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Why don't graduate math texts have solutions to their exercises?
I study mathematics and sometimes I have seen book that contains problems but not their solutions. Why are there no solutions available anywhere?
For example, the books I have read are:

Neukirch: Algebraic number theory,
Lang: Algebra,
Liu: Algebraic geometry and arithmetic curves.

Would you please tell us what level of mathematics you are studying?

This question might be more appropriate at Mathematics Educators Stack Exchange.

I'm really not sure why this is closed, and have voted to reopen. Just because it would be on-topic elsewhere doesn't make it off-topic here.

I second the reopening and wish to add that so far the answers are relevant for other disciplines as well.

Re-opened. If something is on-topic both here and elsewhere, it should stay here... being on-topic elsewhere is not a reason to close here.

One point that may help you is that some professors or blogs will post their solution (often correct) online. One example is crazyproject.wordpress.com which focuses on solutions to Dummit and Foote. A Google search will often point you in the right direction for the more popular books.

For graduate-level math books, the answer is typically not a value but a complete proof---typically of a related but relatively uninteresting topic.  For example, one of the first exercises in the Neukirch book you reference is:

Show that the ring Z[i] cannot be ordered.

For such problems, the proof itself is typically much less educational than the process of struggling with the concepts in order to produce said proof.
By the time that students are taking graduate-level mathematical courses, they are expected to have already mastered the general skills of constructing proofs.  Seeing how somebody else has proved a point is thus not expected to be particularly educational, whereas struggling to prove something oneself forces a student to engage deeply with the material at hand.
Finally, examples of working with the concepts in the exercises are typically already given in the chapter, in the proofs of the main results, so adding extra examples by working proofs for the exercises would typically be of only incremental benefit, but undermine the value of students having to work through the proofs themselves.

Writing a graduate math textbook is a large effort that usually takes several years. The author typically has a vision of what material he/she wants to cover. After writing all the chapters and polishing everything, the exercises are probably the last part he/she works on. They are often meant as a pointer to additional more advanced topics in the literature that expand on the main content of the chapter, and adding solutions could require an effort comparable to writing an entirely new chapter (or several) to present that material in a polished, readable form. So, by that point the author feels that he/she is ready to move on to new projects and in any case the community is best served by releasing the book without exercise solutions. Solutions are sometimes added in later editions if the book is successful and the author is still passionate about the project.
Source: personal experience as a textbook author.
Edit: Another thought that occurs to me is that adding exercise solutions can substantially increase the book's size. If the book is already of a good length (say 300 pages or more) then doing this could make the publisher very unhappy, and could potentially make the book less appealing to readers, who would start being intimidated/turned off by the book's length.
TL;DR: Real Artists Ship; Less Is More.

"the exercises are probably the last part he/she works on" Really? I think most authors would probably collect them over all the years of writing the text. Coming up with a good exercise on a subject is only moderately easier than remembering a joke when prompted to, and if I were to write a book this is the one thing that I would certainly not procrastinate on. (That said, I fully agree with the rest of the answer.)

@darijgrinberg yes, well, I was thinking of my own experience but it may very well not generalize to that of others. Also by "works on" I meant "brings to a presentable format", i.e., I certainly wrote up working versions of various exercises long before the end, but they were the last things I worked on cleaning up and polishing. In any case that remark was not an essential part of my answer.

It is widely believed that there should be no solutions available, even privately, since this somehow ruins the game. This presumes that there should be "exercises" of the traditional sort in advanced mathematics courses, which is already partly dubious, since (as is often visible in commercially successful texts) it leads to make-work exercises often of questionable interest. I'd agree that there do exist significant, meaningful questions that may not fit into a small book... but would argue that then good write-ups of their solutions/resolutions should be available somewhere as models. Otherwise, all the students ever see is their peers' solutions... which in principle could be fine, but, observably, in practice, often overlook (through misunderstanding) ideas (from the text or otherwise) that make the resolution far more graceful and persuasive. That is, without good solutions, the only models anyone ever sees are "iffy".
(E.g., my abstract algebra text originally aimed to work a large fraction of the traditional significant questions as "examples", exactly to overcome the inertia of traditional-not-so-good alleged solutions of them, and have no "exercises" whatsoever. However, the publisher, who'd already made surprising concessions about intellectual property stuff, really-really wanted "exercises". So I made some near-clones of the worked exercises... And I've received several comments that I'm an anarchist for making those good solutions public!)
So, indeed, I think it's a bad idea to try somehow to suppress "good solutions". People will still grasp at bad solutions, and will be learning deficient versions of things to the extent they learn anything.
By the way, it is certainly not the case that the standard graduate mathematics texts provide means to resolve all their exercises. Often there is a considerable disjunction. Typically, the disjunction is that the theorems in the chapters do not at all suggest any quasi-algorithmic devices for doing computations in any particular case. E.g., abstract Galois theory usually disregards Lagrange resolvents, so does not hint at how to solve equations even when they can be proven solvable by radicals...
Nor is it the case that beginning math grad students are adepts at writing... so there is considerable feedback among them of marginal write-up style, marginal technical viewpoint, too much attention to secondary and tertiary details (often strictly demanded by in-my-opinion misguided texts or instructors), and needlessly distorted ambient language. Good writing models would help people "get over" this.

It is widely believed that there should be no solutions available. Really? I'd argue it is just as "widely believed" that having solutions is just great. E.g., Richard Stanley's Enumerative Combinatorics and Donald Knuth's The Art of Computer Programming, surely among the most successful graduate-level math textbooks out there, both have solutions. As another example, my own book was criticized for not having solutions in a review of it published in MAA Reviews.

@DanRomik, I myself would agree that there should be "solutions", or, really, "worked examples", but out of dozens of often-used higher-level textbooks, very few have any reasonable "solutions". Atiyah-MacDonald? Lang's books? Any book on "analysis"? It may be that an MAA reviewer is more in tune with pedagogical reality than some...

I didn't say it is widely believed there should be solutions, only that it is good to have them. Indeed most books don't include them, but I suspect it's not because of some taboo or a negative view of their worth (although who knows, maybe some authors really think that way) but more for the reasons I speculated on in my answer. Certainly those reasons applied to my own experience.

Some years later, to reiterate, and to ping @DanRomik yet-again: I've been told maaaaaany times, lo' these intervening years, by my colleagues, and by other faculty, that it somehow "ruins things" to put good discussions/solutions of iconic/significant examples/exercises on-line. The most hilarious is "well, if you explain to them how to do things, then they'll learn it, and be able to do it!" ... um, and, wait, why is that bad?

One possible reason is that the author foresees that students will be using the book as a textbook, with professors assigning homework questions from it.
Thus, they omit solutions from it.
Another equally possible reason is the lack of space (printing limited by number of pages).
Yet another possible reason is it takes too much time/effort on  the part of the author. (Edit: changed the adjective)

It's a commercial decision driven by the wishes of professors (who assign textbooks).  Not having the answers makes them more important.  I know of one author who wrote a very well regarded textbook with all the answers and had to remove them in second edition because his publisher said it wasn't selling as well.
Note that textbooks from 100 years ago commonly had all the answers ESPECIALLY in college level math.  So we have actually become less liberal, more restrictive over time.
I recommend people consult Schaum's, Kahn Academy, or look for books like Stroud or Granville that contain all the answers.  It very much helps self study or even directed study (since the major learning comes NOT from the professor, but from working problems on your own).

Your comment seems more relevant to undergraduate textbooks. The question asked here is about graduate level mathematics textbook which have very different commercial and intellectual priorities


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Should there be a theorem or proposition that uses lemma?
I was thinking the following: suppose that one writes an article or lecture notes where he or she uses some lemma. I have understood that every lemma should be used somewhere in the document. But is it enough if I use some lemma in an example, or should there be a theorem or proposition that uses that particular lemma?

You'd have better luck at mathstackexchange:
http://math.stackexchange.com/

Welcome to Academia SE. I am somewhat puzzled by the motivation of your question. Why would any sane person impose such a restriction? And even if somebody would, you could just rebrand your lemma and call it theorem.

@Wrzlprmft: Surely there is no such restriction; I think the question is just asking for style advice.

I've had lectures where things were given exactly one of four labels: Definition, Theorem, Corollary, Example.  Some people don't use lemma.  Some that do don't use Proposition; and that goes for virtually any combination of names.

But is it enough if I use some lemma in an example, or should there be a theorem or proposition that uses that particular lemma?

I don't think it really matters.  An example would be fine for most readers, while a few really formal people might disapprove.  However, even someone who disapproves wouldn't consider this seriously problematic.  I.e., they wouldn't think less of you or negatively evaluate your paper because of this.  The worst case scenario is that someone complains about it in a referee report, and even then you wouldn't have to follow their advice.

The typical convention that I have seen is for a lemma to be a theorem that is only of interest as an "intermediate" result on the way to another theorem.  Well-organized presentations thus often use the lemma/theorem distinction to highlight which results are most significant within the material.
There are, however, exceptions to this typical practice.  For example, Urysohn's Lemma is an important result in topology that is nonetheless referred to as a lemma.  I suspect that such examples typically appear for historical reasons (i.e., the result was originally presented as a lemma but turned out to be more important than the associated theorem), though I do not know for certain.

