text:
I have a proof of a result in number theory, shorter than the existing proofs. Can such results be published and how?
Actually I'm proving that ∀n∃p∈P|n<p<en. Which is a result similar to Bertrand's Postulate, but with a shorter proof. Should I publish my result? If so, as I'm not affiliated with any Research Institute how do I do that?
Edit
Since yesterday I've improved my proof: ∀n∃p∈P|n<p<2n. This means I'm proving Bertrand's Postulate with a simpler and shorter proof. So, which is the most appropriate
Journal to publish this result?

Probably start by posting it on arXiv (to establish priority) with a public key (to establish identity).

How significant would you say that this result is?  I mean, is it primarily just a shorter proof for an accepted principle, or does it reveal some actionable insight to real-world problems?

@Nat: The result itself isn't more significant than those stated by Bertrand's Postulate, but the proof is simpler and shorter.

It sounds like you might not (yet) have a doctorate? In principle shorter proofs can be interesting and, in my field at least, it is possible to submit to journals and conferences without an affiliation. However, your problem is determining the significance of your result and for that, you need another mathematician. I don't think we can answer your question, but you should try and find a number theorist at an institute who can, it may even lead somewhere.

have you asked on Math stack exchange?

@aaaaaa https://mathoverflow.net/questions/292477/should-i-publish-my-result-if-so-where-and-how

I noticed you didn't use TeX in the MathOverflow post despite them having it enabled (SE.Academia doesn't, sadly); was that an oversight because you're new to StackExchange?  In any case, if you go to post this proof, you'll definitely want to ensure that it's typeset well.  Poorly formatted work is a huge red flag that'll drive a lot of readers off at first glance while well-formatted work is far more likely to receive attention and understanding.

Any alternate proof is potentially interesting, regardless of length. Well I suppose an extremely long proof of something that can be proved more concisely would be less interesting. But alternate proofs are very helpful in understanding the theorem better as well as connecting it to other areas of Mathematics.

To those who voted to close: how is this even remotely a duplicate of the cited question? OP does not "believe they have solved a famous open problem", since Bertrand's postulate is not an open problem. OP also is not asking anything at all similar to "how do I convince people in the field that I am not a crank?", in fact there is no indication that OP has any concerns about being perceived as a crank - their question is entirely different. Voted to reopen.

@DanRomik Claiming to have a big improvement over a known proof doesn't seem very different from claiming to have a proof of an open problem. Similar pitfalls would seem to apply, e.g., it not being a correct proof, reformulating the problem to something much simpler, etc. In any case, "should I publish" is opinion-based, "how should I do that?" is a duplicate of other questions on the site and "which is the most appropriate journal?" is shopping. So, even if this was closed for the wrong reason, I still think it should be closed.

@DanRomik Based on questions the OP has posted on MathOverflow and MSE (e.g. https://mathoverflow.net/questions/292577/is-my-proof-a-notable-result-if-so-where-and-how-do-i-publish-it ), I think that reopening the question here may not be so constructive. I also agree with the last sentence of David Richerby's comment above

@YemonChoi I’d say the question (or, at least the parts of it that I was addressing in my answer) is a valid question by itself. What facts may be inferred about OP from their other questions seems irrelevant to me. But anyway, all I was saying is that logically, the question is not a duplicate. I don’t have an opinion about whether opening or would be constructive or not.

As @Nat says, do post in on arXiv.  Many journals have a "Notes" section for short results like yours, which people would find interesting, especially if they were teaching similar results.  The MAA Monthly does this, e.g.  After you have the proof up on arXiv, submit it to the "Notes" section of an appropriate journal, following the specific directions for that section.  At least one professional mathematician will look at it, so you'll get some vetting.  Have a look at the Missouri Journal of Mathematical Sciences.

Thanks for your answer. But what would be the best journal to publish for as a non-academic?

"Best" is hard to say.  I mentioned the MJMS because, while it has a good reputation, it's one of the easier journals to get published in, and it has a "short notes" section.

I would hardly say MJMS has a "good" reputation; rather I would say it has a "non-junk" reputation.

It is easy for people with institutional email addresses to say "oh, just post it on arXiv" and incorrectly assume that their interlocutor will be able to do that. To be clear: posting on arXiv can be a significant challenge for people without an institutional affiliation. Unless you're able and willing to personally endorse the OP, the initial advice needs to be tempered quite a bit.

@E.P.   I had no idea.  Good point.  But perhaps a solution:  I know that UT Austin will give almost anyone some e-access.  The public gets to have access to the libraries and such, so it's possible for a citizen to get a UT e-id and library card, and perhaps an e-mail address.  Maybe the OP's local state-supported school has such a service.

@B.Goddard If that works, then I'd be disappointed with arXiv's filtering scheme (or at least, I'd hope they're ready to turn it off the minute it starts getting abused). The restrictions on submitting to the arXiv are there for a reason (note e.g. that arXiv had been running for 13 years when they instituted them), because there's a lot of content (much of which now makes its way to viXra) that we don't want to end up on arXiv.

Can such results be published and how?

“Such results” certainly can be published, if by “such results” you mean genuinely new proofs of well-known theorems, especially if they contain a new and interesting idea (rather than being a trivial modification or variant of an existing proof), and especially if they are shorter than existing proofs, although that is not a necessary condition for a new proof to be publishable.
Such new proofs are published quite frequently. For example, when I was a graduate student I published a new proof of Stirling’s formula. It was published in the American Mathematical Monthly, a respectable journal that often publishes papers in this category.

Should I publish my result?

As others have said, you can at the very least write up your proof as a paper and submit it to arXiv to make it available to the community. And you can try to publish it in a journal - if it’s interesting, well-written and novel, I think you have a good chance of getting it published somewhere.

If so, as I'm not affiliated with any Research Institute how do I do that?

See this question for some suggestions.

Thanks for your answer. I just revisited my proof and I realised I can also prove Bertrand's Postulate with a minimal change. Maybe it's worthwhile publishing it.


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Google scholar citation problem with arxiv
I have a paper that I uploaded to arXiv and google scholar listed it as a publication. The paper cites a number of my papers that are already published. However, Google scholar doesn't add arxiv citations to the already published papers.

This is a little unclear to me. You say "google scholar listed it as a publication ... Google scholar doesn't recognise it". Do you mean it showed up on your profile but can't be found in a Google scholar search?  Or ... ?? A little more explanation would be helpful.

or do you mean that the arxiv paper doesn't show up in the lists/counts of citations for your other papers?

Did you find an answer to the problem you asked? I have similar issues with Google Scholar. It would be great if you provide an answer to your question if you fixed the issue.

@Millad Google scholar will eventually add the citations. It's not quite immediate.

Does this answer your question? Published paper not showing up on google scholar

So apparently you have to wait. There is a delay between your arXiv submission and detection of its citations by Google scholar. But it will eventually happen.

Sometimes citations are missed, though. For reference, I'm currently waiting >10 months for a citation to be added to one of my papers from an arXiv preprint.

@ComputerScientist what to do for those situations?

There is an issue where Google Scholar does not promptly add the full version of a paper to its index if a pre-print version of the same article was previously found. See the discussion below:
Do all preprint servers have the non-updating issue in google scholar
The funny thing is that the final version of the article will show up in a regular Google search but not in a Google Scholar search. Apparently it takes a while for the two version to be reconciled and merged.

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What counts as Research Experience?
I studied physics at a German university and encounter frequently in application regulations for universities from abroad (US/CA/AU) the wish to have research experience. I don't really know what is meant by that and guess there might be some cultural differences and suspect that many universities might generally not have a well designed curriculum. I personally did quite a lot of research intensive coursework. Particularly I did about 42 lab exercises with 12 being exercises with advanced difficulty concerning topics of modern physics. Both of my thesis projects required me to team up with local research groups and independently research and work on a suggested problem. Further I did seminars in which I was trained in scientific writing and presentation and was required to spend about an half year on writing a research proposal and getting it examined to get allowance to work on my master's thesis. I think my university did quite a good job at preparing me for research. But otherwise, I did not do any research outside of university. Also no publication. Both are not very common in theoretical physics before PhD studies. I would be glad to hear your thoughts on this.

Applications for what? Ph.D programs?

Yep, PhD programs.

Everything you have named count as research experience and are good enough for applications in graduate programs. At the moment your master thesis is the most important proof/measure of your research experience.
The main goal of a phd program is to train you to be an autonomous researcher. With that in mind, they are not expecting you to have worked as a researcher outside the university before achieving a Ph.D degree. There are students with some luck that are able to publish an article before the phd, but that is not common.

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After submitting a revised manuscript (moderate revision was requested), what are the steps followed?
I have submitted a manuscript to a reputed journal. After 2 months of peer review process, the response was “moderate revision has been requested” and they told me that the new version is required within 1 month.
After making the necessary adjustments, I have resubmitted the revised manuscript back on the 14th of October 2017. On the 21st of October the status changed from “with editor” to “under review”. To date (16th December) the status is “under review”.
In fact, I had made some readings about late reviews, I found that reviews are normally due 14 days after the invitation is accepted by the reviewer.
Should I worry about manuscript rejection?
Thanks in advance for your help

This is an excellent and to the point question for academia stackexchange. Closing is certainly not reasonable in this case, IMO.

