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If an author declines authorship, may her co-authors publish without her?
This question was raised in discussion of answers on Is it better to submit a paper to an important journal without the supervisor name or to a less important journal with the supervisor name?  There seemed to be a significant difference of opinion, so I'm asking it here as its own question.  I'll phrase it as a hypothetical.
Suppose that researchers X, Y and Z have collaborated on a project.  Each has made major contributions which were essential to its success, and would ordinarily be entitled to co-authorship on the resulting paper.  However, X decides, for some reason, that she does not wish her name to appear on the paper, but she is willing for Y and Z to publish it under their names alone.
May Y and Z ethically do so?
Of course it seems clear that X must consent to have a paper published with her name on it, and she has the right to withhold that consent.  It's less clear whether Y and Z may publish anyway, effectively claiming credit for X's work, even though she consents to them doing so.  It could be argued in this case that Y and Z may not publish the paper at all.
Another possible concern is that, if X has the right to decline credit for her work, she could be pressured or coerced or bribed into doing so, effectively reducing her to a ghost writer.

whose ethics would be violated in doing so?

@akkkk: Y and Z may be acting unethically by claiming credit for work they did not do.

Simple answer: authored by Y, Z, and Anonymous contributor.  You can publish without their name, make it clear that there was another contributor, and not appear to take credit for work you didn't do.  This is, of course, assuming they're declining coauthorship because they don't want their name associated with the paper rather than some reason where you can give a name, but just not put them as coauthor.

@akkkk: e.g. in hiring or promotion committee, it might happen than a paper with one less coauthors looks better, giving Y and Z an advantage over other applicants that would not be deserved.

I'm puzzled. Obviously one of the authors cannot deny to the others the right from publishing their work...

@o0'. This does not at all seem obvious to me. Yes, sure, if the work is easily divided into parts that X, Y, and Z did, then Y and Z can do what they want with their work if X wants to not publish the part that X did. But oftentimes that is not the case - if all three kinda worked on everything, then it is indeed a non-obvious question what happens if one of the others decides that this should not be published at all (for whatever reason).

@Doc, I think your comment would make a good answer.

It seems to me that if authors B and C write in the acknowledgment section that the contribution of person A was sufficiently important that they think A should be listed as an author but that A declined and especially if authors B and C provide a description of the reasons leading to A's refusal which is satisfying to A, in other words if B and C report accurately what has been happening, then no one is behaving unethically.
For a real life example, one can look at the acknowledgment section of S.Bloch and K.Kato's work on p-adic étale cohomology, the third author being in that case O.Gabber and the reason invoked (if I recall correctly) being that Gabber did not think the work was ready for publication (I'm unable to track the precise reference at the moment, it is not Bloch and Kato's article at the IHES in 1986).
UPDATE: Because I haven't been able to track the reference of Bloch-Kato, let me point out Beilinson-Bernstein-Deligne which starts with

Il avait d'abord été prévu que O.Gabber soit coauteur du présent article. Il a préféré s'en abstenir, pour ne pas être coresponsable des erreurs ou imprécisions qui s'y trouvent. Il n'en est pas moins responsable de bien des idées que nous exploitons et le lecteur lui est redevable de nombreuses critiques qui, nous l'espérons, ont permis d'améliorer le manuscrit.

which roughly translates as

It was first planned that O.Gabber would be coauthor of the present article. He chose to abstain, so as not to share the responsibility of the mistakes or imprecisions to be found in it. He is nonetheless responsible of many an idea we exploit here and the reader owes him numerous criticisms which, we hope, allowed for improvements of the manuscript.

+1: Including information about declined coauthorship is a very good (and rarely used) way to address these ethical issues.  (I may add such a comment to one of my own papers: thanks for suggesting it!)  I think that in the case you give, Bloch and Kato found the best solution to their problem, but -- I don't have intimate knowledge here and I don't want to speak too strongly -- a lot of mathematicians believe that Gabber's actions in this and related matters are at least atypical.

The fact that Bloch and Kato are not in any way junior to Gabber also makes the nuances of the situation different from much of what I discussed in my answer.  It would be stranger to write a paper and say "This paper is largely the work of my thesis advisor.  She declined coauthorship."  Wouldn't it?

