but the "old" system cannot cope with the new volume.
Thus, desk rejections will be more frequent, and more aggressive. That is, in particular, editors will not want to annoy/burden their "stable" of expert referees with a higher volume of papers... (One could hope that the pool of expert referees would grow proportionately to the number of TeX'd-up manuscripts, but this seems not to be so.)
Yes, I'd be willing to believe that the rate of inaccurate desk-rejections has gone up... not through malice or prejudice, but exigency.

I guess your "first" and "second" are both about reasons for the increase in number of submissions, but it doesn't read like this because of your sentence breaking.  Also, I guess the development of academia in many countries like China accounts for a lot more submissions.

@Kimball - what sentence broke?  If you see something needing editing, it would be constructive to suggest a solution -- in a comment, if you're unsure, or by clicking on the "Edit" link.

I can accept that there has been a large increase in submissions but I find a hundred-fold increase very hard to believe. Do you have any data to back that up?

If there are more people submitting, there should be a proportionally larger pool to draw referees and even (associate) editors from.

@gerrit, if it were just about filtering for quality, that is plausible (although the shape of the demographic might mean that there are way more novices than experts, etc.) However, regarding status, it would "break the system" if suddenly many more people could "acquire status": journals would lose their rep if they quadrupled their publication volume...

"reasonably-substantive-status mathematics journals has not at all increased" This seems not quite accurate to me, but might be off-topic here.

wouldn't this simply create a situation in which the contribution per paper is expected to grow for the paper to be publishable? This is what happens in other disciplines. Last week, I read a paper on pancreas cancer with 8(!) experiments in it, most of them on animals (which is more work than the ones in a petri dish). Not so long ago, each of these experiments might have been published separately, albeit in a journal with a lower impact factor.

@rumtscho, I think there is a tendency in the direction you suggest, although the "metric" in mathematics may be of a somewhat different nature...

One of the factors that make mathematics different from, say, experimental sciences, is that the expectations on referees is an order of magnitude higher.  Seriously refereeing a medium-length paper is a full week of work, and often takes up to a year since the referee has to find 40 hours (or even more for a longer or more difficult paper) outside of all their regular duties.
There is exactly one journal currently on my refereeing blacklist, and this is a journal that rejected a paper over my fairly strong recommendation for the paper to be accepted.  It might be bad for a paper to be desk rejected, but it is even worse for the paper to go out for refereeing, be recommended for acceptance, and then have the paper rejected because of lack of space or length of backlog, wasting six months to a year or more for the author and wasting a week of work for the referee.
If an editor believes the referee is unlikely to be able to convince them to accept the paper, they should not send it out for refereeing.
Some journals have now explicitly adopted a process where the editor(s) consult with a first referee to get a quick opinion on whether the paper should be fully refereed.  Even journals that don't adopt such a process formally may have editors who informally consult with experts before deciding whether or not to desk reject a paper.  In many cases, informal consultation with someone the editor knows personally is more accurate since they can more accurately convey the journal's standards and go back and forth about the merits of the results claimed in the paper.

"for the paper to go out for refereeing, be recommended for acceptance, and then have the paper rejected because of lack of space or length of backlog, wasting six months to a year or more for the author and wasting a week of work for the referee." <-- in my case 17 months...

I have not ever heard the particular reason for rejecting a paper you cite, despite having been an editor for two of the top journals in our field (computational math) for several years. I believe it's a cop out.
That said, there is nothing wrong for an editor to reject papers without sending them out for review. As an editor, you can often see that a paper doesn't have the required level; or that it is outside scope of simply covers such a small and non-interesting niche that it's not of interest to the readers. If you sent this out to 3 people for review, you'd burn out your referees. It's better for everyone to come to a decision quickly and send it back to the author without review. I am honest in such cases, however, about my reasons to do so.