You may ask the editor in charge. I.e., send an email to the editor in charge of your manuscript. If you don't know who that is, send an email to the Managing Editor.
However, I don't think there's anything to worry about in this case: the change in status doesn't mean it is going to be rejected. It simply means they got your revision and now (sub-)reviewing it again.


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Should I simplify my writing in a foreign country?
As a native English speaker studying in the Netherlands, I often find myself writing (not published) English papers for a Dutch audience, and I worry I'm alienating my superiors with my writing.
I put a sample of text from a letter I wrote for an admissions committee through an array of readability tests, with Flesch-Kincaid Grade Level, SMOG Index, Automated Readability Index, Gunning Fog, and Linsear Write all  assigning it "college graduate" level. For comparison, the King James Bible averages around a fifth grade reading level, and New York Times articles typically produce a reading level around the tenth grade on the same tests.
At first glance, this is exactly how it should be. A university student submitting university documents should be writing at a university level. And yet, despite the truly incredible level of skill widely demonstrated by the Dutch people in the English language, I can't help feeling that I'm disadvantaging myself through use of constructions and vocabulary that no reasonable non-native English speaker could ever be expected to know.
Is there some merit to this? Rather than optimizing my writing for descriptiveness and articulacy, should I instead aim to be more readable by a foreign audience, at the cost of expressiveness?

Those tests are entirely based on metrics related to word length, number of syllables per word, sentence length, etc... For modern English text, that produces a not-entirely-horrible estimate of difficulty. The King James Bible uses a lot of short words and short sentences, so it scores low, but many of those words are uncommon and many of the sentence structures are unusual, nuances the tests don't cover. To the extent readability tests are useful at all (arguable at best), they very much aren't useful as applied to old texts.

"dumb down" in the question title sounds pejorative, since it risks implying that non-native users of English are dumb. "Simplify" would be a better.

Do you mind adding some examples? In my experience some non-native English speakers can have difficulties with idioms and metaphors, but deal pretty well with obscure words (which might have a common origin in their language).

Answers an comments, asides, and general linguistic discussion have been been moved to chat. Please read this FAQ before posting another comment.

In the context of your question, it is unclear to me what "constructions and vocabulary that no reasonable non-native English speaker could ever be expected to know" means. I would expect almost every person with an academic position at a university in the Netherlands to be able to comprehend written English at least as well as an average native speaker. It is the language in which they (we) read (and write) all textbooks and articles, and usually the one in which they communicate with colleagues every day.

Who are in your audience (students, career academics, or both)? Are you writing for a general audience or are you writing field-specific stuff?

Thou shalt not dumb down thy writing, but don't make it a vain exercise of style
I'm a non-native English speaker, and let me put it straight: I may write in simple English, because limited are my English writing skills, but I don't want to read simple English because I want to enrich my vocabulary and grammatical constructions.
But whether you write for a native English speaker or not, write clearly, avoiding unnecessary verbosity just to show off your eloquence.
(And, honestly, stop wasting time using those readability tests)

This.  Scientific writing should be clear, precise, complete, and accurate - these are the ultimate goals.  A scientific paper laced with colourful prose, metaphor, idiomatic expressions, allusion, or other artistic, stylistic elements that do not serve those goals is as equally poor as a paper written in broken, awkward ESL English.  While a fluent English speaker may be able to parse the colourful paper, it only serves to make the exercise more difficult than it needs to be, frustrating the actual purpose of communicating scientific information - whether to a native or ESL audience.

@J... The OP did not specify that they were doing scientific writing (I get that that's the majority of people here, but it's not exclusive).

@J... I wish people's goal in scientific writing was to be clear, precise, complete, and accurate. Many instead write their papers with the goal of "marketing" their papers, some also to show off language skills. The writing style is tailored to the goal - some writers' goal is to inform the reader, others' goal is to get their paper published.

My advice would be to be more direct.  Many business and academic documents benefit from more meaty, direct, gutty writing.
You might even improve your own style, for English readers, if you change your attitude.  Read the following advice:
https://ocw.mit.edu/courses/media-arts-and-sciences/mas-111-introduction-to-doing-research-in-media-arts-and-sciences-spring-2011/readings/MITMAS_111S11_read_ses5.pdf
In particular see the comments on page 5 about "English teacher beaming at you" and "emphasizing clarity and easy readability".  Some of your comments in your question ('dumbing down', 'university students write university level') seem to me to show that you are too in love with showing off.  Real good writing is much more about good ideas and good structure and clarity than it is about fanciness.

As Dr Johnson put it, "I counsel you, sir, always to read through what you have written; and when you find something that you particularly admire, to strike it out"

Or Mark Twain, "I didn't have time to write a short letter, so I wrote a long one instead." Take the time to write a short letter, it benefits everyone. Or Joel Spolsky's example about the Juno dialog text: https://www.joelonsoftware.com/2000/04/26/designing-for-people-who-have-better-things-to-do-with-their-lives/

@user3067860 I wish I could mark the comment as "accepted". The example was nice.

I think what it comes down to is this: Why do you write and who do you write for? If your a novelist you have a different target audience than if you're a technical writer. If you're a novelist writing romance novels you have a different audience than if you're shooting for a Nobel Prize in Literature. Likewise, if you're a technical writer, your style should similarly be different depending on who your audience is. In all of this, I don't think it's about "dumbing down" your writing as you suggest in the title of your question, but it's a careful consideration of what you are trying to do: namely, to communicate something to a target audience. In your case, it's likely to communicate knowledge, not your intellectual prowess.
So do an assessment: Who do you write for? What do they want to get out of reading what you write? What do you want them to get out of it? And then assess what the answers to these questions mean for how you should write.
This may feel sad: If you have a large vocabulary and are fond of complicated grammatical constructions, you may not be able to use those in your technical writing. (Though, of course, you may get to do that when writing to friends or for other outlets!) But using simple(r) language does not make you a worse writer: Rather, if you manage to adjust your writing style to your target audience, then that's exactly what makes you a good writer!

As hinted at by other comments and answers, the very wording of the premise suggests attitudinal problems...
Clear communication is always the goal. Scholarly writing is not necessarily suppose to be "purely decorative" (that is, non-functional) ... of course depending on one's assumptions about the larger goals.
If a thing is simple, its explanation should be simple. If your claim is that any competent professional should be able to understand it, the writing should accomplish that.

Impress, but don't show-off
Your audience wants to be impressed, but they don't want their time wasted (this is true whether you're writing to an admissions committee, a technical journal, or a picture book aimed at 6-year-olds).  I've written and suffered for (and reviewed and condemned for) trying to sound important by using words where I needn't or expressing ideas in the most grand way possible.  Oddly, after reviewing/writing somewhat for academia, it becomes second nature to do so, despite it not being the better choice.
The difference between well-written and showing-off is frankly reflected in a ditty by Dr. Seuss:

It has often been said
there’s so much to be read,
you never can cram
all those words in your head.
So the writer who breeds
more words than he needs
is making a chore
for the reader who reads.
That's why my belief is
the briefer the brief is,
the greater the sigh
of the reader's relief is.
And that's why your books
have such power and strength.
You publish with shorth!
(Shorth is better than length.)

Keep it clear.  Keep it tight.

Food for thought, to help you decide for yourself.
Style and substance go hand in hand. In a creative piece, style is more important and calls for that certain flair vocabulary helps us to achieve. On the other hand in a scientific journal, clarity is key. Where does your writing lie in that spectrum?
The point of communicating is to connect with your audience. Don't look at it as dumbing down your language; look to it as using 'appropriate' language.
The intention behind the writing is pretty important too. For example, if you are writing a literature thesis for university it would be reasonable to expect your reader to have an advanced grasp of the language.
Finally, this doesn't need to be viewed as an either or, there may be ways to communicate complexity through simplicity.
My personal opinion: complex vocabulary is overrated if the message can be achieved with simplicity- including in creative pieces. As the Bard once said: Brevity is the soul of wit.

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What are "General Quality Indicators" for scientific research?
I am currently filling in a CV in the Spanish CVN online system (https://cvn.fecyt.es/).
In the section "Scientific and technological activities" it asks to specify "General Quality Indicators" in up to 3500 words.
I am a mathematician and I have never heard of such indicators, what are relevant things to put here? I.e., seminars organised, papers published?
A side question, at some point it refers to the h-index (https://en.wikipedia.org/wiki/H-index), have you ever seen this been used in mathematics?
TIA

Is this a general system for all fields, or specific to mathematics? (I don't understand Spanish). Often such general systems include things that are not really used by specific fields, in response to your side question on h-index.