Can you add the English translation of your quote? Because as far as I understand the French it's a very nice example of how to deal with such a case.

Declining coauthorship is actually quite common behavior in my field (mathematics).  It is so common that not lightly do I question its ethics.  In most instances I have seen it appears rather borderline, or the ethical questions that it raises are accounted for in other ways by the profession.  However, taken to the extreme I think it would certainly result in unethical behavior.  Thus my comment questioning another comment made on Nate Eldredge's answer:

An author always retains the right not to receive credit for his or her work.

I think this statement is clearly too strong.  If you systematically pass off your work to others, you are participating in a form of plagiarism and giving (assuming that your work is good, which I will since this is the version of the practice I am familiar with) an unfair advantage to your should-be coauthors in what is now an extremely competitive academic environment.
Stage 1: Let's start at the extreme point: if you do all the work on a paper (or project, or thesis) and then pass it off to someone else who puts their name on the paper, I hope we can all agree that not just they but also you have done something deeply unethical.  As I have before, I will point to this excellent short story which describes an especially interesting case of this.  The story describes realistically how the discovery that the main character has written the PhD thesis of his ex-girlfriend would get not just her but also him in trouble.
In this extreme case there is another ethical violation occurring: someone's name is being put on something which they did not have intellectual involvement with.
Stage 2: Let's imagine that a more senior author really did the work of the paper and explained it to someone more junior: possibly their own student, but it happens in another cases as well.  And let's say the junior person writes up the work in the formal sense but not without a lot of help from the senior person, to the extent to which that without substantial guidance from the senior person the junior person probably would not have been able to write up the work in an acceptable way.  The junior person has in some superficial sense "contributed to the work", but I would argue that really he has not.  And to focus ideas let's imagine that this in a field like mathematics (or TCS, theoretical physics...) in which the idea of "valuable routine work" is largely or completely absent: e.g. the junior person did not do any interesting or independent calculations, coding and so forth.
I still feel that this is a serious ethical violation.  If it results in the junior person getting a PhD thesis, then I feel bad about that.  If this is a larger pattern of behavior and results in the junior person getting several publications which advance his career, then I feel terrible about this: I think the senior person is doing something really reprehensible.
Stage 3: Now imagine that the senior person had the idea for the project, had some of it worked out in advance (but not shown to the junior person), had ideas about how the implementation was to take place, but left at least some substantial part of the implementation to the junior person.  Let's say the junior person did at least a substantial part of the work independently, and let's say that he did some things in a way different from what the senior person would have thought to do which is not obviously worse.
This stage is an accurate description of the relation between many thesis advisors and their students in mathematics.  In mathematics this type of interaction probably most commonly results in a solo paper by the student, and the likelihood that this will occur is positively correlated with the research strength of the advisor and the department.  I grew up watching this practice and therefore got used to it.  Once I saw how differently other fields operate I started to wonder whether this was really ethical behavior.  I think in practice it is not such a serious problem because in mathematics who your advisor is is known to everyone who knows you: when you meet someone new or talk about them with a colleague, "Who was his advisor?" is one of the first questions that gets asked.  It is quite common for someone who got their PhD at a top mathematics department to have their first publication in a truly excellent journal on the topic of their thesis -- deep, cutting edge stuff in their advisor's field -- then a short gap, followed by other papers which are minor variants of previous work or are interesting and valuable but in a different, lower-to-the-ground field.  When potential employers see this type of CV, we largely tend to think "I get it: the advisor really did much of their thesis work, and without her the candidate cannot continue doing work of the same quality."  Unfortunately this might be unfair in the other direction: for instance some advisors really don't give much direct help to their students.  That was the case for me, and luckily various people told me that my advisor has a reputation in the community for not doing his students' theses for them, with the result that some of his students have written much better theses than others (mine was somewhere in the middle).  So it's not clear how to arrive at a "standard advisor discount".  Taken the other way, sometimes you do see an eminent advisor writing a paper jointly with their student on the topic of their thesis work, and all of a sudden it becomes less clear what this means: there needs to be an explanation of this in the letter of recommendation (but the explanation is not always absolutely clear or convincing either: every student everywhere always did "at least half of the work" according to recommendation letters).
Most eminent thesis advisors regard the help that they give their student to write an excellent thesis as a one time gift, at which point they leave their former student largely alone to sink or swim.  However in a small number of cases there are eminent advisors who just have that many good ideas and that generous a nature.  Maybe they feel that the way to function as a leader in their field is to feed their former students the ideas they need to do first-rate work.  I cannot imagine trying to tell these eminent people not to do this, but nevertheless the practice seems unfair in a competitive job market.  It contributes to feelings that the top departments form a kind of elite club that, if admission is not granted by the age of 24 or so, will be almost impossible to join later in life.  This is not good for the profession.
There are further stages. To be clear, starting with Stage 4 I would myself be a participant in the process (and sometimes I think I would be a better advisor if I were more onboard with Stage 3).  If you're a senior person and you feel like you made what was really only an offhand remark to someone, then even if that offhand remark was crucial in the writing of their paper you are relatively unlikely to want to be a coauthor.  I respect that very well and I have to: that kind of expertise and generosity is part of being a senior academic (in my field at least; I assume it's not so different elsewhere).  At my relatively middling career stage I have already made plenty of remarks to others that have resulted in acknowledgments in their paper, and I have already turned down at least one offer of coauthorship.  And there was one relatively recent case where I offered coauthorship to a very senior person: he declined, roughly because he had almost forgotten the remarks he had made to me about five years (!!) before.  I hadn't, and they were crucial to writing what for me is a very good paper.  So there is a continuum here and many judgment calls to make; I want to be clear about that.  But I also think that we should draw the line somewhere before "An author always retains the right not to receive credit for his or her work."