Dishonesty in this case actually hurts the author. Any rejected paper that I've had has helped me immensely to go further, because a proper rejection generally comes with constructive feedback that I can use. Mentioning any other reason for rejecting a paper than the real one does not help at all and will only waste more of the author's time.


text:
Statement of purpose and career shift
My B.Sc degree was in an unrelated field. However, I have a strong interest in physics, and mathematics. I'm currently writing my statement of purpose for graduate school applications. I have a background in physics from self-directed study. I wonder how I should write it; should I detail my background, and my preparation first, then write my future  research goals, or should I focus on my future goals from the very beginning? I tried to start by detailing my background, but I found that I it is hard to explain in a concise manner the radical career shift from medicine to physics. I do not want to bore the reader with autobiography. Your suggestions would be helpful.

Your CV shows your background. Your SoP should focus on your future goals and how you will achieve them. Use the background only in support of the future. But make sure that you somehow list the self study you did in the CV and try to do it in a way that it is "verified" in some way. Perhaps some things you did in medicine prepares you for research in the sciences in general, and possibly in physics. Your masters details some of that, of course, so again, put it in the CV, not the SoP.
But the SoP should be forward, not backward, looking.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
I want to review my old college applications via FERPA - is this possible?
Several years ago I applied to a bunch of universities, many of which rejected or waitlisted me. Since then, there has been a lot of discussion about transparency in the college admissions process, including this lawsuit against Harvard and this video about Yale. In the latter case, the student also later wrote an article asserting that people can look at old application materials under FERPA - though typically only for schools they attended. (*I am not attesting to the quality of or agreement with the resources; I'm merely citing their existence.)
I recently remembered this and wanted to see if I could do the same out of curiosity. However, I have two questions regarding this.

Can people do this for schools to which they were not accepted? I read that they might only honor your request if you were admitted. (If this is the case, then is this stipulated in FERPA? And how can they “choose” not to honor the law unless this is the case?)

What is the retention period? I would think that if I applied over four years ago, they might not have my record on file...?

Edit: For clarity, I DO have closure and am extremely content with the outcome. I cleaned up the original question and corrected my wording to provide more context. Thank you to everyone who answered.

Maybe you should get a copy of the law and analyze it.

I can't find it stated explicitly in the regulations, but there are several passages that seem to suggest you only have a right to view records from institutions you actually attended.  E.g. section 99.5 (c) which says you don't even have the right to view your application records if you applied to a different component of an institution you were already attending.

I'm also not aware of any legal requirement to retain such records, so an institution may very well destroy them as soon as the decision is made.  For that matter, they may not even make any meaningful records in the first place; the admission committee could discuss the application's merits verbally and only record the final decision of admit or reject.

On the other hand, it costs nothing to file a request, so you could always try and see if you get lucky.

This sounds to me like the opposite of moving toward closure! You're going to reopen these rejections from years ago and use a fine comb to figure out what went wrong. This is understandable and very human. But if closure is what you're looking for you need to look within yourself. That's where it'll come from... Making your peace with the past regardless of the details. Good luck!

And if you're truly in need of information, do you still have the applications? Is there anyone you could ask to give you their honest assessment of your application strengths and weaknesses? That might be more useful than a very terse comment by an anonymous admissions committee.

For highly selective universities, getting accepted becomes a pretty random process even for highly qualified applicants. Even if you had details there might be no value in that information.

@user2705196 While I appreciate the concern, I think there’s a misunderstanding... I edited my post so there’s more context. I definitely agree that contacting people you know to ask for advice is a much better approach for future applications (especially because you’re in a very different place from undergrad), and that it’s important to introspect and let go of things you cannot change. This thread raises a lot of great points. :) Cheers, everyone!

Can people [request their records under FERPA] for schools to which they were not accepted?

No. From the FERPA text, education records are defined as:

those records that are:
(1) Directly related to a student; and
(2) Maintained by an educational agency or institution or by a party acting for the agency or institution.

and a student is defined as:

any individual who is or has been in attendance at an educational agency or institution and regarding whom the agency or institution maintains education records.

Since you have never been in attendance at the schools who rejected you, you have are a not considered their student and FERPA does not accord you any protections.
This accords with most "plain English" descriptions. For example, it agrees with this description from PrepScholar and this explanation from USC.
As Nate points out in the comments: "section 99.5 (c)...says you don't even have the right to view your application records if you applied to a different component of an institution you were already attending." So there is no loophole if you applied to grad school at your undergraduate institution.
There is therefore no question of "choosing not to honor the law" -- rather, the law does not impose any obligations on the school until a student-university relationship is formed.