Seminars and papers are activities. They are asking to elaborate on the quality of such activities, preferably with some objective indicator. For instance, a seminar can be taught by invitation at an institution that occupies a relevant place in the Shanghai ranking of Universities. Or a paper can be published in a journal placed in the first quartile of its category sorted by impact factor.
The h-index is used pervasively in Spain and Mathematics is not an exception.
Good luck.
EDIT: What is your final goal when filling in the CV? You should find additional information on the specific call you apply to. For instance, if you are thinking about applying to accreditation (i.e. to pursue an assistant or tenure position) then you should have a look at the accreditation agency web site: www.aneca.es

That makes sense. I am applying for a research position and I guess in Maths you cannot really arrive at 3500 characters for this and definitely the h-index is not very relevant. Unfortunately, there doesn't seem to be direct a direct indication of what should be in the CV. Cheers for the answer by the way.

@MatteoVannacci It is not necessary to fiil in the full 3500 characters but at least you have some space to freely point out what you think is most significant from your CV. Think that evaluators have to read dozens of CVs, often from areas that are not directly related to their research. Then, it does not make a difference one paper more or less, but you can point out that some paper received a prize, or it is established as a reference in a very specialized topic or... whatever merit you think makes you stand out from the rest of candidates.

Sorry to bother you again, but is there a place where to write down talks given (and conferences attended) in the CVN?


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Graduate school holding a diversity committee meeting. What do I need to do to be effective?
I created an affinity group for first generation students at my graduate school. Shortly after, the school's diversity committee emailed the student government informing us that there would be a diversity committee panel on the issue of being first gen. It seems like sort of an informal lunch between students and faculty.
I am thinking there are two possible reasons the school is holding this meeting. 1) they are trying to look good by taking initiative before students start making noise or 2) the school cares deeply about the issue. I'm inclined to believe its reason 1 because the school took zero steps to contact me or any of my first gen acquaintances to see what help or resources we needed, and is only having a "first" discussion about this issue right after I created the group even though this is by no means a new issue.
At any rate, not sure the motives for the meeting matter except insofar as me knowing how much I can get the school to change its approach to this issue. In other words how much do they actually care about what I have to say and how do I hold them accountable to act on any requests I make? I have a bunch of (very actionable and easy) ideas - e.g. distributing surveys that ask students questions such as "are you first gen" and then having the school appropriately match an advisor/mentor - but is this the forum to express those ideas? If so, at what level of detail? What I really care about is just getting the school to do the things I want it to do. How much work is done in that meeting, and how do I follow up "behind the scenes"? How much leverage do I have as a student? Any advice appreciated!

@Najib Idrissi: This might mean being the first person in their "immediate family" (can be defined in several ways, but probably means siblings, 2 parents, 4 grandparents, 8 great-grandparents, etc.) to have attended college (sometimes "have graduated college"), although context here suggests that "attended college" might be "attended graduate school" (but this seems unlikely because not clearing the "attended graduate school" hurdle could include more than half of the students).

The definition @DaveLRenfro gives is the common meaning of the term in the US (except in my experience it omits siblings--someone whose older sibling is in college would still be a first-gen college student so long as their mutual parents hadn't attended/graduated from college).

What sort of advisor/mentor relationships are you looking for? Professors who were also first-gen college students? That might be somewhat difficult, depending on your school.

@Fomite yes this is in the US.

To make this first meeting effective, here are some considerations.

Identify the players on the faculty and administration side--people who might be at the meeting and others at the school.

If your institution has first-gen resources for undergrads or other
diversity resources, the people in charge of those could help your
effort, and may be invited to the meeting.
If your school (overall institution or your grad school) has a history of visible conflict
around any kind of diversity, faculty and administration may reflect
that history. Some might be resentful, while others may have learned
and aim to be especially supportive.
Faculty will not show up unless
they care about this issue and/or want to curry favor with the
administrators organizing it. They are likely to be good allies,
though with limited time to devote.

Continue recruiting other students.

Initial interest will shape everyone's perceptions.
You will want to be able to transition leadership and not have everything depend on you forever. Even at the beginning, it's best if other students can share responsibility so you don't take away too much time from your studies.
Accept allies wholeheartedly, but try to make sure they listen more than they talk. (The burden of organizing first-gen resources shouldn't just fall on first-gen students, if possible.)
Instead of a survey before the meeting, I'd suggest a Facebook group or just an email. Spread the word about the lunch (free lunch!) and you can ask people to join the Facebook group or sign a Google doc or something if they're willing to share their first-gen status and give any thoughts of what they'd like to see.

This would accomplish similar things to a survey, while being more informal and building connections for future organizing.
The school probably has better resources to do a systematic survey, and they may even have some stats from the admissions process. If they turn out to be helpful, the administration will be able to do this part very easily.

I have read studies on first-gen college students and talked with colleagues who do research here. As you probably already know, navigating college is harder for people whose families can't provide specific knowledge. You may want to ask your institution for the following resources to address this.

It can continue facilitating interactions between faculty and first-gen students, like this lunch. This can lead to informal mentoring and just more experience of faculty and first-gen students being familiar with each other.

Some of my professors were first-gen, and they would be great to have there.
Other profs may benefit from "practice." I remember at a conference dinner, when a professor asked a student, "Where do you summer?" The student replied, "Most summers I try to visit my family in Detroit." HUGE social class gap that they interacted nicely around, and hopefully the professor learned not to presume or to use "summer" as a verb.

The National Center for Faculty Development and Diversity is a fantastic resource for US universities that your school could subscribe to.

I believe the model is that the institution signs up EVERY faculty member (and/or postdoc, and/or grad student) as having access. Many resources are about demystifying tenure, doing productive research, and other things addressed here on SE. :)
Often, this fills knowledge gaps that students have for a variety of reasons, but that first-gen students (and others) often systematically have.
Politically and logistically, I find that to be an ingenious model, especially as it doesn't require anyone to create a boundary about what "counts" as first-gen or argue that they did not grow up with their educated parent, or that their parents are unfamiliar with the U.S. system of education, etc.)

I'd be interested in reading about what specific difficulties first-gen students find in the US: could you please share some titles of those studies? I come from a generation when virtually everybody was a first-gen student in my country (in my family, among twenty close relatives, only one uncle had a Master's degree, most of the others didn't even have a high-school diploma), but I cannot recall specific difficulties related to this.

There is so much research coming out but here are a few starting points: 1) http://pnpi.org/first-generation-students/ 2) https://alumni.berkeley.edu/california-magazine/spring-2015-dropouts-and-drop-ins/struggle-be-first-first-gen-students-may-be 3) http://www.pellinstitute.org/publications-Moving_Beyond_Access_2008.shtml

This is the most useful paper but it is very long: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2500832
In my own words, I would say that being first gen, specifically low income, in the US is a major cultural obstacle. Just one point is that today -- and I know you mention that you might be from an earlier generation, and I believe things are different now -- there are very few first gen low income students in competitive schools and it becomes very isolating (https://publicservice.fas.harvard.edu/news/what-it-be-poor-ivy-league-school)

@Jazzie3 Thank you for the links, I'll have a look!

@MassimoOrtolano There are also many universities in the U.S. where it is fairly common for people to be first-gen, and professors there may (ideally) discuss more about how what to focus on in college, rather than presuming everyone knows. But in (many) graduate schools and in elite colleges, there is more presumption that students know how to navigate the system, and there are more social and cultural challenges.

Also, parent education, class, and race/ethnicity often intertwine but also act separately. To complement @Jazzie3's great links, here is heftier background. No Longer Separate, Not Yet Equal: thorough, largely statistical book on race and class in elite colleges,  https://press.princeton.edu/titles/9072.html. Paying for the Party: ethnographic book that follows students at a large state school http://www.hup.harvard.edu/catalog.php?isbn=9780674088023&content=reviews Stanford Center for Poverty and Inequality hosts recent research: https://inequality.stanford.edu/cpi-research/area/education

@MassimoOrtolano - When everybody is in the same boat, nobody is facing the problems alone.  But if you were one of just a handful of students with no family with an academic background, then you'd stick out.

We (and indeed you) clearly cannot read the minds of those who have called the meeting, however I'd like to suggest a third option:
Someone in the administration is definitely trying to do something, but because universities are large and cumbersome organizations, change takes time.
The best things you can do are heading to that meeting prepared (which you appear to have done) and with an open mind. Assume the intent is to have a productive meeting, but also one that likely won't have a great deal of actionable things come out of it. First meetings rarely do. Express that you've got ideas, and are willing to work with them. And find out who the people are who you should be talking to - if the meeting does seem like it's sincere, try to finish by identifying at the very least who you should talk to about "next steps".
In terms of leverage? Almost none. But that doesn't mean you can't get things done - university administrators are human beings, and they too care about things. For example, at my university, the problems of first generation students are taken quite seriously and we still struggle at times.

We cannot divine the university's intent, or what the committee you're meeting with is capable of, at this point in time. But it's great that the university is being proactive in wanting to hear the concerns of your interest group. Act on your own initiative. Distribute that survey yourself, before the meeting is held, and find out what people who share your background want to tell the university. Act as their representative and read off some of their comments. The university will be happy to have an official representative, and maybe you can have your needs met as well.