I agree about the unfairness of having some top mathematicians feed ideas to their students until the students have tenure, while other mathematicians leave their students to build their own careers.  Also this isn't just a matter of the top departments being an elite club, it is more a matter of individual advisors (from various tiers of schools) acting differently than other advisors.  I don't completely agree about Stage 2: if the student would not otherwise graduate, and if also the student will leave academia after getting the PhD, then I would give a student all necessary help.

Comment from a field which IMHO tends to err on the side of too long coauthor lists: For (or rather against) stages 1 and 2, we  (chemistry, Germany) declare in our thesis that no help was received other than that listed in the acknowledgements.

@MichaelZieve - what is the societal value of such a Ph.D. degree, presuming that the pseudo-student was and remained unable to write up anything publishable independently?  Perhaps an extreme extension of the basic human right to education?

@JirkaHanika Once a department has accepted a student into graduate school, and that student has passed the preliminary written and oral exams to advance to candidacy, then I think the department has a moral obligation to get the student a Ph.D. in exchange for the student's spending years in the department rather than doing something else.  I don't think about anything so grand as societal value, I just think of the student as an individual human being who deserves some certificate indicating that (s)he has worked at something during these 5-6 years of his/her life.

@MichaelZieve - Some people work harder than others, though.  That's not reflected in the extreme case of the advisor helping the student "write" a thesis which the student barely understands properly, let alone contributing to its content.  There should be some minimum standard of the Ph.D. title holder being capable of doing research I think.

I think that you need to distinguish between the case when everyone agrees that X's work requires acknowledgement as a co-author, but X is being difficult, and the case where X is uncertain or dismissive of the level of their contribution.
I was recently added, at the invitation of the primary authors, to the author list of an article in preparation based on my very last-minute contributions. I felt obliged to have a discussion with the primary authors as to whether I really should be added or should simply be acknowledged. In the end, I deferred to their judgment about the importance of my contribution and accepted their invitation. This is a perfectly natural and appropriate conversation to have.
However, if X thinks that the paper is bad as written and refuses to have their name associated with the work, then the remaining authors have some harder choices. They should first consider the objections or criticisms of X and see if the article can be improved. If it cannot for time or space reasons, then they should consider either offering X an acknowledgement credit at the end of the paper or whether or not they can remove X's contribution and their name from the work entirely. It's entirely possible that this may scuttle the paper submission.
I don't think that the remaining authors should submit X's work as their own if X refuses to be associated with the article in any way.