What is the retention period? I would think that if I applied over four years ago, they might not have my record on file...?

FERPA does not specify any retention period. As noted here, however, state law may impose certain retention requirements.
In a larger sense, the goal of FERPA is protect privacy and allow students to correct errors in their educational record. It is not concerned with the admissions process directly (until the point where admissions documents become part of the student's educational record).
I agree with the commenters suggesting that you would do better to ask professors you know to review your application materials and give you feedback. I admit I am also a little concerned that you are still seeking "closure" five years later, but that is perhaps a separate matter.

While I appreciate the sentiment, you need not be concerned. The insinuation that I can’t let go of the past is due to a misunderstanding (and my admittedly poor word choice). I edited my original post to (hopefully) clarify my intention. Thank you for the thorough and well-structured answer.


text:
Listing inner-department seminars/presentations that focused on presenting current research by other authors?
At my university there are weekly seminars where faculty or students can do presentations for the department.
I had done several of these during my time as a graduate student, although admittedly they were seldomly composed of original work.  They were often taking a recently published paper and presenting the findings, sketching the proofs, and illustrating how it applies to research you are interested in and/or doing.
I started to list these on my CV as a more generic "Department Seminar Presentations" of a given paper/topic, but as I thought about it more I began to wonder if this is actually improper to do?
This is in mathematics.

I don't think it's improper per se, but I would not include them.
These sorts of presentations are more akin to assignments for a class: they can improve your skills in terms of public speaking and also getting deeper into the material.
However, you wouldn't put your course assignments on a CV, and I wouldn't put these presentations on a CV either.
I wouldn't even include them if they were based on original work, unless they are in a format that indicates some level of acceptance or prestige: conference presentations, invited talks at other institutions, etc. Instead, you reference that original work where it appears in public: in publications, for example.
They might be appropriate in a more generic form in a non-academic CV, when the point is to emphasize your experience presenting these sorts of things to a public audience, rather than your academic credentials.

I actually really agree with your point of being "more akin to assignments for a class", but would your stance still be as firm regarding someone who is not a graduated PhD and yet to reach public works?
This section is really more to be a mark of filling a CV as being a "comprehensive statement of your educational background, teaching, and research experience" and try to aid in addressing those three things that public works would otherwise, much more appropriately, fill.
While they did require some approval from either the faculty or graduate cohort, they were in no-way prestigious

@OGV You know, it might be a bit different for math given how delayed your research output tends to be compared to people in my field. If you meant it to highlight some of the academic work you are doing as a student, to say apply for a grant while still a student, then maybe that content would be worthwhile in a CV for that purpose. I also wouldn't characterize my stance as being too 'firm', except for the part about what I myself would do :) - so take the advice with a grain of salt. Your advisor is also a good person to run this question by.

I'd also say I'd be more likely to add it if you feel like you really did some original work in the interpretation of the papers you are presenting, which is something that also might be more special (though not exclusive) to math. If you are taking a published work and turning it into something truly digestible to a broader audience, that's a lot more relevant than just summarizing a paper in what my field would think of as a "journal club" presentation.

And lastly I'd echo @Buffy's "they could be omitted or reduced to a single line" as an option - in that case I think you avoid making it look like you are embellishing something if you just lump it in as "N Department Seminar Presentations..."

I would think it is fine, provided that you think the talks would be interesting to others outside your department. The heading you suggest is appropriate, showing that they were local. And, if you are interested in a career as an educator, primarily, rather than a researcher, they might be especially valuable.
If you are able, in these talks, to focus on insights and not just details, they would probably be especially useful as talks to students - even undergraduates.
I doubt that they would add a lot, and if your CV needs to be short they could be omitted or reduced to a single line (Several departmental talks...).
But, I can't see how it is improper in any way. Not everything in a CV has the same impact, of course and different people will look for different things.