The Yoneda Lemma is another example of an extremely important, powerful, and ubiquitous result that goes by a humble name.  Accordding to the wikipedia page "The Yoneda lemma was introduced but not proved in a 1954 paper by Nobuo Yoneda. Yoshiki Kinoshita stated in 1996 that the term "Yoneda lemma" was coined by Saunders Mac Lane following an interview he had with Yoneda."

As far as I understand, a lemma is a mathematical statement that does not have an aesthetic value of its own, and exists only to serve a technical role in proofs of other more interesting statements. The usage of a lemma need not appear in the same document, or in the form of a theorem. For example, it would make total sense for a paper to say "the main result of this paper is a lemma that we think would be useful for proving some fancy theorems in the future. However we still don't know how to use the lemma, and reserve the fancy theorems for future work"...
The question you should ask yourself is whether this is a technical statement that has no internal beauty but can be very useful for other proofs. If this is the case, you can call it a Lemma. However if it is aesthetic and/or unravels some deep truth, it should be a theorem (if its proof is long or complicated) or a proposition (if its proof is short and elegant).

I don't think any paper actually would say that, though.  Mathematicians still have to "sell" their work--to convince referees and editors that their paper should be published.  If the name of one of the authors sells the paper on its own, that may be warranted, but for most people I think it's in their own best interest to describe their main results as "Theorem", even if they're convinced it's just some dinky little lemma-class step on a way to something "actually interesting" (and a lot of us think that about or results no matter what!).  +1 because this is the "role" of "lemma" I learned.

The usage I'm familiar with is opposite to the one you describe. To me, a "lemma" is a result of central importance—a strong branch on the tree of math that supports many twigs, leaves, and flowers. Lemmas can be beautiful: Bézout's lemma, Burnside's lemma, Schur's lemma, the Yoneda lemma, and the Borel–Cantelli lemma are some of the prettiest results I know. On the other hand, lemmas don't have to be beautiful: I admit that I find Euclid's lemma and the tube lemma somewhat mundane, though extremely useful. [cont. ...]

[... cont.] A "theorem," by contrast, is just a beautiful result; it doesn't have to have any importance larger than itself. Leaves and flowers are theorems; twigs and branches can be too.

On second thought, Vectornaut is right. A Lemma can be beautiful or just a bunch of technicalities - what defines it is the fact that it supports proving other results.

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Using the title of famous books as titles in presentations
I want to give a presentation in which I want to use the title of famous books as some of the titles of my slides to add some taste to it. Am I allowed to use for example (Great Expectations) in the title of a slide regarding the copyright?

Titles aren't copyrighted. They may be trademarked, but usually aren't. Go for it.

If you are still a student, I would probably stick to a more conservative approach, instead of using pompous titles in your slides.

It sounds like you want to use these titles to help build sort of a humorous narrative.  From a legal and ethical perspective, this is totally fine: you're using only a few words and in a manner that is clearly referencing the original in a transformative manner.
From a practical perspective, however, I would generally advise against this sort of humor in presentations.  The reason is twofold:

This sort of "cute" idea is often distracting from the main narrative.
Different people have different senses of humor, and this is especially true with the extremely diverse cultural range that you are likely to encounter in academia.  Thus, jokes are likely to fall flat with some parts of your audience.

Still, some people can make it work, and if you're a student giving a relatively low-stakes presentation, you should feel free to experiment.

Legally there are no problems. In reality I have seen successful talks including good results, bad results and ugly results, or "Do you feel lucky, punk?". I have also seen such attempts fail pretty badly, especially when the speaker referred to the same joke over and over again.
One rule which I try to follow with jokes that you must always pretend that you did not make a joke or reference.

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If the arXiv had referees, would conventional journal publications still make sense?
In the last decade, more and more researchers read the scientific literature on electronic copies or on printed copies, but not anymore directly from the printed journal.
Nowadays, I think the most important role of journals is therefore only to offer a well-established editorial and refereeing platform.
Anyway, there is a sort of economic loophole. Let me explain.
Research institutions pay both researchers and journals (to have online access and for printed copies) where researchers publish. On the other hand, journals offer a refereeing platform which is based on the unpaid work of referees, which are, again, researchers. Therefore, research institutions pay for all, and journals earn money for the research published. I could be a little naive here, but I think not far from truth.
Therefore, why are journals useful, apart from refereeing?
For instance, imagine that arXiv, or another open-access archive will introduce refereeing and some sort of editorial filtering. In this scenario, will conventional journal publications still make sense?

This is a hypothetical question that asks for pure opinion/guesswork/discussion answers, and as such is probably going to be ruled out of scope for Stack Exchange.

I see your point. I made a small edit. The point is that I really ask why journals are still useful. I used this hypothetical scenario as a counterexample

why are journals useful? Two words: editorial rejection.

Right now the main paid added value of journals is their prestige (which do influence further career possibilities); so there is a mismatch between good things for individual scientists, and for science/society.

If arXiv added peer review and editorial filtering, then it essentially would be PLOS ONE with a $1,350 discount on the publication fee.

but if referees are unpaid and if there is no additional editorial filtering (the arxiv does already filter submissions, although not like, e.g., Nature...), the arxiv would essentially remain open access and with no publication fee. Did I miss something?

PLOS ONE doesn't pay its referees, has similar minimal editorial filtering, and is open access.  The only difference is the publication fee (thus my "$1350 discount" statement).

The arxiv is for physics, mathematics, and quantitative sciences. PLOS ONE is not. That said, what would prevent the arxiv to be open access with refereeing and without publication fee?

@sintetico I'm sorry, but you are simply incorrect about the scope of PLOS ONE: it has no restriction in scope (i.e., the topics it covers are a superset of arXiv topics).  Publication fee is somewhat beside the point: arXiv isn't zero cost, it's just got a different (and currently very lightweight) business model: you're really just haggling over price there. My main point is this: if you gave arXiv peer review and editors, it would be a "conventional journal."

I don't know PLOS ONE actually, because no one in my field (physics) that I know ever published there. The fact that it has no restriction is irrelevant. There are no relevant physics literature on PLOS ONE. The fact that I "haggle" over price is because my question was focused on the economical aspect. You seem to try to answer a different question, not mine.

+1. The answer is simply 'it would be a megajournal'. I suspect these fields find arxiv as a preprint repository more useful than another broad-scope megajournal...

PLOS ONE doesn't accept pure mathematics, but apart from that, it is pretty much a superset of the science (incl. applied mathematics) side of the arXiv

I used to think in a way similar to the question, but I had a meaningful conversation with a prestigious scholar one time in graduate school, who pointed out that I was missing a key purpose of journals: permanent archival.
The arXiv has been around for about 25 years. We have no idea whether the papers on it will be readable in 100 years. But we know that we can read documents on paper from ancient Egypt, and we have every reason to  believe that journals printed on paper and stored in archival libraries can last just as long.
The scholar I spoke with was not particularly worried about refereeing. He was worried about whether his work would still be available in 1000 years. Of course, I didn't ask him if he thought anyone would still be interested in it :)

This is a good point. I haven't thought about this before. However, permanent archival is important, but how many people could be really concerned about this problem?

Journals are actually printed on paper? Regularly? Or just specifically so they can be archived? (in which case there would of course be no reason that an archiving entity should not do the same for everything uploaded to arXiv)

This is a little inaccurate, in the irrelevant sense, first, that it wasn't really "paper" per se, but "papyrus", which had (and necessitated) a different technology... and was (from an archeologist's viewpoint, I gather) notoriously deteriorate-able... so that the Rhind Papyrus was a rare example... The broken clay shards from other places ... who knew? ... have  survived vastly better...

@O. R. Mapper: yes, the vast majority of journals are still printed on paper and mailed to archival libraries. Not all libraries still subscribe to all paper journals, because of cost, but the journals do certainly print on paper. I have a few that arrive in my mailbox each month.

Moreover, if you start with the arXiv, and then have people referee selected papers, and then pay a press to print the ones that are accepted by the referees, and then have libraries archive those printed versions -- well, all you have done is to re-create the journal system we already have!

Oswald, I think that last point is the big one: Curated journals will continue to exist precisely because the service they provide of filtering out stuff that isn't up to standards for clarity, interest, and reproducibility is valuable to many readers -- but those journals may or may not be distributed and archived in new/additional forms. Meanwhile, arXiv and the like will provide a mechanism for unfiltered publication akin to privately published monographs but with wider distribution, perhaps evolving some kind of trustworthy crowdsourced reviewing... or perhaps not.

As a professional mathematician, the main use of the arXiv for me is earlier access to papers that will end up being published in a journal a couple years later. It seems to me that people are just as likely to use their personal webpage or a blog, compared to arxiv, for notes that they don't plan to publish.  I don't need peer review to "filter out" papers for me, I can usually tell quite quickly if the paper is likely to be of interest. Perhaps things are different in other fields.

I don't trust the publishers to do the permanental archiving correctly. For example, if you buy Springer math ebooks from the late 90s and early 2000s you often get scans of the books, not real pdfs. Why is that? I asked one of the authors and he confirmed that Springer had actually lost or intentionally deleted the LaTeX source files that he had given them.