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Is there an academic\ethical reason for omitting place names in environmental science papers?
I hope this is the right SE site for this question. To be clear, I am not asking anything about the contents of the paper, but on the practice of omitting certain information that I thought should be included for completeness and clarity.
I have been reading a paper titled: "Spatial and temporal occurrence of pharmaceuticals and illicit drugs in the aqueous environment and during wastewater treatment: New developments", which deals with measurements of drugs' concentrations in river water in the UK.
I was surprised to see no mention of the name of the river anywhere in the paper or the supplementary material. This seems on purpose, since the authors describe the river's properties that are relevant for the study, but neglect to mention which river was it.
Could it be related to some academic practice I am not aware of, or perhaps is it a safety measure to prevent mass panic among the residents of the area?

Fascinating question.  It's probably not too hard to identify the river in question (there's a drawing of it, it's in Yorkshire, and they give the population of the area).  My best guess is that they only got permission from Yorkshire Water for some access by agreeing not to explicitly name the river so as not to attract news coverage.  But it's weird to me that such an agreement wouldn't be mentioned somewhere.

I can think of a few reasons for which it might be sensible for names to be withheld, usually relating to not attracting large numbers of the public to a place. For example, a rare bird's nesting site, an endangered seal's haul-out area, or other places of delicate ecology.
However, it would seem reasonable for the authors to make the location known to other researchers on request, as otherwise there is no way to verify or reproduce their findings.

I can't speak directly for environmental science, but that sort of thing is common practice in education papers. Institutions and individuals are given anonymous identifiers, eg student A.
One reason for this is ethical considerations. An ethics approval form will ask about all potential harm that could arise as a result of the study. Reputational harm is one form of harm.


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Why do even prominent institutions hire publishing houses (Springer / Elsevier etc.) for their journals?
The Institution of Engineers (India) is a prestigious organisation with more than one million members in 15 engineering disciplines in 114 centers or chapters in India and overseas.
Yet, it doesn't prefer to publish its journals itself. All of its journals are published by Springer. This concerns me slightly because it helps in maintaining the monopoly that publishing houses have on research publications.
Why do even such large and reputed institutions not choose to publish on their own?

It's not trivial to run a journal. You need so many things:

A journal management system
A desk editor to constantly keep in contact with the editorial board, answer author queries, etc
A content editor familiar with the subject matter to identify topics for invited reviews, perform editorial screening, etc
A typesetter who can set every manuscript, no matter what format it's written in (Word, LaTeX, etc) into the journal's style
A copyeditor and proofreader to check the paper's English
A marketing executive to promote the journal, e.g. by finding related conferences and getting insertions
An epub executive to handle the journal's website, epub files and distribution, deal with copyright infringement, and so on
A sales executive to handle subscriptions, payments, and customer service
An artist to design the journal cover, its promotional materials, and so on
Someone to liaise with printers to print hardcopies of the journal, and then get them delivered to conferences / subscribers

Note this list covers a wide range of skills. It's unlikely a single person can do all of them without extensive training. But publishers already have people who specialize in all of these. By engaging Springer / Elsevier etc to handle their journal, the Institution of Engineers saves themselves the trouble of having to learn how to publish a journal. In this, it's not that different from trusting one's university's IT technicians to keep the IT network up and running. One could learn how to maintain a network and do-it-yourself, but why not just leave it to the professionals.


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What is included in Springer 'Accesses'?
What kind of accesses are included in the Springer 'Accesses' number?
Opening the Abstract Page / Opening Full Text HTML / Downloading Full Text PDF / Opening Full Text SharedIt Link

According to the Springer website:

Access counts - The number of times an article has been accessed on SpringerOpen or BioMed Central and SpringerLink.


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Does Springer publish conference proceedings for free?
Does Springer publish conference proceedings for free?
It does seem very unlikely given the significant amount of work they do to publish the proceedings.
However, I have spent hours reading through their website, but there is no mention of any fee.
Could the experienced experts guide me please?

Are you asking about potential (or lack of) fees for authors or fees for readers?

@Buffy I am asking about lack of fees for authors and editors.

In general, they publish for free, unless the Open Access option is used (either by the editors of a proceedings volume or by the authors of one particular paper in a proceedings volume).
Their business model relies on subscriptions and (probably to a lesser extent) sales of volumes and individual articles: Universities pay plenty of money for subscriptions, so that they have access to the published volumes. For researchers that publish in Springer, that typically even includes the access to the published versions of their own articles.

Slight clarification:  the answer is no.  Someone is always paying.

@AnonymousPhysicist Someone is paying, but not for the act of publishing. The payment is for the act of accessing the published material.


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Is it ethical for a professor to ask students to pretend to be gay
My professor is requiring students to pretend to be a closeted LGBT student for a day/or to perform actions that are “trans”. It’s worth 10% of the grade.
Edit: I’m queer and in my opinion this trivializes queer students and also creates unsafe situations for them
Edit for context: the assignment was not  discussed. Not voluntary. The course is “religion in modern culture” and in the religion department.

This question needs more context. What is the course about, in which field is this, has the assignment been discussed with the students in advance and is participation voluntary, etc.?

Not discussed. Not voluntary. The course is “religion in modern culture” and in the religion department.

Are you supposed to imagine yourself as if you were gay and then write about a hypothetical experience? Are you required to go to a gay bar? Pick up a gay date?

How would a closeted LGBT student be distinguishable from a heterosexual one? Sounds like the easiest 10% ever.

So would getting students / people to spend a day in a wheelchair be an issue - so they start to consider the issues?

I think this is a really interesting question and not BS, but as it is it’s missing a lot of context and information so I voted to close as “unclear what you’re asking”. Can you please edit it to add more details? To give a meaningful answer, at minimum we’d need to know what precisely the professor is requiring the students to do. It would also help to understand your objection - how does the assignment “trivialize queer students” and in what way does it create unsafe situations for them? I’m asking to try to help and not to sound dismissive of you or your concerns.

@Najib the fact that the prof can't know the students did the assignment honestly without following them around all day long is true for almost any homework assignment, so I don't understand how you see this as evidence that the question is made up. As I said, the question is missing important details, but you have a very poor basis on which to accuse OP of being a troll, so I'd say you are being a bit rude here. (Also, if the question were well-written, would it really matter if the scenario was real or not? Wouldn't you rather discuss an interesting made up question than a boring real one?)

I'm guessing the idea is to teach mostly straight cisgender students about everyday LGBT experiences, going beyond an academic "we learned about this in class" understanding to an "I experienced genuine fear from simply walking down the street" understanding.  Basically, it's to develop empathy.

... this trivializes queer students and also creates unsafe situations for them.

The idea is probably to make the students feel unsafe: all the students.  And afterwards pose the question "if this level of safety is unacceptable for you (even for just a day), why is it acceptable for LGBT people?"
I get that it trivializes queer students by boiling their identities down to superficial acts.  It's also a bit weird that there's an implicit assumption that there are no LGBT students in the class.  But no assignment is perfect.
Is it ethical?
It's kind of edgy.
There would be valid religious objections to this assignment.  However, I find it hard to believe that a professor of religion is unprepared for this possibility.
It is possible a student could get attacked or arrested while conducting this assignment.  At the same time, this is the point: this "safety risk" is "everyday life" for LGBT people.
However, there's ways to "play it safe" by conducting the assignment from home (and it wouldn't be too dissimilar from the LGBT people who experience anxiety at a level where they are afraid to leave the house).  E.g. present yourself as an "identified" gender, and post an anonymized picture of yourself to a transgender website and see what they say (I used to do this when I was closeted, so it's an official Transgender Experience™).


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How to write Master's thesis summary for PhD application
I am currently applying for several PhD programs (in mathematics) and for many of them, it is required to write a short (approx. 2 pages; no more than 10.000 characters) summary of my Master's thesis. It should contain the motivations of the thesis and research, the methods used as well as the results obtained in my research.
Now, the application commitee is probably less interested in the precise topic of my research or in the project itself, but I guess that the aim of this writing in my application is more for them to examine my ability of writing and explaining my research to others, as the latter is one of the key abilities a scientist should probably have, in my opinion.
My questions are now the following:
(1) How detailed should such a writing be? In my specific case, I am appliying for a math PhD and many things which I did in my thesis, which lied in the border of math and physics, are very abstract, so it not always easy to explain them in simple, non-technical, terms (and I guess, this applies for most of the projects done in pure mathematics). So, should I aim in writing this text in a more "popular" science way, or should I "confront" them with full technical details (the middle way is, as written above, hardly possible, as the things are kind of abstract).
(2) Should I aim in writing this stuff more formally, or more from a personal point of view? So, should I, for example, write about my personal reasons for chosing this particular problem, or should I more concentrate on the scientific reasons of why this type of questions are interesting?

A thesis I'd have supervised (not in math, admittedly) would have a summary/an abstract in the beginning which could be used just like it is for your purpose. Does your thesis not contain an abstract/a short summary?

Hi, yes my thesis does contain an abstract, but this is rather small (half a page) and really just contains the technical contents and result.... So  its written similar in spirit as an abstract of a paper...