text:
I'm unhappy with my PhD
I started work on my project in January right off the back of losing a very close family member, which didn't give me a very good mindset to begin with.
I had an initial doubt in my mind that the project wasn't for me but I suppressed it, thinking that over the coming months it would die down as my experience increased.
4 months later and the feelings are still there, it's at the point now where I dread the thought of having to work on my project and I feel myself staring at the clock almost obsessively. I'm still not allowed back on campus and have very limited contact with the faculty (to make matters worse I'm the only PhD student in the group) so I'm almost totally cut off in that respect.
Moreover, my motivation and interest simply aren't there any more and there's no point in me lying - I'm simply really unhappy and don't know what to do.
I haven't told my parents or supervisor because I really don't know what to say other than "I'm extremely unhappy and don't know what to do".
I recently had to sit some exams as part of the training I'm doing and they were almost impossible for me to answer which pushed me further into this way of thinking. I truly am very unhappy and don't know what to do. I'm only in my first year so I suppose it isn't too late.

This sounds like a situation that should be discussed with a professional counsellor. Perhaps the university has an office that can help. Many do.

If you doubt the project, that's a red flag, independently of anything else. You need to be enthusiastic with the idea from the outset, because in a PhD you will have to master a number of dry spells. Change now, you'll find it harder to turn around the deeper in you are.

As @Buffy says, you should probably talk to someone about your situation in general. A PhD is hard under optimal conditions, let alone when coping with loss and depression. There’s no need for you to suffer alone.
As for your research progress, nobody here can give you a right answer. You should talk with your advisor whose job is to resolve such issues. They may suggest switching fields, techniques or collaborators; they may give you a different problem you like better; they can tell you that you should quit the program and do something else. This is all very dependent on you, your advisor and your institution’s attitude towards grad students.
If your advisor is not someone you can discuss this with, you have a bigger problem on your hands. Talk to an ombudsperson, senior mentor, student counseling services, vice dean for graduate matters or any other resource your school offers. You may get a different advisor, switch to a masters or a plan will be worked out with your existing advisor.
Good luck!

I have been in the same situation as you. At the start of my PhD I had suspicions that maybe the project wasn't right for me, but I went ahead anyway. I thought maybe it will get better.
Now, here I am four years later and that doubt was correct! I am still having issues. If I could have changed things I would have been more upfront with my supervisor early on and worked on radically changing the project in the early stages. A PhD is hard and takes long-term focus and commitment. You need to be mentally onboard and committed - doubts must be assuaged, they will not go away and just sort themselves out.
It is crucial that you talk to your supervisor about this. Be totally honest with them. They want this to work for you but you must be up front. If you feel you cannot speak to them about this, I would question whether it's right for you to be doing the course at all in its current state: if that is indeed the case, you need a new supervisor as well as a radical change of tack.


text:
Should I offer co-authorship to colleagues who worked on a problem with me only initially?
I am a postdoc in theoretical aspects of CS/ML working on a quite theoretical problem. I discussed it extensively with two colleagues for a while. We all dedicated working hours to it, however, none of us got any results. The problem was formulated by me; I was the one majorly driving it.
After about a month almost everyone gave up. But I kept working on it, and I have finally solved it. The solution does not involve any ideas from my colleagues, but they did invest their time initially on it. Should I inform them and ask if they would like to join the paper? Or should I just publish on my own?

Remember that exploring dead ends is also a valuable contribution, even when no part of that exploration gets used. Because without it, you might have had to explore all those dead ends yourself.

My best guess (pure math, cs background) is that you should be first author and the others have likely gained an authorship position as it is likely that they contributed to the insight you gained, even if by cutting off unprofitable avenues. At a minimum they have earned a strong acknowledgement.
Yes, you should contact them and discuss this. For a lot of reasons, ethics among them. But if working together has produced something now, working with them in the future is likely advantageous.
The path to a theoretical result is seldom straight, with many unprofitable side paths that must be explored. You did that with your colleagues. Acknowledge it.
And even if this seems a bit generous, it is profitable to all in the long run. And long term thinking is good for a researcher and academic.

I wonder if the notion of "first author" exists in the OP's subfield.

@MarcGlisse Even if it is unconventional in OP's field, it can be explicitly stated in an "Authors contributions" section at the end of their paper.