@Thomas Kahle: publishers don't do the archiving: university libraries do, with the hard copies of the journals. There is a general suspicion about using electronic versions of anything for permanent archival.

@OswaldVeblen Hmm, I rather have a general suspicion against non-electronic(!) versions of anything for permanent archival.  Going forward from here, all archiving should be digital with many copies distributed all over the place. Of course the perfect sources should be archived, not the digital -> paper -> digital scan. In case the source is lost (Egyptian manuscripts) a scan is totally fine, of course.

Another issue is paper quality. Because of budget constraints publishers are cutting down there too.  The paper used to print todays journals may be good for 100 years, but probably not much more.

@Thomas Kahle: my sense is that the general consensus in the archival community is the opposite: they trust paper copies, because we know those have the ability to last for thousands of years, and they do not trust electronic copies, because we really have little idea how long they will be readable. Do you have any source for the claim that the paper now being used in print journals is not archival quality?

@OswaldVeblen Sorry I must pass on references for the paper quality. It's just memory that I have read something like this, so it may be wrong. I'm not an expert on library archival, but I'm still surprised about this 'general consensus' (references?). Weird and proprietary formats: granted! But a source code that is UTF-8 or even ASCII encoded, with open language specifications? We will not loose access to that.  The likelihood that the few libraries with the paper copies burn down is higher than that of losing the last copy of a file.

Like most human pursuits, research is not planned top to bottom.  Things evolve in a historical context. The historical context here is that some journals have long histories and publishing in them is prestigious because important work has been published in those journals before (and consequently they can be very picky).  Yes, this argument is a bit cum hoc ergo propter hoc to begin with, but still there is a whole host of consequences following from the reputation of journals.  For example grants, jobs, publications in other journals, and in general evaluation of ones scientific output is measured in terms of which journals one publishes in.
As other people have noted, turning arXiv into a journal would not make journals obsolete, because that alone would not give it the filtering effect.  In my field, mathematics, and maybe also other fields where arXiv usage is widespread, publication in a journal is a stamp of quality that is added to a paper.  It is not publication in the sense that the paper is then public and was not before.
As I wrote in a comment, I don't trust the journals with permanental archiving.  Libraries are probably better with that, but they can't afford the paper versions anymore... so there is a problem (independent of your question).  Another thing is typesetting: If the authors care, then typesetting of the arXiv versions is usually much better than in the journal versions because Springer, Elsevier, etc. have all outsourced typesetting and cut down proofreading.  Typically more errors and oddities are introduced than removed in the final typesetting process.
So to answer your question: If arXiv introduced refereeing, then it would turn into another online only journal with little to no impact to the remaining journal system.  But, its production cost would substantially go up, potentially endangering it.

Your latest argument (introducing refereeing would increase production costs) sounds strange to me. AFAIK, practically all refereeing and editorial work in respectable journals is volunteering (service) and, therefore, cannot impact production costs of a journal. In regard to formatting, with all my positive feelings to arXiv, I wouldn't say that papers there are better formatted than those, published in Springer or Elsevier journals, quite the opposite. Of course, this is more of a function of authors' attention to details & aesthetics rather then journals' formatting requirements.

@AleksandrBlekh Yes, all refereeing is done by the community, but there is still a subtantial cost for maintaining the editorial technology. Ask the people who run diamond open access journals. Usually this is subsidized in the form of Libraries providing the infrastructure. Regarding typesetting: I'm speaking mostly about my own papers. I care a lot about typesetting. Granted, an average arXiv preprint may look worse than the published version.

I understand about typesetting. As for the costs, you are right about editorial technology being a significant, if not the only, cost factor. However, such costs should be similar for both cases (today's arXiv vs. arXiv with editorial functionality), if arXiv would use some of the mature open source academic publishing solutions. For examples, please see my relevant answer.

I have used at least OJS, and it falls behind the commercial solutions. You need staff to run the open systems for journals publishing more than a few papers a year. Also look at the cost of arXiv now, without this whole part. It seems like it's just a website where people upload papers, but the projected cost for 2015 is slightly south of $800,000 according to https://confluence.cornell.edu/download/attachments/127116484/arXiv+Business+Model.pdf

Perhaps, you're right about the issues with limited functionality or not that fancy and elegant UI / UX. I definitely don't have enough experience to argue with that, though, per description, some open source software (OSS) solutions have comparable or, at least, good enough set of features. With that in mind, I'm wondering whether the differences in functionality between commercial and OSS solutions are not essential for editorial and workflow functions, but, rather, reside in the dimension of convenience functions, mostly for editorial staff.

In regard to costs of maintaining arXiv, the amount that your referred to, frankly, does not seem significant to me, considering the fact that we are talking about a global academic portal, covering a large number of fields of study. Even though that amount is not likely to be significant to Cornell University in general, it likely generates some ROI due to excellent exposure of the university's brand worldwide.

Finally, additional step that I think would make much sense in minimizing the effect of costs factor (as well as in enriching the functionality of OSS publishing solutions) is to aggregate efforts and resources of many leading universities (in a form of consortium or foundation, such as edX) toward creating more open and fair avenues of sharing academic results and knowledge. This IMHO is especially true in light of global nature of portals like arXiv and their extensive coverage in terms of disciplines and fields of study.


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Why won't good journals retract papers that were proven wrong?
I saw some research papers still present in good and reputed journals even though they were proven wrong by other papers. The subject is cryptography.
If a paper is proven wrong, it does not contribute a valid result to the corresponding topic. What is the reason for keeping them intact, which can cause issues for newbies?

I mean entirely proven wrong by another paper... @corey979

@corey979 In cryptography I saw such research papers...

If they have been cited, then basically you are advocating ripping apart the basis for understanding and progressing knowledge. That is a horrible thing to contemplate much less actually do.

I don't know what it would mean for a journal to "revoke" a paper.  Did you mean "retract"?

Isaac Newton's book "Principia Mathematica" has been proven wrong by experiments confirming General Relativity. Does that mean it should be removed from the history of science? It might mislead newbies into thinking of gravity as a force.

@NateEldredge Yes, it's pretty clear that OP means "retract" - OP may want to edit it. In any case, JonCuster makes the point and should be expanded to a response - scientific history is not a git repository, you do not wish to rewrite science and need to know where ideas come from (even if they are wrong).

Well, if we're talking about retraction, then I don't understand @JonCuster's point, since retracted papers don't disappear.

@NateEldredge Ok, now I understand your question.

@PatriciaShanahan indeed it is my understanding that all published articles including Einstein's General Relativity will eventually be proven wrong.  It is not a bad thing.  It is the march of progress.

Without knowing the specifics of the papers you are referring to, it's difficult to respond exactly.  In general, however, there is more than one way for a paper to be "wrong", and most "wrong" papers should not be retracted.
The thing is, a paper typically contains more than just a single assertion. When you say that a paper is "proven wrong", it sounds like you are referring to the high-level conclusion, e.g., "Cryptographic protocol X is secure against replay attacks."  Then somebody else comes along and shows that actually, there is a way to do a replay attack after all.
Such a refutation, however, often does not actually invalidate any of the actual technical methods or results presented in the original paper.  Instead, it will more typically involve showing that they were insufficient in some way for supporting the high-level conclusion.  For example, the problem statement might have been formulated too narrowly, or the authors might have drawn a conclusion that was stronger than their evidence actually supported.
In such a case the conclusion of the paper may indeed be wrong, but everything else is indeed correct.  Careful phrasing by the original author may in fact mean that the conclusion is even still technically correct (e.g., "According to this formulation, cryptographic protocol X is secure against replay attacks.").  In short, the results stand but their implications are much less than the original investigator may have believed.
Bottom line: many refutations may be understood as changing our interpretation of results derived using valid methods, while retraction is generally reserved for invalidating flaws in the methods themselves.

+1.  In a sense, a great deal of crypto is all about proving things "wrong."  If we didn't actively propose new ideas and attempt to find flaws, I'd hate to think of the current state.

Think of the history of scientific papers as being something like an informally maintained blockchain. The integrity of all depends on the continued presence of the old things whether they have been superseded or not. Even if they have been superseded for errors. The reason for this is that things get referenced in newer work. The new things may be corrections or may, in fact, rest on a shaky ground. But future researchers need to be able to resurrect all of the contextual history of ideas and their expression so that science can advance without needing to start over whenever something is found wanting.
In fact, if an old paper is made to somehow disappear and a newer one covers the same ground, but correctly, then the newer authors are, arguably subject to claims of plagiarism since they "used" some of the old words and ideas that they weren't able to find by searching the literature. There are likely old versions of the (incorrect) paper cached in various places. Better for the old paper to remain in place so that references to it, especially correcting references, remain valid.
In some fields, having access to old, incorrect, papers can be especially valuable to a student. If the superstars of a field go wrong in proving something important, it is useful to know how they went wrong. That way, similar errors can possibly be avoided in the future. In analysis, for example proofs that contain lots of conditional clauses with quantifiers (for every, there exists, ...) can easily get out of control and hard to follow. Many of these have actually occurred in the literature. It can be fun to find them, and not so easy, in many cases, to correct them.