@Snijderfrey I'm not sure that's a good advice in generality. Many job applications I see which contain the abstract of the thesis don't look very convincing - this might just be correlations, but just putting the abstract makes a very un-excited impression. And who wants to hire unexcited students?

Note that your essay will be read by other mathematicians, but most of them won't be in your specialty. An overly detailed presentation, such as you might present to your advisor won't be the best.
You are probably correct that they are looking for a writing sample, so focus on the writing at least as much as the math.
A personal view of "why" you chose this path is probably not the right focus, though a sentence might be fine.
First, though, what is the most important result in your thesis? It might be a theorem, but it might also be an interesting (thought provoking) proof technique. Talk about that result primarily, and situate it within the mathematical literature. Talk about why it is an important result. If possible, talk about what it might lead to, though you may not yet be sophisticated enough to understand that.
If the work gave you any special "insights" into the wider world of your specialty (or math in general) include a few words about that. Is there follow up research that is indicated?
As to the level, think about how you would explain the thesis to a good upper level undergraduate class. I'm guessing that such a level might be the best, of course, but all of your readers (various mathematicians) would be able to understand it.
The details are in the thesis, of course, and the committee will probably have access to that as well, so a higher level (or lower level, if you like) presentation is probably enough.

Thanks a lot! Yes indeed, I also uploaded the full thesis in the application.

I join this answer to ask If it could be a good idea to write the MSc thesis summary in the form of a scientific article. Consider the following template provided by springer as a possible example: https://www.overleaf.com/latex/templates/springer-conference-proceedings-template-updated-2022-01-12/wcvbtmwtykqj

Make it in 3 parts

Synopsis: This is what you have written at the start of your Master's
thesis.
Brief description of your work: Describe what (and how) you did in
your Master's project.
Results: What new goals you achieved in your work.

The whole language is slightly technical, without many complex formulas and equations.


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PhD-Application: After how many weeks (approximately) is it fine to ask the committee if I didn't receive any decision?
I have applied for a PhD position at a university in UK at the end of January (in time before the deadline, which was also at the end of January). Shortly after, I was invited to an interview, which (in my opinion) went quite well. However, since then I haven't heard anything. So, it is now approximately 12-13 week since I submitted my application and approimately 9-10 weeks since I had my interview. There is also a online system where one can check the application status, but it hasn't changes since I firstly signed up.
This is my first PhD-application, so I have no idea how long it usually takes and I also have no idea about the university system in UK. However, on the homepage of the university they wrote that it usually takes a "few weeks", so I am beginning to worry a little bit.
After how much time is it not too impolite to write an email to the admission comitee? At their homepage, they wrote that one should not ask questions like "How long does it take?" or "Do you have already a decision?", which I of course totally understand, but at some point I think I should ask in order to check if nothing went wrong with my application...

I think it would be very appropriate to send a follow up email directly to your potential advisor at the University after this amount of time.  In my experience Professors and admission committees are often extremely busy and it is not unusual for these admission decisions and processes to take multiple months before being finalized. In my experience a politely worded follow up email has never been poorly received and often serves as a good reminder to the admission committee that you are an eager and interested applicant. I would avoid being pushy or frustrated about how long the decision process has been taking and instead use the follow up email as an opportunity to remind the committee of your interests and skills and update them on any new accomplishments, projects, publications, or courses you have been part of since you applied.
I recommend sending a polite inquiry to the primary professor you are hoping to be working with. I would keep the follow up email fairly short. Reiterate your interest in the position, ask if they need any additional information from you, and attach any updates you have like new publications or revised versions of your CV that might be relevant.
I have always found that consistent and polite communication with potential advisors is an important part of the process of finding a good fit between yourself and a supervisor. If you do find that your follow up email is poorly received or if you don't hear back from your potential supervisor it's probably a good sign that this wouldn't be a good fit for you in the long run.  When selecting a PhD position it's important that you enjoy working with your advisors and feel comfortable communicating with them or it will make your PhD experience very long and uncomfortable overall.
Additionally, I think a follow up email restating your interests is advisable even if they have already filled the position as you never know when another unexpected opportunity might pop up.  Often times you will not be selected for a position you originally apply on but a Professor may recommend you contact someone else in the department who has an interesting project or opportunity that is a better fit.
Overall, I think a follow up email is an excellent idea at this point, you never know what might come of it!  Good luck!

There has been plenty of time, actually, assuming the deadlines for application has passed.
It is appropriate now to ask for an update on your application. You can also ask if there is anything more you need to provide.
But you might also consider waiting unless there is a reason for wanting an answer beyond anxiety. If there are other offers you need to consider or planning for attendance, then you have a need to know.


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Applying for twice the same supervisors via different calls
I am in the following situation:

I have officially applied to some PhD position of some research institution (its for math and no research proposal was needed; so I didn't apply for any specific and pre-defined topic). This research institution is not a university, but rather an external institute for research, which has close collaborations with the university in the same town. Within the application, one had two specify his preferred supervisors and hence, I have chosen two Profs, in which works I am interested a lot, working at that university.
Let me mention: Unfortunately, I have never been in touch with these Profs. I wrote an email to them before applying, but they never answered, since they are quite busy. Hence, I just decided to officially apply for the call in order to see what happens.
Now, I have seen that another call was published very recently (approx. one month after the deadline for the application above). This call is NOT from the same research institution, but rather it runs jointly between two universities including the university from the two Profs mentioned above. Now, it happens that the two profs mentioned above are exactly associated to one of these universities and are also listed as possible supervisors. (again, the application is without a proposal, however, the research area is already specified as opposed to the application above, where I literally only applied for math and just wrote my interests and research experience in the statement of purpose.)

Is it appropriate to apply for this position too?

Let me stree again: I do NOT ask for applying for twice the same position at the same university but with different projects, because clearly, I know that this is not really allowed. These are two completely different calls, from different institutions and with a different application procedure. It just happens that my two preferred supervisors are involved in both programs.

Is it appropriate to apply for this position too?

Yes.


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Can I work on open-source projects while being a part of an academic institution?
I'm working on a software framework with the goal of creating something that is open-source, so that the scientific community can use, understand and improve it freely.
However, a little birdie told me that universities have rights to all the work we do as researchers.
How can I develop and distribute the software on a collaboration site and at the same time make sure that the university does not have rights (making it proprietary)?

Optional question -
What about the projects that are owned by other institutions, and I modify it (by making some changes to their source code) and push it to the main repository. Will my university insist on partial rights to this software if I worked on it?

The first question you ask is a good one, but the one in your last paragraph seems off-topic here: it has nothing to do with academia; it's a general question about contributing to an open source project. I suggest you restrict yourself to the first part.

Whether you can contribute to open source projects as a faculty member, staff member, or student at a university and how this might effected by your use of university computers, office space, and other facilities depends on the policies of that particular university.  Have you entered into any agreements (either by explicitly signing them or by enrolling subject to the university rules) about "intellectual property"?

Yes, it is very possible to work on open-source projects in academic settings.  The exact legal and technical details vary from university to university, but many universities are very open to open-source contribution.
There are a lot of variables that you don't specify in your question. I am most familiar with U.S. universities, so my answer will focus on those.
Short version: work with your adviser to discuss it with your Office of Technology Transfer.
In most U.S. universities, the university owns rights to code that is created as a part of sponsored projects or with their resources. The following easily trigger it:

Using the computer provided by your university
Being funded on a research grant
Being funded by the university

Often, work done entirely on your own time on your own computer equipment, sufficently unrelated to your paid work that it cannot be considered part of it, is yours without any problem. Coursework is also often yours, although using university equipment may muddy that point. The exact details depend on university policies.
Your university policies will contain information about the precise rules. However, there is often a fair amount of difference between how the policies are written and how they are implemented in practice. I have been affiliated with 3 universities, and at all of them have had no problems obtaining suitable permission for open-source software release.
The relevant office is generally the Office of Technology Transfer or something like that. You should start by talking with your adviser - they will start the Tech Transfer discussion - but there is a good chance that your adviser will not actually know the detailed rules of your university. In practice, there's a lot of open-source code released without going through the proper channels for official university sign-off.
Some universities officially vest faculty with the authority to authorize open-source release of software developed under their supervision.  If that is the case, then the conversation is very short.
In other cases, tech transfer will need to approve to have everything be formally legal. It is possible that they will not fully understand what is going on - I've seen cases where the relevant authority didn't really understand software copyrights and open-source licensing.  My current institution's tech transfer office takes the perspective that their job is to help faculty achieve their goals with technology licensing and commercialization, and has worked with me to get university counsel to sign off on a couple of standard open-source licenses, making subsequent releases very easy.
Unfortunately, most universities' formal policies for invention disclosure and review do not interact well with the realities of open-source software, particularly continuous development in the open.  You'll need to work with university officials to navigate that.
I have generally found university officials to be receptive to my argument that open-source release is a cornerstone of my approach to disseminating the results of my research and promoting reproducible research in my field.