@Buffy's answer sounds reasonable, and most likely no harm will come to you from adopting its recommendations. Potentially there will be benefits, since you will make your collaborators happy and that can end up helping you in various ways.
However, let me add this: if you honestly think that your coauthors genuinely contributed nothing intellectually, then personally I don't see why they should be coauthors. Offering them coauthorship would be a form of gift authorship, and would be ethically dubious. The fact that each of them spent a few hours trying to make a contribution is irrelevant.
Well, I'm not sure if you actually think they contributed literally nothing. By your description, this sounds like just enough of a borderline case that if you make the decision of what to do on purely utilitarian grounds, then whatever that decision is I think no one is likely to view it as some kind of moral transgression. However, from a more utopian or idealistic point of view, my point is that the most intellectually honest thing to do would be to not offer coauthorship to a person who didn't contribute either to the formulation of the problem or to its solution. If you did everything yourself, I'd prefer to live in a world where you get all the credit.

For all we know, the intellectual contributions and discussions may have helped the OP arrive at the solution more quickly, or at least, not waste their time on fruitless ideas.

@Mari-LouA sure, we don't know the details of what happened, so we can't give a definite answer. But I suspect that OP does know whether the collaborators' suggestions helped or not. If they didn't, my answer would apply.

I think @Buffy's answer is generally excellent, as it seems so does the SE community.
However, I'ld like to suggest a supplemental caution/refinement.
I'm wondering; even "quite a theoretical problem" in "theoretical aspects of CS/ML" may turn out to have practical applications which lead to other events related to awards (with monetary and career-building impacts) and intellectual property filings later on, and later transactions related to said IP, which could be subject to becoming unexpectedly contested.
Those may not be specifically limited to this one result, but might also apply to some derivative work based on it.
While a bit of "generosity" can certainly be "profitable to all in the long run" in the academy, a lack of accuracy and/or clarity in a published attribution of effort may have unforeseen effects later on.
@Buffy says, correctly:

At a minimum they have earned a strong acknowledgement.

Acknowledgments offer the opportunity to define and constrain the nature and extent of the acknowledged contributions.
Some journals provide a space to outline the extent and nature of the contributions of each author beyond what we can infer from the ordering of the names. You can consider where you'd like to publish, and if it offers such a space and authorship is offered to others, it's best to agree upon the wording there at the same time, rather than surprising folks later and suddenly have a potential second-order disagreement on your hands.


text:
Is repeating a mathematical formula or equation in a scientific paper considered bad writing?
I'm writing an engineering paper which is filled with equations (physical demonstrations in the theoretical section and numerical methods demonstrations in the methods section).
I want to rewrite one of the first equation I introduced, because I introduced it in a particular context and now I want to use it in another context and show different properties of it. Is this considered a bad practice?
Since all equations are numbered, there would be an equation which is numbered twice. I could solve this problem by not numbering just the second appearance of this equation. Or I could just reference the number, and let the reader go back a few pages. But that would affect the readability of the text (all the other instances in which I reference some previous equation are usually in the same paragraph, so there's no need to turn a lot of pages).
What should I do? Redundancy and readability or conciseness and elegance in spite of readability?

It would help to know the length of the paper, and the number of equations you might want to repeat.  Looking back four pages is not the same a look back forty pages.

Amplifying what Terry Loring said: If it is a document broken into chapters with quite different topics, it is more likely to repeat an equation. A book, a long survey report, a PhD thesis, etc., are good candidates. If it's a research article with one main topic, it is less likely to require repeats.

I'd suggest just referencing the previous entry. People reading technical articles are pretty used to skipping back if necessary. It might be confusing to repeat it with a new number, especially.
An alternative would be to repeat it along with the original number, making a note of what you are doing:

...repeating equation (42) x = y + z...

But the reference to the equation is likely enough.

In general, I think “readability” is overrated in technical material. You should absolutely try to be as clear as possible, but repeating an equation is a micro-optimization that saves the reader only a few seconds. Remember that the vast majority of readers are not even going to read the technical content, while those that want to understand it in detail will spend much longer on the paper. Properly understanding a bunch of equations can take hours, so making the set of equations longer just to save the reader a few seconds on the first skim seems counterproductive.
A better solution is to describe the equation qualitatively, such as “In this context, the dissipation equation (45) implies...” This helps the reader by giving context.