Exactly. This aids in future research. "Smith (1990) claimed that a hyperparallelized matrix can be shown to be closed in fivespace by applying a transverse coordinate swap to the complex manifold, but Jones (2003) demonstrated that that result only applies in five-spaces with polynomial bases. In this paper, I generalize a proof of how to determine whether a fivespace hyperparallelized matrix is closed..."

Simplest case: Publications by Newton and others. Clearly, at that time ideas of light particles and the Newtonian gravity were right (explained observations at the time) but later on have been shown to be either special cases (GR) or highly insufficient (photons, duality of waves and particles).

In many fields, and probably especially cryptography, the evidence of an incorrect result can be very relevant either:
1) to reduce the effort in a “wrong” or incorrect or less-fruitfull direction,
2) to provide an impetus towards a solution or a solution for another direction or method.

Exactly. There is much more information in "wrong article + article explaining why the previous article was wrong" than in "no article at all".

@EricDuminil Articles that are retracted still are available to read online, they just are noted prominently as retracted. Of course, there's no way of recalling all of the printed versions either. So a retraction would serve to put a "here is what happened" notice on top of the old article.

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


text:
How to Correct for a Less-Than-Complete PhD career when wanting to go into academia?
I want to have a career as a tenure-track research professor. I have a little over a year left in my PhD in a science/mathematical field, and I don't feel I learned enough during graduate school. I know I can (read: have to) finish my thesis in a year because my adviser is the type to just cobble something together and get you out of here (and there is no funding left)! However, I really love science, I love learning, I love reading, and I love thinking! I just feel due to various reasons (adviser putting me on projects that failed after which I had to switch, etc.), I am grossly underprepared!
I have grown intellectually so much since staring my PhD, but when speaking to professors and postdocs at conferences I feel like I can't hold my own. I know part of this is imposter syndrome that I have always struggled with, and part of it is that people can always "talk about" their research and "sound smart" in the short time we're all discussing, but I want to feel like I really understand these topics and that feels like I need more time!
They say "thats what postdocs are for!" but I get the feeling its the exact opposite! Professors hire postdocs to do something well and fast, not really bolster their education or mature as researchers. How can I convince someone to hire me as a postdoc, and allow/help me to "fill in the gaps"?
Note: this question was also posted on quora, but has so far gone unanswered.

"Professors hire postdocs to do something well and fast, not really bolster their education or mature as researchers":  That does not at all match my experience, at least in mathematics.  Professors hire postdocs so as to have someone on-site to work with for a few years, who shares their interests and has enough of the appropriate background to make the collaboration reasonably productive.   It is expected that along the way, they will "bolster their education and mature as researchers". It's not a matter of "here is an assignment, get it done perfectly by yesterday"...

... If they wanted that, they would hire a technician, not a postdoc.

By the way, you might get more directly relevant advice if you can be more specific about your field.

That's great!  That's just how you should feel (1st 2 paragraphs, at least if you're a normal mortal).  It means (i) you're not an arrogant fill-in-your-favorite-anatomical-term-here, and (ii) you're motivated to understand things rather than just get out papers.  This is what a scholar should be.
I felt like there were too many huge gaps in my learning when I was a grad student.  I felt like that when I was a postdoc too.  I felt like that when I was a new tenure track.  I have tenure now, and I still feel that way.  I just learned a lot of basic things over the past year that I can't believe I didn't know 5 years ago.  Part of this is the impostor syndrome, but part of it is just realizing that there there is so much out there to learn.
There is so much out there, and fields are so rich after centuries/millenia of development that you can only learn bits at a time, and you need to find a balance between solving new problems/getting out papers and learning what has already been discovered.  This is true for bigshots as well as littleshots.  Ravi Vakil (an algebraic geometer at Stanford) says the following, quoted from this MSE answer:

...mathematics is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you'll never get anywhere. Instead, you'll have tendrils of knowledge extending far from your comfort zone. Then you can later backfill from these tendrils, and extend your comfort zone; this is much easier to do than learning "forwards".

I was surprised to hear one of my friends, who is a hotshot and always seemed to know everything, once tell me something like: if we weren't expected to do research, we would spend all of our time just learning the beautiful mathematics that was already discovered.
At least in math, any postdoc mentor will expect you to have gaps (otherwise you wouldn't need a postdoc), and most mentors will want to you learn a lot of new things, though it is true that some mentors focus on being productive while learning as little new as possible.  So, instead I think you should focus on finding a mentor who you think you can learn a lot from.  Here are 2 things to look for:

They work on things at least somewhat different from, or at least from a different perspective than, what you/your advisor do.  Then you will be forced to learn more new things working with them.
The professor themself seems to know a lot, so you'll learn a lot just from regular interactions with the professor and their colleagues.  This also indicates they're less likely to be of the philosophy of publishing without learning.

thank you so much for your answer! I can't tell you how comforting it is to hear someone whose made it "all the way" (to tenure and beyond!) admit these feelings too. Too often I feel academics put on a show of dropping vocabulary words and sounding intelligent. I appreciate your honesty and advice!

There are multiple different types of postdocs out there.  Some people are just looking for a warm body to fill a technician job more cheaply.  Other postdocs give a chance for re-skilling or for more exploratory research, and some (especially in non-university research institutes like foundations, national laboratories, and think tanks) are specifically targeted at giving people the freedom and opportunity to develop their own research identity.
So yes: "that's what postdocs are for."  You just have to look for the right types of postdocs.


text:
Should I mail to the journal to request to submit the revised version?
Recently I have got a rejection from a journal in mathematics. But I am sceptical about the journal decision. The reason is that the referee has written a full 1 page report. The first line of the referee report starts with there are several errors in the results. Here are comments and suggestions.
Now when I read the comments and suggestion, the referee clearly pointing every single errors and more importantly, suggesting how to correct those and make it authentic. The referee has given some ideas to include more results based on my existing results. I have never seen such a positive reports, specifically, the positive suggestions to make the paper authentic.
The reports ends with the words here are some more suggestions and then suggesting to rewrite the references and other important issues. This seems the referee is interested in the work.
After reading this report I believe that I can address all those points raised by the referee. The referee nowhere said against the paper, didn't say to reject it either but suggested to make correction. So I want to submit the revised version in that journal.
However, the journal returned the paper without asking revisions. I don't know who was the editor, i got mail from the journal coordinator. It is a good (not top) journal of World scientific publication.
I am much confident about my work and got more confidence after the referee report. Since the referee has given lot of time, I wish to submit the revised version. So my question:

Can I mail to the journal to ask/request to submit the revised version ?

Thanks

Let me start this answer with the following important observation: referees do not decide whether a paper should be accepted for publication, editors do.
It might well be that the based on the report the editor decided that the paper even after the corrections will no meet the standards of the journal. Maybe even the referee communicated such an assessment to the editor in a confidential note.
Let me therefore suggest a different course of action: revise the manuscript based on the referee's suggestions and then submit it to a different journal.

I like your 2nd para. That might have happened

You certainly can, but keep in mind that they rejected your paper, so they're technically not willing to reconsider it even if you improve it.
Still, it's possible they change their minds. So it depends on how much you want to publish with the journal. The worst case scenario is they reject it again, in which case you're wasting time.
In the end it's up to you.

well thanks for your comment. My only doubt is that they did not provide any particular reason for rejection. Just said based on the report, it is being denied publication in this journal. However the referee suggesting how to make the errors correct in the whole report. I still don't know who was the editor because in the online submission status, no editor was assigned/displayed. Otherwise I could have contacted the editor directly to know his/her reason for rejection

@Masmath When you want to contact the editor, you should write to the journal. They will send your communication the editor.

@user151413, thank you for your suggestion

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text:
Timeline pros and cons for applying for grad school in statistics
I am a third-year mathematics major from outside the US and intend to apply for a US or Canadian Phd program in statistics.
The issue I have is that I will be taking measure theory in my 4th year and I hear that this is very relevant to a stat grad program. This means if I were to apply for the Fall intake of 2024, Measure Theory and some other advanced math courses would not appear on my transcript. I could of course wait till Fall 2025, but I would like to start as early as possible.
Do you think the absence of these courses in the transcript I submit will affect my admission chances? (FYI: I have already done all my stat courses in my 1st and 2nd years and have good grades on all of them; I did stat for a minor)
Also, would it help if I took the Math GRE test to make up for missing courses of the 4th year? Thanks in advance. Any other PhD related advice is also most welcome :)

I can't speak for Canada, but in the US it should pose no difficulty. Admission is given based on a broad analysis of the likelihood of success. I realize that things have changed, but when I was a student (previous century), measure theory, even in pure math programs, was a grad level course.
I suggest you apply for the start date you prefer. If your transcript predicts success, irrespective of individual courses, and you have good letters of recommendation then you should be fine.
And you might have it mentioned somewhere what your final year courses are, perhaps in a letter of recommendation or a section in your CV.
There is no real reason to delay. Every student is in the same situation because of the lag between application for grad school and graduation from undergraduate. Just. Do. It.

Measure theory is a graduate level course, and in my opinion it should always be a graduate level course. Learning it at an early stage might not be so helpful.

I see. Does the Math GRE factor into the admission decision at all? Would a statistics admission committee be impressed by a high math GRE or is it just down to a good GPA, recommendations (in my case, from pure math professors) and SOP?

Some places use GRE and some don't. A good score will be "a positive" if it is used at all.