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Is it possible to publish without adviser?
I participated in an exchange programme as a PhD student for 1 year in another country. The very moment I got in the new institution I signed a contract according to which I have no intellectual nor material rights over the results obtained on the territory of the lab I joined.
The subject of my study has changed on the go so after the first 4 months I started different analysis compared to the one written in my project (project funded by academic exchange program).
After going back to my home country my local adviser asked me for the results I have. I refused to submit because I am not the owner and because I found out my adviser is sharing my work with another student for money. Almost 3 years later and after repeating some of the results in my home country I managed to defend successfully.
However I would like to publish my research from my exchange programme. The issue is this:

My foreign adviser is not responding quick enough to my messages - it took him 4 years to revise part of the paper. And I am planning on writing another two!!!
My foreign  adviser retired.
Apparently my both advisers made some sort of a deal to hand over my work to the student I described above.

What is your advise in that situation?

The response to this depends to a degree on the type of institution you were studying at and the norms for that educational system.
In most countries now the norm would be for the Graduate School to have the final say on matters like this. Particularly if the advisor(s) involved are retired (or remaining as semi-retired adjuncts).
Given your OS research was on exchange, the Graduate School at the host institution would typically defer to that in the home country on matters like this.
If the agreement you signed appears to be binding they may discourage you from publishing. If not, I expect they would encourage you to publish. They may even recommend this irrespective of the opinion or the status of the advisor, but that would depend on the culture (and politics) of your home institution.
Graduate Schools often have expertise on these kinds of issues as IP issues are common in collaborative projects. Broadly speaking, most Graduate Schools want their PhD candidates and graduates to be publishing. It's a good look for them and its what they are there to support you to do.
My advice would also to be raise the apparent sharing of your work as a separate issue. Not that I'm saying don't raise it - but if your goal is to be able to publish the results of your research then aim to sort that out as a separate issue.
I would then consider if you think that the sharing of findings with other students looks like the kind of academic misconduct that is defined by your institution and if so consider raising this as a separate matter. I would handle the prospect of academic misconduct with care if you are thinking of raising this.


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What are the consequences of mistakenly publishing existing research?
**I'm asking this in the context of mathematical research if that changes the answer.
I've heard stories on Quora and from my professors about instances where researchers were banned from journals and, in some cases, thrown out of their universities for plagiarizing research. It did seem that their plagiarism was blatant, but the explanations weren't too specific.
I was wondering, with the number of papers that exist today and the number of journals they can be published to, it seems almost impossible to definitively know whether research already exists.
With all the work that's been published in any one field, is it the sole responsibility of the researcher to make sure their paper does not exist in any journal? And if they're unable to find prior proof of their work, will the consequences be so severe? It seems like two people stumbling across the same idea is not an uncommon occurrence. I think the most popular instance of this is between Leibniz and Newton. So, at second glance it doesn't seem feasible to discipline every researcher who manages to mistakingly publish existing work. But I'd like to know for sure. Am I right? And what would the consequences be?

One would need a very long answer expanding that of @astronat (plus one) as there are many possible circumstances and nuances. Being considered a bit sloppy (at least at that specific work) should be the most likely outcome. Plagiarism is something else, and if spotted, is usually clear.

"is it the sole responsibility of the researcher to make sure their paper does not exist in any journal" How would your paper exist in a journal already if you did not submit it there? Or do you mean if you simply weren't the first to publish on some aspect of the field but thought you were?

I'll note that you can't accidentally plagiarize. It is an act of will. You can accidentally work in parallel with others or fail to know everything, but plagiarism is different. Failure to know what you should know is sloppy, perhaps, but not evil.

Working on the same problem isn't plagiarism. If you publish your own work it's not plagiarism. If you publish someone else's work under your name it's plagiarism, but you can't do that mistakenly!

@user253751: But people who notice similarities can easily claim it's plagiarism.  Lots of examples, like Newton & Leibniz, Darwin & Wallace...

Did you really mean to Ask "What are the consequences of mistakenly publishing an apparent duplicate of existing research?" In that case, you would prolly need to apologize, at worst.

@jamesqf are people seriously accusing Newton and Leibniz of plagiarism?

Related: Is there such a thing as fraud in mathematics?

@user253751: I don't know how common the actual word is, but I've seen quite a few arguments about who came up with the idea first.  E.g. Darwin presenting his theory early because he'd received a letter from Wallace discussing the same basic idea.

FYI: “Mistakenly”, not “mistakingly”

I partially disagree with the answer given by astronat, since I think it does not reflect how common it is in mathematics to rediscover existing results (and to publish them without knowing that they already exist). So here is a somewhat different perspective:
Terminology.
What the OP calls mistakingly publishing existing research is, in my experience, more commonly and with a less negative connotation, referred to as rediscovery of existing research.
Distinction from plagiarism.
This point has already been explained in astronat's answer: independently rediscovering a result (and publishing it without knowing about its former existence) is something completely different from plagiarism.
Consequences.
What will happen if you publish a result which is already in the literature but you have not been aware of?
Nothing.
The math departments of this world would be empty halls if every mathematics professor who has unconsciously published a theorem or idea that already existed in the literature was banned from the university. (See the point "Prevalence" below.)
Of course, if this happens very often to you, this might have a negative impact on your reputation; but it happens to almost everybody now and then, so there is not much reason to worry in case that it does happen to you. (Unless in very, very obvious situations - if, for instance, I claimed to be a functional analyst and then published a "novel" result which turns out to simply be the Hahn-Banach theorem, chances are that I would have a much harder time to be taken seriously from now own. But this really refers to extreme cases only.)
Prevalence.
This is one of the points where I disagree with the assessment in astronat's answer. Experience shows that results are rediscovered and re-published (without the authors knowing or citing the earlier occurrance(s) of the result) all the time.
I could write a lengthy list of examples where this happened in papers I read or to people I know or to myself. But there are much better sources for this claim than my personal experience.
Just to get an impression, see for instance these two MathOverflow posts (post 1, post 2) or this blog post by Terry Tao.
Some reasons why this happens.

In earlier days, mathematical results could not be distributed as quickly as they are now (in particular, due to the internet).

Even today, access to many results is somewhat restricted, for instance if they are published in somewhat obscure journals (or, say, proceedings of small conferences) which are hardly accessible, or if they are published in languages which are not widely spoken.

While we have the internet and search engines available nowadays, the amount of published mathematical literature has also become much larger than only a few decades ago, which makes it literally impossible to know everything that could be relevant to your work.

Moreover, search engines are only useful if you know the right key words to search (which is often not the case due to varying terminological conventions).

There a many different ways to phrase or describe a mathematical result (and every more so for a mathematical idea). So even if our idea / argument / theorem is essentially present in a paper and even if we have a close look at this paper, it can sometimes be very hard to recognize it there. Since there are numerous papers which we ought to take a look at before we publish a result, there is simply no way to read all related papers in depth, and we will probably spend more time reading those papers which are obviously very closely related to our work. So if a similar idea occurs in a related, but not closely related paper, and if it is worded quite differently from how we would phrase it, there is a considerable chance that we just miss it.

Many ideas are so fundamental that they occur in many different fields of mathematics (and in many different forms). Our knowledge of a particular mathematical field will typically depend monotonically on how close the field is to our own field. So if a similar idea or result occurs in another area, it is quite likely that we are unaware of it. (The fact that different mathematical areas often use quite different terminology and notation for the same thing doesn't make it easier.)

In my experience, people tend to publish a lot of research work, while it is less common to write expository work (to some extent, this is certainly due to incentives imposed by typical career options in academia). For instance, I can think of various mathematical topics where, in my opinion, a comphrehensive survey article or an up-to-date monograph is missing. This is part of the problem since well-written surveys and books are an excellent aid in identifying relevant earlier results.

Some points to be aware of.

While results or arguments or ideas are often re-discovered, it happens more rarely that two papers have very similar content. Quite often, while some results in a paper might already be in the literature (but unknown to the author), there will be other results or insights in the paper that are still new. This is closely related to the point about novelty that user2768 made in their answer.

Even if some results in two papers are very similar, it will sometimes (though not always) happen that their proofs are quite different.

What to do?
That's a difficult question, and the answer that any particular mathematician gives to this might depend very much on their personality. Here are a few suggestions (biased by my own point of view, of course):

Obviously, we should carefully study the literature before we publish something. Citation databases (in mathematics these are, in particular MathSciNet und zbMATH) can be very helpful for this.

The more work we put into putting our results into context, the more we help potential readers of our paper to also become familiar with earlier research and results on the topic. For instance, there is a considerable difference between merely citing papers and explaining, if only briefly, the relevance of these papers. For instance, compare the following to ways to cite relevant literature:
-- "Recently, there has bee a lot of work on this topic [1, 3, 9, 10, 12, 15, 21, 23, 24, 25, 31, 36]"
-- "Interest in the topic abc originally stems from the study of xyz spaces, because their geometric properties can be classified by abc [9, 10, 36]. Later, abc has been extended to a more abstract setting in [1, 3, 21, 23] which made it possible to also classify the geometry of xyz' spaces [24, 25]. In the present paper, we build on the so-called fgh approach to abc recently developped in [12, 15]; combining it with the, at first glance unrelated, ijk technique from operator theory published in [4], we show that all major results in abc theory are actually independent of the foo assumption. This allows us to classify the geometric properties of very large classes of xyz* spaces. In addition, we obtain recent results from [31] as special cases of our general theory."