Indeed, and being sure to name it "the dissipation equation" (etc.) at its first occurrence. Descriptive names are much better than purely artifactual numbers.

repeating an equation is a micro-optimization that saves the reader only a few seconds If only. Time is not the only thing you can optimize for. There's plenty enough out there to suggest that locality of reference helps in both understanding and retention of the material, at least in the earliest stages of knowledge acquisition, i.e. when it's all new to the reader. Repetitions that improve locality of reference are hardly a micro optimization: their absence is a premature pessimization hell bent on file sizes (i.e.: who cares!) with no regard for human consumers of this knowledge.

Do as you please, just be clear as to what you're doing. E.g.,
We rewrite Equation (1) by x, y, and z:

... (1a)

Because a, b, and c.
In the example, the goal is to make it clear to the reader that an earlier equation is being rewritten and the reasons why it is being rewritten. I've labelled (1a) to show a relation with (1). Perhaps the label isn't necessary, it depends whether you want to refer back to (1a) having introduced it (or you think others might want to refer to it).


text:
Is 14 references enough for physics research?
This is my first research and I don't know how many references I can use. So far I have collected 14. Is this enough? My research is about physics.

What do you mean by "references"? Citations of other work?

Yes, by references, I mean the quotes that I will write at the end of the research

Is this for a term paper?

The first relativity paper by Einstein did not have references at all.

How long is this paper?  Is it reporting on an experiment or is it theory.  A review paper?

How long is a piece of string?
The answer is that there is no limit. You should cite as many or as few other works (papers, books etc) as you have used and built on in your research. Adding pointless citations to get your reference count up to some arbitrary number is silly and clutters your work with useless information. Similarly, using or building on someone else's work and not giving them credit via a citation is wrong.
Cite as many other works as you need to.

+1, generally, but especially for the first sentence.

You ask "is this enough?" almost as if there's a cut-off for the number of citations. There isn't. Just cite however many articles you need to so that you have actually referenced everything that you've used in your research.

Look at how many citations other publications have in your target journal or field. How many citations do your 14 references have? There is no hard and fast rule, but you should be able to defend that you searched the current literature and point out who has done what and other research that supports some of your claims. In engineering, we typically have ~30-50.
My guess, since you are asking, is that you need more.

People like to add references to make the paper look more informed. An advisor I had kept a huge list of references he added to every paper remotely related.

Obviously, you should cite any article where you have used their material, and exclude any that you have not.
That said, one should consider that there are several reasons why it is helpful to cite a paper! These factors might alter how much time you might spend on a literature review and what directions you spend your effort.

If you are publishing in journal X, it is often appropriate to have a citation to articles in journal X. This demonstrates to the editors interest in field and relevance to the existing literature.
Citing a paper means it is marginally more likely you will be read by its authors. If there are particular authors in your subfield of 10 or even a 100 researchers for whom your work is relevant or helpful to, a citation helps make them aware that you exist.

Again, you should not cite articles that you are not using.

"exclude any that you have not."  This is not correct for physics.  You can cite any relevant work.

I would consider "using" a concept as engaging it in any way, even offhanded references.


text:
Can I use images from Wikipedia in my paper?
I am new in the field of writing papers and publishing them. This is my first work. While writing my paper, I thought it would be great to explain some concepts I have used in this paper beforehand. I am also planning to include images of "how the thing works". Can I take an image from Wikipedia and use it in my paper? Will it be plagiarism?

The license of individual figures on WIkipedia should be checked. That is definitely a factor to consider.

Any image you use at least needs to be checked for copyright and permission from the author.  Depending on the image and how good it is, it might be easier to re-make a new version in your own style.

Also read carefully what terms you sign with the journal. It is not uncommon that you sign over copyright of the article and all materials in it to the journal, which you can't really do with third party material under e.g. creative commons.

There are two potential issues.

You avoid plagiarism by providing adequate references. When referencing Wikipedia, make sure to use a stable link with timestamp.
You avoid copyright infringement by examining the license for the image and using the image only within its constraints. It probably is some kind of creative commons license that allows commercial use, but it's best to check for each one.