A small addition on my transcript. Since I will not have finished my program by the time I apply, my transcript will read "incomplete". Would a scan of this still be acceptable to an admissions committee? On a related note, do I need to have a physical copy of my "complete" transcript in hand when I get enrolled at the PhD program? How else would they verify that I have actually completed my degree?

Missing a few relevant courses should not be a problem as long as you meet the prerequisite requirements. You can also take measure theory at graduate school as well or learn it yourself.
Statistics graduate programs could range from relevant to extremely irrelevant to measure theory. It is helpful for some areas such as stochastic processes, but for many, probably you will never touch measure theory, and it is fine.
Many (applied) statistics professors I know who have done a great job as a researcher only use human language to understand statistics, and some of them have never learnt measure theory before.
In my opinion, measure theory is quite a beautiful subject. It will make sense of many concepts you learnt in a measure-theoretic probabily course; however,learning measure theory too early has a (really) big disadvantage. It is possible that after mastering measure theory, it will be harder for you to see the real world the way it is and you somehow will get stuck there for a while.
I wish I could have erased the part of measure theory I learnt temporarily, by the way.


text:
What is a Chartered Scientist/Engineer & how do you become one?
British societies (and commonwealth countries) offer the title of chartered scientist/engineer.

Is it based on my education only or work experiences (and research outcome such as publications)? How do they judge an application?
Do they need a final degree for the process: do they just contact my university to verify the degree or must I have obtained the degree from specific universities (e.g., accredited programs)?
Is this British professional qualification useful outside the commonwealth countries? For instance if applying for a job in US or Germany?

This page might be useful: http://www.ima.org.uk/membership/becoming_chartered.cfm.html

I'm basing my answer on Ireland, where my Brother became a Chartered Engineer.
In relation to the points of your question.

Normally in Ireland you obtain a Bachelors (Hon) degree (up to 2012 now a masters degree) and can become an Associate member of the Engineer Institute. After a period of time, or either further study or in the workplace you may apply to become a Chartered Engineer Regulations here. I know in my brothers case for his application he had to write up any course he took after becoming a member and also any details of any project that he worked on.
It appears a masters degree is needed now but a Bachelors (Hon) degree awarded up to 2012 will be accepted up to 2020. Page 7 of the regulations linked above have details of progression routes available.
There are a number of accords that ensure cross-border recognition of the qualification. Again as an example, my Brother was able to secure a Engineering Job with a European multinational Engineering firm in the UAE within about 6-8 weeks of moving there.

It is possible that the Irish and British systems are similar due to the historical link between the two countries. Unfortunately as per your question I have no information on the term Chartered Scientist.


text:
How to get honorary academic position in UK universities?
To my knowledge, it is common in the UK universities to offer honorary faculty positions to their partners from other universities or outside academia.
Correct me if I'm wrong, these positions are non-salary for the sake of official bonds.
Then, how one can express interest for this kind of positions and official connections? Who is responsible for granting these positions?
AND do other countries have similar positions?

I don't think one "applies" for these posts. It is more of a "Don't call us, we call you" thing.

A number of UK universities have their policies on the appointment of Honorary positions on their websites. It appears from a number of them that the appointments are usually made upon the request from for example, the head of a school, within the institution.
It appears (from the University of St Andrews) that appointments are made when it is deemed to be beneficial to both parties.

An Honorary appointment is an arrangement which allows distinguished individuals from other institutions and organisations to collaborate with academic staff at the University of St Andrews and have access to certain University facilities to further their own research, cooperate on joint research or contribute to the teaching of the University.  It recognises an ongoing association with the University.

In all of the policies it appears that the Head of School makes that application and it is the HR department that makes the final decision on the granting of the Honorary position.
I relation to gaining a Honorary position, I would think that if you are well known in your field of research there is a better chance of gaining one.
Here is a list of links to policies for the following universities.

University of St Andrews
Swansea University
UCL
Cambridge

In Ireland (my home country) I believe they are occasionally awarded. Trinity College Dublin have Honorary positions in their listing of academic titles

They also exist in Australia, and work in exactly the same way. You might be able to get one by asking a collaborator who is a senior faculty member in good standing at the university.


text:
Using Wikipedia definitions in research paper
I'm writing a research paper in finance. I'm taking help of Wikipedia  definitions for the introduction part. Do I have to mention it in the Appendix part?

By "appendix" I think you mean "bibliography" or "references"?

By "Wikipedia definitions" do you mean wiktionary? Or do you mean definitions given in articles in Wikipedia? It's important as Wiktionary is a secondary source while Wikipedia is a tertiary source.

I would recommend that you do not use Wikipedia definitions---they're good as a starting point for informing yourself, but aren't generally considered reliable enough to be citable literature.
Instead, follow the references provided on the Wikipedia page to back up those definitions, and you should be able to find a more primary-source document that is appropriate to take definitions from and to formally cite.


text:
Are there cases where an accepted paper is retracted for lack of originality?
Following the answers to this question that it is quite common to inadvertently reinvent the wheel in theoretical/computational research, have there been cases where the decision to accept a paper to a journal/conference has been revoked on this ground, because someone found out later that the results were not actually original? In such cases, how would one distinguish between oversight and plagiarism?

By "revoked," I assume that you mean retracted. I have often heard of papers being retracted for plagiarism, but never for reinventing the wheel.
I believe that the reason is, there are so many different ways to invent wheels, that it is almost always possible to tell if an idea is actually an independent invention.  A reinvention will likely use somewhat different terminology, have a different formulation of the problem, use different types of evidence, or whatnot.  There will be so many small differences, that it would be clear that the work is original, in the copyright sense, and not an academic fraud.
The fact that is it a reinvention of an idea that was already discovered elsewhere, however, means that it is likely to sink into obscurity once this fact is discovered... except... sometimes, a reinvention is not just a reinvention.  Sometimes, the reason for a reinvention is that an idea has not reached a community.  In that case, the contribution may not be the reinvention, but the importation of a mature body of work from elsewhere, in which case even a reinvention of a wheel may constitute a legitimate scientific contribution, in the form of bringing together two strands of research that complement one another and allow vital new progress to occur.

The OP doesn't necessarily mean "retracted"; it could be that the paper was accepted, but the editors changed their mind before the paper was actually published. Unlike a retraction, this might not result in them printing a notice.

@NateEldredge I think that would still count as an ordinary rejection, not in the spirit of the question... but perhaps the OP can clarify.

@jakebeal I did mean "retract". Thanks for your answer1

I like the part about bridging disciplines. This happens all the time between math and physics, where obscure mathematical formalisms are employed many years after their development only because some bright mind managed to make the connection to the physical world.

jakebeal answered most of the question just great, but I would like to comment on this a bit more:

how would one distinguish between oversight and plagiarism?

I think this is no big issue in practice. Typically, people start talking about plagiarism if and only if the similarities (text-wise, or, in rarer cases, idea-wise) are so substantial that it would be very unlikely for the author(s) to have arrived at their text without knowing the original. When authors honestly have "just" re-invented the wheel (as it frankly happens all the time in research), it is very unlikely that the end product would be so similar that they get accused of plagiarism.

This may differ from computational work, but the concepts overlap, I think. In experimental science, it is traditionally expected that a published contribution is original, to the extent that you often have to sign a document essentially claiming originality upon submission. However, for numerous reasons (nicely explained by John Ioannidis at http://dx.doi.org/10.1371%2Fjournal.pmed.0020124, and cited 2400+ times!) replication of work is valuable in the sciences. We all have biases and make mistakes. And it is literally impossible to control for everything that may affect the outcomes of your experiments. So doing the same thing someone else has already done is actually a really nice validation of the previous work. It can demonstrate that two (or more) investigators have done the same or similar experiments and (hopefully) arrived at the same conclusions.
The original work will probably remain the exemplar of the phenomenon explained and garner all of the citations. But the "me too" experiment will make everyone who comes after more comfortable that the phenomenon is a real thing and not just a statistical fluke because of the weather on the day of the experiment or someone wearing cologne or forgetting to wash their hands.


text:
Job advertisement: "Liaise professionally"
Australian academic job advertisements often ask for candidates to show they can liaise professionally with people in certain other academic roles.  What sort of experience or achievements are they looking for?

Can you post some precise sample language from such job advertisements? I suspect the reason your question hasn't gotten much attention is the vagueness of "[...] with people in certain other academic roles." Is that literally what's written in the ad?

No, but if the ads were not vague I would not be asking.

If you want us to tell you what they mean, you should at the very least report their words, not just your interpretation.

In short: soft skills, eloquence, and persuasiveness.

This one is pretty easy. The requirement that you've mentioned simply asks for some proof, at least, informal one, that a person is capable to successfully facilitate professional interactions by communicating with people from various subject domains and convert ideas and information between domain "languages". In other words, successfully act as a subject domain translator.
The simplest example of such role from the industry would be a business analyst, which most often requires to translate requirements and other project information between business-focused groups and IT-focused ones. Roles of project / product / program manager are related, though different.
Therefore, to meet such requirement, which is very typical for both academia and industry due to their collaborative nature of work, I would say that listing successful projects (with specifying roles and relevant tasks & achievements of facilitating interdisciplinary cooperation) in a CV is enough.