The purpose of publishing a paper should be the dissemination of knowledge and not merely the attribution of credit to the right persons for its discovery. If the authors Y and Z believe that the work is of any importance whatsoever to the scientific community, it would be unethical for them to NOT find a way to publish it. Such considerations could override some of the considerations of fairness of attribution that many here seem to be concerned about.

I agree that Y and Z's belief that the work should be published should carry some weight, but I don't think they ever have an ethical obligation to publish anything.

They should, if their jobs are funded by taxpayers' money, or if the work is of use to society.

Science is ultimately about creating knowledge and understanding. Considerations of credit and plagiarism, or, in the present case, the danger of committing "inverse plagiarism"  serve to keep the incentive system fair. But withholding knowledge under this auspices is leading the thinking ad absurdum: it is putting the cart before the horse. The incentive system should serve the expansion of knowledge; the expansion of knowledge should not be sacrificed for keeping the incentive system in place. And, mentioning that the co-author declined to be named may penalise the remaining authors.

In a comment on the earlier thread, I claimed that a co-author always has the right not to receive credit for work done with respect to a particular paper. I believe this is because there are certain rights and responsibilities that researchers have with respect to publications. Particularly relevant here is the right to receive appropriate credit for their work.
However, associated with any right is also the option not to exercise said right. For instance, author X may believe that co-worker Y has contributed enough to merit co-authorship. If Y chooses to decline co-authorship, this does not prevent author X from publishing the paper.
At the same time, by exercising the right to co-authorship comes additional responsibilities. Among those is the responsibility to participate actively and constructively in the preparation of the manuscript. It is unethical to insist on  co-authorship for the purposes of scuttling a manuscript through inaction.
In general, though, none of the above places the restriction on authors voluntarily relinquishing intellectual property rights to the paper (that is, not have their names appear as co-authors, but still allowing the manuscript to proceed). They also have the right to "take their marbles and go home"—essentially withdraw from the complete process, which can of course be much more difficult in collaborative projects involving multiple groups.
In short: authors have the right to accept credit, and the right not to accept credit, but must accept the consequences of that decision.

This is exactly the reason why care must be taken when inviting some other researcher into team for collaboration. If he has once been written as a co-author, he has a certain right to block the publication of the shared work. This may or may not be fair.
As a result, it is better to invite additional researchers only if they can contribute some substantial new results or perhaps some type of analysis that is difficult to do without they help (writing and evaluating some complex mathematical model about results, for instance). In such cases, the contributed part can be identified and removed, publishing without it.
Differently, if the invited researcher contributed in general discussions and planning over all project, there is no clear way to get rid of such contribution easily. Then all that remains is to negotiate, if all sides agree to publish with the fewer authors, maybe that is ok.


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Published papers with incorrect solutions of famous problems: how to raise concerns with editors?
I recently discovered the following two papers:

Bruckman, Paul S. A proof of the Collatz conjecture. Internat. J. Math. Ed. Sci. Tech. 39 (2008), no. 3, 403–407, DOI: 10.1080/00207390701691574.
Bruckman, Paul S. A proof of the strong Goldbach conjecture. Internat. J. Math. Ed. Sci. Tech. 39 (2008), no. 8, 1102–1109, DOI: 10.1080/00207390802136560.