@DanielHatton I think it's generally agreed the burden for that falls on Wikimedia. I don't think you can be held liable for things that were fraudulently licensed upstream.

@DanielHatton to what extent are you responsible for checking whether you are buying stolen merchandise from a store? The onus is on the provider of the copyrighted/licenced material to have everything in order, you cannot legitimately have any idea whether the provider - for example - does not have some private contract that allows him to use provide it like that.

@OrangeDog: Wikipedia expressly disclaims all liability for misinformation, which presumably includes misleading copyright notices. You have sole responsibility to verify them. If you don't like doing the legwork, then buy an image from someone who is willing to indemnify you for it.

@Kevin that disclaimer also explicitly excludes the license, and is for Wikipedia, not Wikimedia Commons (where the images come from). My advice is to ask a lawyer if you're really concerned.

@OrangeDog: That sentence is clearly intended to be limited to the text's license, not the image's license. If the image is neither GFDL nor CC-BY-SA 3 unported, then it definitely does not apply. If the image was (wrongly) declared to be GFDL or CC-BY-SA 3, I don't know what a court would do, but I imagine it would be a huge expensive mess for everyone.

Technically you maybe can, but you shouldn't.
First, if you cite correctly, it is not plagiarism. However, if you want a publisher to publish your paper, you also need to care about copyright issues. Because plagiarism is an academic concept and copyright a (mostly) commercial one, they don't exactly overlap. If a figure is published in a paper and you cannot resort to a fair use clause, it may violate copyright even if it is cited correctly. That will also depend on the license of the figure on Wikipedia, and whether the publisher will agree to having a separately licensed figure in the paper.
Second, even apart from copyright/plagiarism issues, I would argue that it is often a bad idea to include figures from Wikipedia in a research paper, even if for illustrative purposes. Research papers address an expert audience and should focus on aspects that are novel for this audience. If there is a figure on Wikipedia, it is probably a relatively basic concept for your target audience. In that case, it would be better to just cite a standard textbook or similar reference regarding these concepts, and use a figure to illustrate what is new about your paper.

I disagree with the second paragraph. Images should be evaluated for relevance, certainly, but not rejected simply because they appear on wikipedia. Wikipedia and wikimedia are very clear in their licensing restrictions/permissions. Mostly they are fairly permissive. henning gives better advice about licensing.

@Buffy My second paragraph is not about licensing actually, so I edited to clarify that.

My comment about paragraph 2 still holds. The licensing comment was a separate idea.

It's not even just for Wikipedia really. I would give the same advice if someone asked whether it's a good idea to include a figure from a basic textbook in a research paper.

I'm not sure why you think wikipedia only has only "basic" information. I find some pretty high level math articles there. Settled knowledge, perhaps, but not necessarily basic. And many cited papers are also settled knowledge.

Minor note, 'basic concept images' are often relevant in papers that cross traditional field boundaries. Recently was reading a paper about motion tracking that included some basic explanations of certain biological concepts (around limits on facial human motion). For copyright reasons they - I think - created their own images, but those images could've been taken straight from a textbook.

Regarding the first paragraph: a great many Wikipedia images are public domain, many are permissively licensed, only a subset use toxic licenses like CC-BY-SA. Regarding the second paragraph, a common use for images is to include them as a sub-part of a more complete diagram and Wikipedia sources are fine for this.

I strongly disagree with but you shouldn't. As a counter example, one of my favorite ecology papers uses a photo from Wikimedia. The paper (https://esajournals.onlinelibrary.wiley.com/doi/abs/10.1890/080209) was published in a top ecology journal.

@RichardErickson Which figure are you referring to in that paper? From what I see, the external figure sources are: Library of Congress, Harvard University / Forest archives, and the R Foundation. None of them mentions Wikimedia.

@silvado you're correct. They are not from Wikimedia. My memory was wrong. They are generic stock photos from sources such as the US Gov't or the R Project. As a broader answer, using stock photos/images (with proper attribution and copy license) should be okay.

@JackAidley What makes CC-BY-SA "toxic"?