"We're looking for someone who can communicate and work with these people better than we do."

@keshlam: This might be another way to put it. However, the phrase is focused on relative performance, which, while very important, is not a unique factor in hiring decision making. Plus, it places a candidate in an inconvenient position, as it implies that there is a need to show their superiority in communication and other relevant skills over existing staff, which is often not the case.

After careful consideration, I have decided this does not answer the question.

@AnonymousPhysicist: No problem at all. Of course, you are free to change your mind as you wish. Just keep in mind that IMHO there is a difference between answering a question completely or comprehensively (typically denoted by an accept)) and answering a question partially or adding value for better understanding question and/or potential answers (typically denoted by an upvote).

My guess is that the ads mention this because these universities are trying to get more interdisciplinary work going, and they want to hire people to whom interdisciplinary work comes naturally.  Also, there's the communication thing that keshlam mentioned.
It couldn't hurt to ask one of the departments who mention this in the ad what they meant by that.
Here are some ideas for things that might support this aspect:

Gave a talk about your work to a non-specialized audience
Published a paper with a colleague from a different discipline
(This one is focused on communication, not interdisciplinary research) Served as peer advisor in such-and-so organization
Served on campus-wide advisory committee on such-and-so topic

In short: soft skills, eloquence, and persuasiveness.
Any certification that involves the above should do the trick. Certification might include English communication certificates, multi-linguistic competence. Other achievements could involve experience as a spokesperson, any role of leadership at your previous institution, or your role as a coordinator in an event such as a conference or a symposium.


text:
How to cite simple definitions when writing university papers?
When writing any kind of paper or homework at the university I am supposed to give references for my citations. At the same time, sources like Wikipedia are not considered good for university level. Now let's say I am writing about malware, and I want to give definition about virus. Wikipedia has a good explanation, but I obviously cannot just copy without references (right?), and to give reference to Wikipedia is considered unacceptable.
So how am I supposed to give reference to such an item? Am I supposed to change the sentence in such a way that it cannot be tracked where I took it from?

[...] to give reference to Wikipedia is considered unacceptable. Why?!

For university level it is, because it's considered not reliable source, as regular users can edit articles.

Another nice example how ivory tower rules like "no wiki" makes no sense. Why don't we try Encyclopedia Britannica? ;) But seriously: even for proper academic notions, it is hard to find proper references. I would recommend to properly rephrase it, and google "malware definition": there are cisco, MS, merriam-webster etc   links, they say all the same, pick which is accepted by your prof.

as for the wikipedia issue, there is a whole question about it http://academia.stackexchange.com/questions/19083/are-there-instances-where-citing-wikipedia-is-allowed

@Greg I also think that if the OP thinks wikis are not reliable, why doesn't he refer to more reliable encyclopedias and dictionaries?

If the wikipedia article offers a citation for what you want to use, go to the original source to double-check the information and then cite the original publication.

If your only source for something is Wikipedia, you must cite Wikipedia.  If your instructor tell that citing Wikipedia is unacceptable, what they really mean is that using Wikipedia as your only source is unacceptable.  You're supposed to read and cite primary sources, which Wikipedia is not.  (Neither is Encyclopedia Britannica, @Greg.)

This seems to be an undergrad issue, which is off-topic, here.

Standards for papers and homework is not the same as for publications. Moreover, there is nothing fundamentally right or wrong about a definition as long as you introduce it as such ! (in University words mean what you decide they mean -- within reason, that is). You can definitely write something like

In this paper I will use the definition of a virus as a '...' (1)

and refer to a footnote that says

(1) definition taken from Wikipedia article Virus, retrieved on
  2014-10-04".

Of course if Wikipedia's definition is taken from a printed reference, use the latter.
If you want to be extra-cautious you can have a look at the change log and discussion of the Wikipedia article.

Of course if Wikipedia's definition is taken from a printed reference, use the latter. — Only after reading the printed reference yourself, of course.

Two points to remember:
1) Always give a reference for anything which is not your own! Changing the sentence in such a way that it cannot be tracked is NOT an acceptable substitute.
2) For as long as you are a student, the university sets the rules for what is considered an acceptable source.
Since your university, like many others which I am familiar, does not consider Wikipedia to be an acceptable academic resource, you should not cite Wikipedia in papers/homework. (When writing for an audience other than your professor(s), you be the judge. This question provides a nice overview of the pros and cons of citing Wikipedia.) For the example you've given, the relevant Wikipedia page has many linked references. The usual workaround is to follow those references, find one which contains the definition you need, and cite that reference rather than Wikipedia. Of course, as JeffE noted, be sure you've actually read the source you are citing!

That is not a "workaround"; it is precisely how it is meant to work, even if your university does not explicitly say that, and is why those references exist. If you follow a reference and it matches Wikipedia, cite that; if you cannot find a citation that matches Wikipedia, then you are just reading text by an anonymous stranger, and shouldn't cite it at all.


text:
What are my chances of being accepted in a Ph.D. program with poor M.Sc. grades?
I'm currently studying for a computer science Masters degree in a top UK university and I wish to pursue a career in academia by getting a Ph.D. degree. I got perfect coursework grades, however, I didn't do well in my exams which count for 90% of the total grade in every course. Unfortunately, I'm 90% confirmed that I'll fail one of the courses and even if I resit it I'll only graduate with an overall pass due to the department's regulations related to failed courses. My current thesis supervisor, who also supervised my research course last semester, is very pleased with my work and offered me a Ph.D. position in a newly funded project. However the department's regulations admit only distinction holders, especially students graduating from the same department.
Is there any chance of me being admitted or is it impossible for a "pass" Master holder to continue their studies?

You need to talk with your thesis supervisor to find out whether the department's regulations are "hard" or "soft."  Many departments have clear regulations which are "soft" in the sense that they can have small exceptions made if a professor can make a case for why such an exception should be made.  This is very often the case, and if this is the case for your department and your supervisor wants you as a Ph.D. student, then you are fine.
Sometimes, however, a department will not allow such leniency for its professors.  If this is the case, and your supervisor wants you as a Ph.D. student, then they should also be able to advise you on what to do to try to get yourself into compliance with the regulations.

If your thesis supervisor has offered you a Ph.D position and the project is a newly funded one, then you are very likely to be accepted. I have seen that figure in a couple of top universities in Europe in which what counted more was the acceptance of the professor who will agree to supervise you. The other stuff, e.g. submission of grades and certificates from your M.Sc. is just administrative stuff. Try not to lose that opportunity and start talking with your future supervisor about your research work plan for your Phd studies, and funding (which I suppose you are entitled also for that) in case that you need it.
Good luck!


text:
What is an “academic qualification concept”?
I’m applying for a position in Germany but it requires an "individual qualification concept." I don’t know what this means. The job posting mentions that the "individual qualification concept" should outline "the academic qualification they are aiming for in the context of their work at the [university]."
Is this document meant to address how I meet the prerequisites for the position? Or is this a document where I address which qualifications I hope to obtain by the end of the period of the position, for instance, Juniorprofessor or Professor?
I also emailed the departmental contact for this position to ask about what they expect from a qualification but they’re out of town until next week.
If anyone has ever written one before and can give advice, or if anyone can point me in the direction of any sample essays, that would be very helpful.

You should tells us what exact position you are applying, as currently I have no idea what this individual qualification concept is.

If you translated the word it might be helpful to also post the original German word. Even if the advert you saw is in English there is a good chance a German version exists as well and then the original German word would be useful.

Here is the link to the job posting. I haven’t found the German-language posting yet but if I do, I’ll post it here. https://arthist.net/archive/39390

Here’s the German job listing, which asks for a Qualifizierungskonzept https://stelle.pro/jobposting/2142995631907f99c6ff81ce7d96060c192663a0

What else do you want to know, in addition to the paragraph in the job listing explaining what to do? "Applicants are therefore requested to submit a written application of max. 4 pages (including time schedule) outlining the academic qualification they are aiming for in the context of their work at the Academy of Media Arts. The possibility of a doctorate is given. Applications with a postdoctoral project are welcome."

I’m from the United States and we don’t have an equivalent type of statement. I don’t know if I need to state that “I hope to obtain X position at the Academy during a 6 year period,” or if that would be presumptuous. I can discuss any future book projects and other academic goals, but I don’t know if that counts as a “qualification” I am “aiming for.”

I asked my wife, who is a professor at a Fachhochschule. She says that "Qualifizierung" is a broader concept that just a qualification, it means your plan for academic development not just "will get a PhD". They want you to explain how this role fits into your wider academic career development plans.

Thanks, @JackAidley. That’s definitely helpful to think about it as overall academic development, not just as a “qualification.”


text:
How long should a direct quote be in order to be put in quotation marks?
Let's suppose there is a short definition in a source and that I want to report such definition in a paper but adapting the initial wording to the sentence.
For instance

Definition: a bottle is a container made of an impermeable material that stores and transports liquids.

(this is from Wikipedia by the way, but assume it's copied verbatim from another source, called Source A).
In my paper I want to write

There are multiple containers used for carrying water. For instance, bottles are containers made of an impermeable material that stores and transport liquids. [Source A]

I know I have to cite the source of the definition (Source A) but should I use the quotation marks for direct quotes in this case even if the part "copied and pasted" is extremely short (less than a sentence)? Should I write the following?