Mathematicians probably do not need to read any further to see where I am going with this.
For non-mathematicians, the Collatz and Goldbach conjectures are two of the most famous unsolved problems in mathematics. In addition to being the focus of active research, they are also popular targets for non-experts, who have proposed countless numbers of erroneous proofs over the years.
The MathSciNet reviews for the two articles (Collatz, Goldbach), which are written after publication by independent reviewers, identify a critical error in each, which invalidates their results.
The journal in question is apparently reputable (otherwise I would not bother) and is published by a major commercial academic publisher, though its main focus is on topics in mathematics education rather than pure mathematics.  It appears that the chief editor has been in charge since before 2008.  I did not find any errata or editor's notes regarding these papers.  (A corrigendum of the Collatz paper was published, but it fixes minor typos only, and the MathSciNet reviewer apparently took these corrections into account.)
It seems to me that the papers cannot have ever undergone proper peer review - the titles alone should have subjected them to extremely close scrutiny - and that they ought to have been retracted long ago.   But in light of their age, I wonder if it is it still appropriate to raise the issue with the journal's editor, or if people will just see it as "water under the bridge".
I am also not quite sure how to explain the issue tactfully.  I think with most professional mathematicians, I could just show them the citations with no further explanation, and they'd immediately understand why this is bad.  Obviously that didn't happen in the first place, but I'm not really sure how much more background I can give the editor without potentially appearing condescending or insulting.
I saw the question I found a published paper that looks dodgy. What to do? But I think this case is more egregious than that one, in that the papers are not merely "dodgy" but in fact flatly wrong, and frankly, an embarrassment to the journal.  The two answers there suggest "comment on PubPeer" and "do nothing", neither of which seem adequate.

Some nitpicking: "(...) the titles alone should have subjected them to extremely close scrutiny (...)" -- I am not a number theorist, but I suspect a proper referee would be able to spot a (major) mistake without need for extremely close scrutiny. I don't imagine every paper claiming to solve a famous problem is very closely scrutinized -- I would imagine most of them get summarily rejected.

@tomasz: I don't really agree with that.  Finding errors in mathematical work can be very difficult.  If the paper is written clearly in a standard way by an experienced mathematician, then the right person will probably be led "by smell" to the trouble spot, but it may still take some work to identify the error.   If it is written in an eccentric, non-standard or obscure way, then what any sentence means can be up for grabs.  Anyway, I think what Nate means is "extremely close scrutiny if they want to publish it".

Having said that, I read the MathSciNet review for the Goldbach Conjecture, and the author uses an identity in which a sum of values of an analytic (on (2,infinity)) function f over all primes p > 2 is exactly equal to the integral of f/(log x)  from 3 to infinity, provided both sides converge.  That just doesn't sound good, and as the reviewer points out, the first function f one might choose gives a counterexample.

This case seems kind of special. Considering that Jeff Lagarias cites the Bruckmann paper on Collatz in his 2006 review "The 3x+1 Problem: An Annotated Bibliography, II (2000-2009)" as "This paper asserts a proof of the Collatz conjecture. However the argument given has a gap which leaves the proof incomplete. The erratum points out this gap and withdraws the proof." it seems like no action should be taken…

@Dirk: I just looked at Lagarias's article and Bruckman's erratum.  The situation is as Nate says, not as Lagarias says: the erratum points out misprints only.  It doesn't withdraw anything.  (An interesting maneuver on Lagarias's part!)  Of course, after many more words, I came to the same conclusion as you: "[I]t seems like no action should be taken."

For what it's worth, this journal used to publish an occasional article of mathematical interest to me (mostly in the 1980s and 1990s; some of these are cited here, for instance), but in the past 10-15 years it seems to have devolved into something that I've not been particularly motivated to look through the table of contents very often anymore.

I believe it is a waste of your time. When you see such a claim "solution of Goldbach" etc. and the paper is not published in the Annals (or something close to it) then the author knows that there is a flaw somewhere in the paper,the editor and the referees know there is a flaw in the paper and you also know that something is wrong. Just ignore it.

@PeteL.Clark: I never meant to say that finding errors in mathematical work is easy in general, even for a specialist. What I'm saying is that someone claiming to solve a particularly notorious problem is very likely to either be a) a crackpot, in which case finding mistakes could very well be a routine exercise for an undergraduate student, or b) a non-specialist way out of his depth, most likely trying to pursue a line of proof which just doesn't seem right or is a known dead end, and in either case, a specialist should be able to spot the error without scrutinizing the whole paper.

@tomasz I did have in mind what Pete said - that the paper should not have been published unless it had withstood extremely close scrutiny.  I agree that in this case a much lower level of scrutiny would have sufficed to reject it.

@NateEldredge: I thought as much, hence the disclaimer about nitpicking.