@RichardErickson: Very few images on Wikipedia are going to be properly credited to Wikipedia even if they are found on there.

@AzorAhai-him- Toxic is perhaps too strong a word, but something released under CC-BY-SA can only be redistributed in a work licensed with the same license (roughly speaking, I'm not a lawyer). This is problematic for the use in a paper that you intend to publish

This varies by the image. Be sure to check the license carefully.
For example here's an image from Wikipedia:

I can safely reproduce this because it is in the public domain. Wikipedia's page on the image is here, and I quote:

This work created by the United Kingdom Government is in the public domain.
This is because it is one of the following:

It is a photograph taken prior to 1 June 1957; or
It was published prior to 1971; or
It is an artistic work other than a photograph or engraving (e.g. a painting) which was created prior to 1971.

HMSO has declared that the expiry of Crown Copyrights applies worldwide (ref: HMSO Email Reply)

Not every image will have a similar license. You will have to check the image you want to use.
Edit: here's another example, from the Wikipedia article on parallax.

This image was drawn by Wikipedia editor JustinWick. I can safely reproduce this because it is CC-BY-SA, i.e. I can share it as long as it's attributed & I use a similar license if I modify it (which I have not). The license is here:

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:

to share – to copy, distribute and transmit the work
to remix – to adapt the work

Under the following conditions:

attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

You can find more details about how to reuse Wikipedia content here if you need them.

Though in a case like this wouldn't it make more sense to cite the original source which Wikipedia got it from (Library and Archives Canada)?

@aquirdturtle right, this might not be the best example. I'll add another.

Is including a CC-BY-SA image into a scientific paper considered creating a work that evokes the share alike paragraph? In this case it would not be possible to use the image as the publisher of the article surely will not use CC-BY-SA, but their own license.

The CC-BY-SA license does not forbid modifications, you just have to license any derived work with the same license. A license that would not allow modifications is CC-BY-ND (but that one is usually not allowed on Wikipedia).

You might not be allowed to. When your paper is accepted you will later have to sign a copyright transfer form (content depending on the publisher). Depending on the content of that form you can fulfill it or you cant. So you need to ask the publisher first if they were to accept such pictures.

Indeed, they will want to see the license, which is why it's important to examine it beforehand.

@henning also, if you do not have copyright, you cannot transfer it (but it depends on the wording of the contract)

Not all publishers require copyright transfer; IMO the better ones don't.

It's good to explain some concepts, but it is a paper you are writing to show what you are working on, it is not a book (nor a review paper, I guess).
This means that concepts has to be clear to the reader, or you provide a very short explanation and a reference to someone that presented the concept before and in detail.
If you need figure to express the concept, draw them by yourself. It takes longer, but then you can reuse them on presentations, reports, talks (with minor modifications, sometimes you give up all your rights with publication...), without your presentation having a figure "taken from wikipedia", which would look like to the casual attendee of your presentation as "I put this yesterday evening from wikipedia because I knew no better"...

Yes, you can use free images from Wikipedia. However, please validate whether the image has copyrighted.
I suggest that you make your own image or modify the existing image to avoid copyright issues.

I agree with Silvado's answer "Technically you maybe can, but you shouldn't," but I'd like to elaborate an another part of this. Like it or not, if you cite Wikipedia like this in a professional paper, it will inevitably come across to many as lazy or amateurish. In my experience at least, citing Wikipedia is rare for professional articles, and common in student work. When they see this, readers will consider two possibilities:

The figure is simply the perfect figure for the paper at hand and using it was a principled choice.
The author is inexperienced and isn't familiar with standards in the field, or being is lazy.

Publishing is generally pretty competitive. I don't know what your field is or where you're trying to publish, but you don't want to give readers an excuse to dislike your paper, so doing anything even make people consider #2 above is probably a bad idea. Similarly, many (correctly or not) still don't view Wikipedia as a very reliable or professional source, especially in something as formal as a scientific paper, so referencing it will inevitably wrinkle some noses regardless of the figure's merit.
As a side note, I suspect it's pretty rare that #1 is actually true. In my experience you typically can (and should) customize even a simple a figure to be more tailored towards your novel work in the paper. This can help keeping the style consistent as well.