When writing a referee's report about a paper, we should take much care to point out missing references. In particular, I strongly support the idea that, as a referee, we should point to relevant articles by different authors, and not only to our own (obviously super-important but - heaven knows why - completely underappreciated) work which might not have been cited in the paper under review.

If we have made a preprint publicly available, and - before publication - we get aware you relevant literature that we have missed, we should, of course, make a serious effort to include it in the paper before publication.

If it is too late and you get aware of relevant references after publication, don't rack your brains over it. As explained above, this happens very often. Just make sure to properly include your newly gained knowledge when you write another article on a related topic (of course, this does not only mean to cite the references you now became aware of; it also means to take these references as a starting point for yet another literature search).

It is, in my experience, very uncommon to take any formal actions (such as notifying the journal, or even submitting an erratum) if you become aware of prior relevant work after publication. (But please note that I don't make any assessment as to whether I approve or disapprove of this practice; I'm just pointing out what is common practice.)

@Espresso: For what it's worth, I've encountered many rediscoveries in mathematics. A good example is described in the first two paragraphs of IV. MOST C-INFINITY FUNCTIONS ARE NOWHERE ANALYTIC in this 9 May 2002 sci.math post, where I discuss the apparently independent rediscoveries of the same result made by Morgenstern (1954), Christensen (1972), Darst (1973), and Ramsamujh (1991). See also my comments to this answer.

On the reputation end of things, my impression is that it mostly depends on how much your colleagues think you "should" have known about the prior result. Knowing the literature is one of the core skills of researchers, and the fact that you didn't find the paper reflects, therefore, on your competence as a researcher. - How good a researcher would you have needed to be to find the prior article? Each of your colleagues will have an opinion, and will likely conclude your skill level is thus somewhere below that level.

@R.M. Indeed. And a great deal of potential blame can be deflected by writing a convincing account of how much effort was produced in looking for antecedents.

If my mathematics paper mistakenly duplicates existing results, and I submit it to a math journal, it is hoped that the referee will know that it is not new and point that out.
The following sometimes happens, though.  A physicist (or other scientist) finds a mathematical result, and submits it to a physics journal.  The referee for the physics journal does not realize that it is already known in mathematics.  So the physics journal publishes it.1
There was an infamous example in 1994 where a medical journal published something, but it turned out that actually it was what is called the "trapezoidal rule" in calculus texts.

1 Why a physics journal would publish a pure math result is another question

I think I once submitted what I thought was a new proof of a result in algebraic geometry and the referee simply told me that it was a known proof, there was no issue.

Authors and their reviewers are responsible for research novelty. Authors must distinguish their research from existing works, and reviewers should be convinced by claims of novelty.
Authors and reviewers sometimes miss existing works that limit novelty. Ultimately, some novelty will likely remain, since two distinct works will likely have solved a problem differently. Consequently, research impact will likely be reduced. I'm unaware of broader consequences (except in cases of plagiarism).

I'm restating, in greater brevity, what other answers have expressed somewhat circuitously.

I've heard stories... where researchers were banned from journals and,
in some cases, thrown out of their universities for plagiarizing
research... It seems like two people stumbling across the same idea is
not an uncommon occurrence.

These are two distinct situations.
Plagiarism is taking the actual written words of another person and re-presenting them, fraudulently, as your own piece of writing. It is among the highest violations in academia and publishing, and well worth harsh sanctions. It's basically impossible to do by accident.
Multiple discovery is when two or more people independently discover the same principle, and separately write up different accounts of it. This is moderately common in science, and it's indeed possible without any fraud involved. It is passingly common that Nobel awards need to take this into account, possibly giving the award to multiple simultaneous discoverers.
Now, if someone re-discovers and tries to publish an idea that was first discovered and published some time ago, the person who tries to do so will look rather foolish and appear to be a poor researcher for not having found that in their literature review -- and be highly unlikely to get published. But this is not the same as plagiarism, and no further sanctions are due in this case.

While I like your very concise summary of the distinction between plagiarism and multiple discovery, I am a bit baffled by your last paragraph. As pointed out in my answer, trying to publish an idea which is already in the literature, but which the author overlooked there, happens even to the most famous mathematicians. (And actually getting it published is not at all "unlikely", but happens very often.) I have never experienced that anybody to whom this happened was considered "rather foolish" or "a poor researcher" (except for really extreme cases).

@JochenGlueck I don't have a lot of experience in these matters but I'll note that I once saw a paper written by possibly the best mathematician alive today that published a result that had been published prior to his paper, and I doubt he was ridiculed, so I think you're probably right.


text:
ACM in-text citations for specific locations in a lengthy referenced work?
I'm using the ACM citation style format for my paper.  In the text of that paper, I wish to cite particular passages in a 50-page reference, so the reader will not have to wade through the entire thing just to find the relevant material.  How does that work?  For example, would the following be proper?

We could, of course, compute its value to at least five decimal places, using Algorithm 3.1 on page 39 of [1].

(Several paragraphs later:)

From Definition 2.1 on page 12 of [1], a foo-representable thingy is a thingy that can be exactly represented by a Foo of finite length.

Or should each location have its own entry in the bibliography?

There is a comment at http://bogost.com/writing/blog/why_i_hate_acm_format/ by I. Bogost (from June 21, 2013) stating that it would be [1, p. 12], but I do not find an authoritative source on that.


text:
How to compensate students who face technical issues in online exams
I am teaching a college level course, and a few students had technical issues during exam 1 (held online) and where not able to complete various parts of the exam.  One option that I could think of is to use their grade from a future exam (also held online) as their exam 1 grade. Designing another complete exam 1 is not an option in our case.
But I am wondering if there are better alternatives.... could you share your experiences regarding dealing with such issues?

Arbitrarily choosing another assignment to count for double credit doesn't seem like a great choice - it can give an advantage/disadvantage if that other assignment is any easier/harder than the one that was missed. Simply not including Exam 1 in the scoring for students that missed it is probably more fair.

Is this a course where grades must be on a curve?

What I have been doing this year, depending on the class, is to either allow the students who have technical problems to take a makeup exam in another day on the part they couldn't complete, or to compensate with an additional question at the oral exam.
From your question, I'd either integrate the missing parts with an oral discussion, if oral exams are acceptable in your country or university, or with a written test with a few questions around the missing parts without redesigning the whole exam though.

I guess this answer won't be popular, but my strong suggestion is that you rethink student evaluation from the start. Exams aren't the only way that you can assess student learning and they are a poor way, in any case, to assess real competence in a field like CS. Add in all of the ways to creatively cheat on online exams and it quickly becomes a near impossible task to validate results.
Some ideas, but I don't have a comprehensive list:
Assess in smaller units more frequently so that "high risk" isn't a factor.
Make the grading scheme somewhat forgiving, so that a few bad answers don't have a large effect on grades.
Take "time to finish" out of the equation as much as possible to account for technical glitches.
Lessen the importance of "question - answer" grading in favor of things like projects that require deeper and more comprehensive knowledge.
Use questions that don't have trivial answers than can be quickly looked up. Likewise don't reuse questions that might have archived answers.
Lessen the importance of "individual work" at least somewhat. Effective teamwork is an important skill in many fields, including CS.
For some students it may be necessary to provide a communication channel to clear up misunderstandings. But make it global. Everyone should see every question and its answer.
For some student issues it may be necessary to talk to professionals skilled in the various communication difficulties that arise (dyslexia...).

@Roland, their profile suggested that this is their field. But it applies to many fields: Philosophy, say.

All good suggestions but not always practical.

@ZeroTheHero, certainly impractical if you blow them off. Nothing works until you make it work.

I already do a lot of the stuff you suggest but - for instance - it’s not terribly practical to have projects in a class of 75 students.  I have colleagues who chose to go the essay route, but reading 100 5-page essays is overwhelming, and while it cuts down on copying it doesn’t cut down on plagiarism: students just cut-and-paste from the web...

@ZeroTheHero "it’s not terribly practical to have projects in a class of 75 students" My university regularly does projects in classes composed of hundreds of students. My understanding is that one of the tricks to making it work is to have all the students enroll into tutorials of 20-30 students each, and then getting the tutors do the marking. Additionally, if you make the projects group projects with teams of 5, then 75 students becomes 15 teams, which is a lot easier to mark.

@ZeroTheHero "I have colleagues who chose to go the essay route, but reading 100 5-page essays is overwhelming," Well, that's one reason why you might consider assigning them more practical projects instead. In CS, you might assign them coding assignments, in Engineering you might have them design CAD files for a device, in Science they might need to solve a particular problem using the scientific principles they've studied, etc.

@nick012000 Don’t get me wrong: one can mitigate some of the effects.  I do (team) projects as well in smaller classes where each team has a different project, but in a larger setting with  10 teams working on solutions to the restricted 3-body problem you displace the problem to one of plagiarism.  My point is: in larger settings and in more junior classes, there’s a trade-off not there in smaller classes.  Exams remain the compromise solutions for larger classes, and presumably carefully designed final exams - e.g with quasi-randomized questions -  will mitigate some issues.