There are multiple containers used for carrying water. For instance, bottles are containers "made of an impermeable material that stores and transport liquids." [SourceA]

It seems overly pedantic to me, but I would like to be sure of that to avoid committing plagiarism.

Pedant's note: Bottles can also be used to store and transport solids or gases (and when they are "empty" they are implicitly storing a gas).

Speaking of pedantry, it's worth paying attention to the verb-subject agreement. In the original version, it is the container that stores liquids. In your versions, the implication is that the impermeable material stores liquids, but this makes little sense - the same material in a non-container shape might not keep any liquid inside it.

Tangential issue, but there's a logic error here: the quote doesn't support the claim made. Consider the one-word replacement: "There are multiple containers used for carrying lava. For instance, bottles are containers made of an impermeable material that store and transport liquids." or "There are multiple containers used for housing sharks. For instance, fishbowls are bowls for the keeping of live fish." The fact that bottles can contain certain liquids, does not necessarily imply that they can contain the liquid under discussion. So you'd be better off finding a more specific quote.

@Ben Pedanter's note: Bottles are jars with a curving neck. Jars can be used to transport anything.

It seems overly pedantic to me

It's not overly pedantic. There is an actual difference between the information conveyed by

There are multiple containers used for carrying water. For instance, bottles are containers "made of an impermeable material that stores and transport liquids." [SourceA]

versus

There are multiple containers used for carrying water. For instance, bottles are containers made of an impermeable material that stores and transport liquids. [SourceA]

Both of these formulations tell the reader that you are relying on "SourceA" as the reference for your definition of bottles. But the second one indicates that you have rephrased the definition from SourceA in your own words. The first one indicates that the quoted part comes verbatim from SourceA.
Depending on the context, it may be fine (and even sometimes preferable) to paraphrase the definition in your own words. Wanting to keep the discussion somewhat informal, or wanting to avoid giving an "overly pedantic" vibe, or just plain preferring your own way of saying things to that of the source, are all valid reasons to paraphrase. But as long as you are echoing verbatim the phrasing of the source, you need to indicate that this is a quotation. In formal writing, double quotes are the standard way to do this, but note that there are other ways to indicate quotations, such as the one used here on Stack Exchange:

This is a quote.
      -Abraham Lincoln

"This is a quote." [citation needed].

“This is a quote.” [Dan Romik, personal correspondence] - is that better @Buffy?

Note: single quotes are acceptable for indicating a quotation in British English. ‘I don’t know if this is also true in other varieties of English’ - Neil Tarrant (2024)

@NeilTarrant The problem with using single quotes is that they have a specific function. You use them when you have a quote within a quote. e.g. "Note: single quotes are acceptable for indicating a quotation in British English. ‘I don’t know if this is also true in other varieties of English’"  - Neil Tarrant (2024)

@NeilTarrant For whatever reason, this is the exact opposite of British English.

@MiniRagnarok If the world were logical, Australians would use non-inverted commas. :)

@MiniRagnarok it’s a little more subtle. In British English you can use either single or double quotes, and then alternate for nested quotations.  Double quotes are maybe a little more common as the first level of quotation, but both are acceptable.

There's another difference between your two examples. The second, without quotes, fails to make clear how much of the paragraph is being cited. Is Source A also responsible for the information that there are multiple containers used for carrying water?

I would recommend either rephrasing the entire sentence and leaving it unquoted, or quoting it with a [bracketed] inline edit, as: For instance, bottles are containers "made of an impermeable material that [store] and transport liquids." [SourceA] - otherwise, because "bottles" is plural here but singular in the source, the quote looks like it's talking only about the storage capability of the material, rather than the bottle.

@DewiMorgan good suggestion, I hadn't noticed that issue. This grammatical mismatch could be another valid reason to paraphrase the definition instead of quoting it.

"This" [Oxford dictionary] "is" [Cambridge dictionary] "a" [Abraham Lincoln] "quote" [Dan Romik]

i was embarrassed to be told after my MA exam that my quotation marks were all wrong in my bibliography. Only later did I discover that they were perfectly acceptable in British English, but that the American examiner was apparently unaware of this. (I was in the US, but other varieties of English were perfectly acceptable provided one was consistent and I was using British punctuation and spelling throughout.)

Yes, you should put direct quotations (that are less than 40 words) in quotation marks, even if it is just one word. See the examples on the American Psychological Association website. The direct quotation in quotation marks is just 13 words.
In your case, you are quoting a definition. The site I linked to states "Use direct quotations rather than paraphrasing: when reproducing an exact definition [...], when an author has said something memorably or succinctly, or when you want to respond to exact wording [...]."

I disagree about the "just one word" part.  It's just silly.

I agree with the "just one word" part.  Example ... Freud used the terms "id", "ego" and "superego".

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To reiterate the other answers, the length of the citation is irrelevant -- quotation marks are used to indicate that you got the text (definition, word, phrase, sentence, or paragraph) from somewhere else, and did not put it in your own words.
Thus:

There are multiple containers used for carrying water. For instance, a bottle is "made of an impermeable material that stores and transports liquids." [SourceA]

is correct (slightly modified from yours for clarity), whereas

There are multiple containers used for carrying water. For instance, bottles are containers made of an impermeable material that stores and transports liquids. [Source A]

is incorrect, and finally, something like

There are multiple containers used for carrying water. For instance, bottles can be used to store and transport liquids including water. [Source A]

would also be correct. In the last example, we have reworded to put the definition in context and only kept the part(s) that are actually need for our own point. Of course, we still need the citation as it is the supporting material for this information. Consider which is clearest for your own purposes.

It seems overly pedantic to me

It is! After all, the point of formal writing is to be pedantic about every detail :)

The first example is not correct, because it fundamentally changes and misrepresents the quoted text. In order to make it an adequate quote, “stores and transports” (which you silently changed to “stores and transport”) should be changed to “[store] and [transport]” – or alternatively, the subject should be made singular to match the source (“For instance, a bottle is ‘a container… that stores and transports liquids…’”). As Anyon’s comment to the question says, it’s the bottle that stores and transports liquids, not the impermeable material.

@JanusBahsJacquet Should be fixed now, thanks. (Though as to bottle vs material, IMHO the Wikipedia quote could probably be read either way.)

"the length of the citation is irrelevant" - until you get long enough to use block quotes.  These provide another way of making an exact quote obvious, if done correctly.

Yes, you should put quotation marks around the part you are quoting directly. The amount of text you are quoting is well within the range that you would be expected to mark as a direct quote. Sometimes when adapting the wording of a definition slightly, you will still need to quote it but with the changes marked with square brackets: []
For example:
There are multiple containers used for carrying water. For instance, "[bottles are containers] made of an impermeable material that [store] and transport liquids." [SourceA]
This shows that the "bottles are containers" part is essentially part of the quote, but that you have adapted it slightly to fit the grammar of the sentence. I don't think this is necessary in your example, but can be useful when you are quoting a definition and need to change the tense. As noted in the comments, it gets pretty clunky in this example and you'd probably be better off rephrasing the start of the sentence to be more in line with the original quote, or rephrasing the whole thing.

Should also replace "stores" with [store], here. Better off, at that point, either changing the start of the sentence to be more in line with the original quote, or rephrasing the whole thing.

If you copied the wording verbatim from a specific source, you need to either use quotation marks around the copied text or put it in a block quote. The length of the quote only affects the type of quoting ("inline quotes" for short ones or block quotes for longer ones, specifics varying by style guide).
This may mean you're quoting single words or short phrases, such as when the author is using words in a way unique to their paper. This may also mean that a verbatim phrase in your paper may happen to appear in a source you used but not require quotes because it is very, very generic, to the point that it could appear in any paper on the topic. For example, a phrase like "Shakespeare's last work, The Tempest, was..." is generic enough that multiple authors are likely to come up with it verbatim (and a search suggests they did).
If you're in doubt, paraphrase instead.
Quote formatting (or lack thereof), when done properly, conveys a lot of information about the original text. For example, for MLA that includes:

Original capitalization
Whether or not the beginning of the sentence was quoted
If words were omitted mid-quote
Original verb forms

Some of the examples they give would look more elegant if they put even a single small word (like "an") from the quote outside of the quote marks, but they didn't. (MLA, however, is more extreme in their rules for bracketing than other guides.)

There are three options for you:

Paraphrase. Give the information using your own words. Then there are no quotes and you refer the author of the idea/conclusion. [Citation]
Short direct quote. Copy the text verbatim. Then you need to emphasize the text is not your own by using quotes. As deee said: "Yes, you should put quotation marks around the part you are quoting directly." [dee]
Long direct quotes. Copy the text verbatim. Use different paragraph style to emphasize the difference (usually different margins serve well).

"Yes, you should put quotation marks around the part you are quoting directly."
-[dee]

Note that there is pedantic issue (my novel ideas / others' ideas / others' words verbaim) and aesthetic issue. If you have one two-sentence quote in the whole paper and the rest are few-words quotes, there is no need to introduce the paragraph. On the othe hand, if you have mainly long quotes, I'd put even few words in special paragraph. Just to keep it consistent.
Also note that the special paragraph gives the quote a punch.


text:
I am not getting academic credit for code I have written for my PhD, when it was later used in other research. Should I complain?
During my PhD, I developed a data analysis code. My PI encouraged its development, expecting it to stay within the research group. The code was used in some published papers and gained attention when doing benchmarks for a Huge Science Collaboration (HSC).
As I left academia, I handed over the code to others in the PI's group, notably to X, who placed it in a private git repository. My understanding was that, as a courtesy -- and as I was forced by PI to do with others -- I would be offered authorship on papers using the code, a courtesy I would have declined the first time and would not have expected again, since citing my papers or acknowledging me would suffice. However, despite an agreement for a public release and a science paper using the code led by X that has not been published yet, I was often minimally acknowledged or not mentioned in subsequent papers using the code.
X moved to a new research group and published a paper using the code. Recently, HSC papers have cited only X's paper as the main reference for the code, downplaying my contributions, with the code still being private. After complaining, some corrections were made, but issues persist.
I feel my main scientific contribution, as well as for others who worked on the code, is not being properly credited. And I find unfair that, without a science paper on the code, only X's paper is cited. Am I overreacting? Or in the wrong? What are my possible outcomes?

What is the copyright/authorship blurb in the code? Is there any? For instance, if it were GPL'd, your author name would have to appear in all code derivatives (if I am not mistaken, it's a time ago that I looked at such things).

"My understanding was that, whenever the code were used in a research paper, I would at least be offered authorship of the paper" - this is not a standard for authorship. For papers where you specifically wrote code for that paper, authorship may be reasonable when that entails a substantial intellectual contribution (which it almost always does). Subsequent papers that reuse that code do not earn you authorship, they earn attribution/citation.

Are you certain that the code has not been changed since you left? Or is it possible that you wrote the first version of the code, and others - perhaps even X - have written later versions?

Many have modified the code since I left, including X and myself, with my latest major contribution dated end of 2023 (in my spare time, as I graduated in 2020). This contribution is still in the current (unreleased) version. Yet, of all the people that modified the code, only X has been credited in the latest papers of HSC, which I find unfair (notice that X is listed as one of the authors of the papers, meaning that X could have credited everyone, if they wanted to). I don't want X to be removed from the citations, I'd just wish for other people (including myself) to be credited as well.

that's why you release your code!

In the three years since the group decided to release the code, I did nothing that could block or delay its release, but also I could do nothing to accelerate it. Still, the release hasn't happened yet.

How can you expect a third party (HSC) to credit you if you haven't produced anything citable and X's paper is the next best thing?

First, let me stress that PI and X are both in HSC, so I wouldn't consider it a "third party" per se. There are numerous papers that have been produced that use the code, exactly as X's paper, some of them mine, some other not. And HSC is aware of this. Why cannot those papers be cited along with X's? Why should be X's paper the next best thing? This is what I don't fully get.

What you are describing is a difficult situation, because a couple of written or unwritten rules are in conflict:

Those who made intellectual contributions to a piece of research should get the contribution.
Students or postdoc that are leaving a group should not (and should not be able to) block the scientific work of the rest of the research group.
If you made a building block to be used in scientific work, you get credit for it by being cited - your software being used in some work does not give you the right to demand authorship of the paper.
Writing software is not automatically an intellectual contribution.

Additionally, it looks like the whole issue was not handled very well.
From your question it looks like you never wrote a proper scientific paper on your software. If you had, your scientific paper could just be cited in all papers using your software, and you would not be an author of the papers in which your software is used. Then all rules above would have been satisfied.
Because you never wrote a paper on your software, there is now a conflict. You can't expect to be in the author list of every paper using your software just because it was not public, because that would mean that by not publishing your paper on the software, you get authorship on many papers essentially for free. At the same time, you can't expect your former group to not use your software, because then you would be blocking their work. Most likely you also got funding from the PI (if not, on the legal level, this may be different).
At the same time, it's certainly bad style that your contribution was forgotten in some cases - you should have been mentioned in the acknowledgements. After a few years of not publishing the paper about your software, you shouldn't be surprised to be forgotten, however.
A different issue is that X is still using your software after leaving the PI's group. If you got funding from the PI, then there may be the expectation that your PI has unlimited usage rights of the software, including sub-licensing it to X - which may have implicitly or explicitly happened, especially if X continued to work on it.
Now what are the possible solutions apart from "forget it"?

Ask X if she/he wants to co-author a paper on the software with you. If you don't have enough time to write it completely on your own now, perhaps that is an option?
Publish a short paper on your software, so that you can still find enough time to write it. It doesn't need to explain everything, but enough to be citable. Do so with the knowledge of the PI and X, so that in future papers, they can cite you correctly.

(I'm happy to update my answer if I forgot possibilities).
Note that rules 3 and 4 above may come in minor variations in some fields of research. In computer science, for instance, it is quite common to propose new algorithms that crucially depend on some other existing work — still, the authors of the existing work do not get authorship for the new work. Only if the existing work (which could come implemented in the form of a tool or library) needs to be modified in intellectually non-trivial ways, the authors of the existing work are typically invited to also be authors for the new work. Rule number 4 is addressed by some academic conferences having "tool papers" to allow researchers taking the time to write complex scientific software getting some publication credit for it.

I think this answer more or less covers it - with this being central: "From your question it looks like you never wrote a proper scientific paper on your software. If you had, in all papers using your software, your scientific paper could just be cited, and you would not be an author of the paper in which your software is used."

Thank you, and I apologize if I sounded petty.
It's hard to reply in 500 characters, but I'll try.
Blocking the group's work was never my intention; I handed over the code without any issue and only expected fairness. I mentioned authorship offers, but never intended to accept. My PI always said that asking others for authorship was a courtesy, so I expected the same. I didn't write a paper on the code because the decision to release it happened after I left. I never received funding directly from my PI.
Lastly, being forgotten is not a problem; my efforts being credited to someone else is.

At least conceptually, it does not seem right that you can expect perpetual co-authorship for papers to which you did not contribute in ways other than having developed a code years ago. The right approach to getting credit is getting cited, not being a co-author on work to which you did not concretely contribute.
The way to address this is to write a paper about the software that others can then cite. It should be written by all those who have contributed to the code by now, and since you started the software, it's not unreasonable that you would be first author. Such a paper can be a lot of work, but it doesn't have to be: the Journal of Open Source Software (JOSS) publishes citable papers that require fairly minimal work.

Sadly it was not evident enough in the post, but I would have expected to be asked for authorship the first time as a courtesy, I would have decline it, and then would have never expected it again, exactly as I was force by my PI to do with others on my papers. Writing a paper with the group might be difficult right now, but the problem still remains, that X's paper, including only people not from PI's group, is being cited as the main/only reference of the code, downplaying the contribution of myself and other people in PI's group that worked on the code

X only published a paper that uses the software. What I'm proposing is to write a paper about the software. Check out the papers published in JOSS. They're meant for exactly the kind of case you describe, where there are only papers that discuss certain aspects of the software, and applications, but not the software itself.

I see your point; however, writing a paper about the code with the people that contributed to it means cooperating with PI and X as well. I wouldn't feel comfortable in writing a paper with them now, as I think that they have already misrespected me and all other contributors. They are also authors of the HSC papers, so they could have credited all people involved from the beginning. Instead, they deliberately and repeatedly decided not to do this, Also, even if we decided to write this paper together, it would take time, and more HSC papers might come out, only crediting X's paper.

@Quasark I've got no advice about this. Your choices are (i) to continue to be upset about the issue and not do anything about it other than complain anonymously at a forum such as this, (ii) have a plan to write a paper to address the situation, and then talk to everyone who needs to be involved to put the plan in action. Which option you want to go with is your choice.

Thank you, I will get what you say under serious consideration. It's not easy but, as you say, something must be done.

My career has primarily been in computational physics. I have done seven projects in this field. Four of them have been published and three have not. In all cases, there has been some form of written documentation. For the three that have not been published, to the best of my knowledge, I have not even had an acknowledgment. In all three cases, there has been at least a reasonable reason for this, if not perfect, and I am quite happy that either the work has been used or that I have had the opportunity to learn and add to my credentials. I have had a 15 year career in computational physics, which I love, and am quite proud of this and it has been the true joy of my life. I hope you can enjoy your career so thoroughly too, and be proud that your work has made a difference.
The great news, and what makes me feel a lot better about all of this, is that I have a great CV and resume following all of this, and several documents documenting the work I have done. What you can do, if there is any confusion over what work you did, is describe it on your LinkedIn profile and resume and CV. As others have suggested, you can either publish something on it or write documentation for it. You can document it in the github archive itself, you can make the documentation publicly available somewhere such as a website. Github itself has a website, or maybe your university has one you can edit, or there are some free website services available. Another iffy possibility is that maybe you can write an quasi-formal document and post it somewhere like Research Gate (maybe, depending how unofficial it is-- my unofficial thesis-- unusually extensive general exam document due to transferred classes-- for my third Masters in astrophysics is there). A lot of these options might work even if the code isn't public, depending how vague or clear the documentation is. You may or may not need your former collaborations approval to publish.

Thank you for your really hopeful and reassuring answer! It really helps, when considering the worst case scenario. I have a few things to consider now, but this definitely helps.