@nick012000 For Freshmen CS, doing scientific work with papers is too much, coding (projects) should IMHO only be a small part of CS.  For us it's mostly down to small proofs and checking whether the students understood a set of basic concepts.

@ljrk "coding (projects) should IMHO only be a small part of CS." That's how you get university graduates that don't know how to code.

@nick012000 Which is fine by me.  They're academics/scientists, not coders.  Noone is asking a medical researcher to be able to perform surgeries either, or a theoretical physicist to be good at wiring your home.

@ljrk, actually, the OP does seem to be in CS/SE from the profile. So, coding is a necessary skill, needed at a pretty high level for all the other things.

@ljrk If a student is getting an undergraduate computer science degree, they're training to become software engineers and the degree should be focused to provide them with the skills and qualifications to get a job in industry; undergraduate degrees in general should be focused on giving students the skills needed to get jobs in their fields upon graduating. They're not academics or scientists, and they're not training to become academics or scientists until they start a research degree like a PhD.

@nick012000 I find that absurd, being academic is not a "more trained" engineer, that is, you shouldn't first need to become an engineer to become an academic. These are simply different branches of equally worth paths to go along. That's why there's Computer Science, Computer Engineering and Information Technology, or B.Sc., B.Eng. and B.A. degrees. It doesn't make sense to see an academic as a more highly qualified version of an engineer. (but that's already rather offtopic here, I just wanted to note that programming tasks are not always the right thing to do)

@ljrk "That's why there's Computer Science, Computer Engineering and Information Technology, or B.Sc., B.Eng. and B.A. degrees." I don't see the difference between these that you're emphasizing; they're basically just different names for the same thing, unless "computer engineering" is supposed to be an actual Engineering degree about designing physical computer components, rather than an IT degree about programming them.

@nick012000 One is academic, with the goal of research, IT gives you almost craftsman like skills, and engineers are the middle ground, system design etc.  The IT student needs to be skillful programmer commonly used languages, while the academic focuses on more general concepts.  These are different branches, just like a MD is different from a medical researcher, and shares only basic skills. The latter aren't just "better qualified" MDs, they pursue a different degree. It's simply absurd, to think of an academic CS as someone who continued after becoming an engineer. But this is all OT.

Thank you for your answer. I agree with many of the points you raised. Unfortunately sometimes we need to follow specific rules of a college.

@nick012000 If you see "Computer Science, Computer Engineering and Information Technology" as all roughly synonymous, then I suggest you re-examine these fields.  They loosely overlap, but... that's it.  Software Engineering is also a degree students can pursue.  Computer Science is the most mathematical of these fields.  The fact that more universities traditionally offer CS than CE, SE, or IT is a result of the history of these fields and how they developed, and that situation is slowly changing.  You couldn't get a degree in SE 30 years ago at all.

@BenI. Not "roughly synonymous", entirely synonymous. Literally just different names for the exact same thing: three or four years spent learning how to code computer programs (again, unless "computer engineering" is about designing hardware rather than software - "software engineering" is also entirely synonymous with the other three).

@nick012000 I don't know what to say to that. There's no benefit to conflating these fields. Programmers get computers to do things. Computer Science has been about the underlying science and maths of automatic computation since the coin was termed.  You need almost no understanding of the underlying mathematics to do the former, and virtually no ability as a programmer to do the latter. Plenty of middle school kids can create phone apps but can't talk about NP-hard, and I'd venture that most mathematicians who expand complexity theory can't code up a simple web app with a linked database.

@BenI., note that some universities do, actually, use different terms for the same thing. Some "Software Engineering" programs are really CS, even though the meaning is quite different. Some of this is just historical accident. But I agree, that at base, the fields themselves are very distinct.

@BenI. The purpose of a university is to teach students the skills they need to find work after they graduate; that's why students go to university. Do you think employers care about NP Hard? No, they care about coders who can produce good code - so that's what the university should care about teaching.

@nick012000, that is a very limited view of the mission of a university. The CS degree is not a coding school.

@nick012000 I don't think I could disagree more strongly.  You're not the first, nor will you be the last, to say that about the purpose of education, but I find that view to border on morally repugnant. I don't think we're going to reach any agreement here if you begin from that premise, so at this point I'm just going to wish you the best of luck in your future endeavors, and a good and meaningful life.

@BenI. And I find failing to equip students for their future careers equally morally repugnant.

My philosophy is that the vote is my best statistical estimate of the student's preparation on the whole of the course's contents, based on what I can evaluate during the exam. If I taught 30 topics during the course and I ask 3 of them during the exam, then I can assume their answers reflect their preparation also on the other 27 topics. There is an error bar, of course, but that's unavoidable, given the limited time I can put in for each student.
So, if you have more tests, you are good; just skip Exam 1 (EDIT: I mean, ignore it just for the students that could not complete it; students who have a full set of grades should still be evaluated on all of them) and renormalize the outcomes of the further exams. The error bars will be larger, but this is unavoidable.

By this logic, there's no point in having two exams at all--just ask one question at the end of the term and score everyone pass/fail! Less pithy: This response ignores the time dependency between scores and the possibility that one exam is harder than the other, and it doesn't provide students with a uniform incentive to try to do better on the second exam or learn from their mistakes on the first.

@Max The point of having two exams is that error bars are shorter. Choosing how many questions to ask and how many exams to make is always a tradeoff between effort and grading accuracy. Exam difficulty, of course, should be included in my grade estimation. I am not sure I follow you on the incentive thing. Why is it important that they have a uniform incentive? How can I even give the same incentive to an A+ student and an F student? How is this relevant in the context of this question (some students skipped one exam for technical reasons)?

If you throw out exam 1 for the students who missed it and leave it in for the students who didn't, then there is greater variance in the scores of the latter group, and thus their final grades offer less indication of their knowledge of the subject than the other students'. If you throw out exam 1 for everyone, then a student who does worse on exam 2 can justifiably claim they weren't graded according to this syllabus.

Not to mention that if you show the students that having technical issues negates the score entirely, then the dominant strategy for a student who did well on exam 1 is to claim to encounter technical issues on exam 2. And you probably do not want to be in the position of having to judge subjectively which claims of technical issues are valid or not.

@Max The last argument is a good point. I was assuming that we know exactly what happened in these technical issues, but this may not be true. (Again, if you see the exams as a statistical test, this makes sense: the fact that the students affected by the problems are a random sample independent from their score is a hidden assumption).

"Variance" is a synonym of "error bars", essentially, so we are saying the same thing. Given the technical issues, I do not feel compelled to follow the syllabus, since those rules have already been broken for external circumstances and I don't think they can be recovered since OP states that a makeup exam is not possible.

What I'm saying is that if the situation necessitates violating the grading policy on the syllabus, you should take care to ensure that it gives students the same grade or better as they would have had according to the original policy (to the extent possible). Otherwise you are just asking for grade disputes. If you got an A on exam 1, a B- on exam 2, and a B- in the class, it would be justifiable to be upset, no?

I am advocating skipping exam 1 just for the students that don't have a valid grade on it; maybe this was not clear from my answer so I'll edit it.

I agree that that policy is marginally better, but it still has the unequal variances problem. An A average over two exams is a stronger indication of understanding than an A average over one exam, but this distinction won't be reflected on students' transcripts. And you have to take care to ensure that if exam 2 is harder/easier than exam 1, then the students who only took exam 2 don't get unfairly penalized/rewarded.

@Max Unequal variances are not a dealbreaker under my philosophy. Anyhow, every solution to this problem is going to increase variances (unequally) or increase effort; if you have a different tradeoff to suggest, feel free to add your answer.

"Unequal variances are not a dealbreaker"
So you are fine with someone receiving a mark of 5+-0.01, and another student receiving a mark of 4.5+-0.75 ?
Please put this at the header of the answer. It makes clear that you are not interested in giving equal examination.

@EarlGrey It is already written in my answer: "The error bars will be larger, but this is unavoidable". I don't think it belongs in the header.

Fair marking requires by definition a common error bar. Ignoring that, you are implicitly saying that you are giving markings for the same course, for the same students, with two different methods.
This is not fair, by definition.
I still think your answer is helpful, it helps focusing on the correct definition of mark/grades, thanks!

@EarlGrey There are unequal conditions here: some students completed an exam, some couldn't due to technical issues, and the exam cannot be repeated due to practical constraints. Discussing 'fairness' for spherical students in a vacuum won't help us here.

Your claim about spherical student it's absurd, especially coming from someone in STEM.
Here we have real students, that deserve fair grading. Technical issues may hamper the variance (error bar, if you like) on their marks. You propose a solution based on the assumption that variance in marking is not important (talking about spherical students...) which is very helpful, in remarking that variance is important in markings.

Grade the complete exams, for everyone, then remove all the "various parts of the exam" that could not be completed for everyone, give marks again, pick the higher mark for each student.
It's the only fair thing you can do, given the conditions.