My experience from the I.T. world suggests that no matter how condescending you think it would be to explain something in clear language, the number of people who will greatly appreciates it far outweighs the few snobby people who will feel they are insulted.  Actually, clearly explaining something doesn't have to mean "talking down" to your audience, but simply ensures your communication is fully understood--always a good idea.  (I have found that the "snobby few" are usually imaginary and rarely materialize in actual practice, you only worry that they will.)

@Wildcard The issue here is that whatever is communicated to the editor, the message will be "you were grossly negligent in allowing these papers to be published in your journal". It is hard to imagine anyone being happy about that message.

@TobiasKildetoft, I would phrase it as an inquiry: "I was surprised to see your publication of the proof of ...etc., etc.  As I have never heard this famous conjecture to be otherwise than an open problem, I delved further and found a retraction published ___ date.  I am interested what sort of expert review process papers undergo before publication in your journal.  Was there a note about the historical/disproven aspect of these papers that was mistakenly not published?  Were they for curiosity only?  I fear other readers may have been misled into thinking them accurate proofs.  Signed, Name"

It is interesting to see that these articles are indeed retracted now.

Paul Bruckner also solved the Riemann hypothesis. That was a lot easier than the twine prime conjecture. See: http://www.pme-math.org/journal/bruckmaninterview.html

It is a strange case.  You say that the author of the two papers is deceased.  Given that and the other facts you have presented -- in particular both papers were published almost ten years ago, their flaws would be immediately suspected by any mathematician and are documented in the MathSciNet reviews -- it seems to me that the principal culprit and the principal victim are both the International Journal of Mathematical Education in Science and Technology (IJMEST).

The journal in question is apparently reputable (otherwise I would not bother)

Is it reputable, though?  I hadn't heard of it before.  Taking a look now, it is hard for me to tell.

and is published by a major commercial academic publisher,

Come now: we all know that being published by a major commercial academic publisher is no certificate of quality.  Elsevier was caught publishing a several journals that were essentially reprinted advertisements for medical and pharmaceutical companies.  That's memorably egregious, but other big companies have skullduggeries of their own.  Conversely, big companies which do some really shady things also put out some really good journals, Elsevier being a good example.  Taylor and Francis is a less good example: of the 46 journals they publish in mathematics and statistics, I only myself recognize three as being good...but three is enough.  So major publishing companies publish good journals and bad journals: I don't think one can deduce much from this.
Back to the journal.  I looked into IJMEST, and I find it a bit strange.  The journal's aims and scope center it on (a kind of) mathematics and science education:

Contributions will be welcomed from lecturers, teachers and users of mathematics at all levels on the contents of syllabuses and methods of presentation. Increasing use of technology is being made in the teaching, learning, assessment and presentation of mathematics today; original and interesting contributions in this rapidly developing area will be especially welcome. Mathematical models arising from real situations, the use of computers, new teaching aids and techniques also form an important feature. Discussion will be encouraged on methods of widening applications throughout science and technology. The need for communication between teacher and user will be emphasized and reports of relevant conferences and meetings will be included.

I wanted to remark that I have a colleague who is (to say the least) active in the mathematics education field, so I know that the above description is not really that of a modern research journal in mathematics / science education.  It is more along the lines of creating a shared community for mathematical teachers (which is also a worthy goal, and one that my colleague is interested in).
But the above description does not seem to be a good match for the papers in which IJMEST has published in recent years.  These papers seem to be almost entirely in the field of mathematics itself: most papers state theorems and give proofs.  Sometimes they knowingly give proofs of old theorems and their angle is to give new proofs, often accompanied by the claim that they will be easier for the student to understand (although in my experience as a mathematician it is common for new proofs to be accompanied by such claims).  But many, perhaps a majority, of the articles, seem to be entirely devoted to mathematics, usually of the kind that is broadly understandable: e.g. lots of Fibonacci numbers.  So the published work of the journal looks to be a lot closer to what is published by the Mathematical Association of America (MAA)...but without nearly as much attention to the quality of the exposition as given by articles published in MAA journals.
So something has gone terribly wrong for this journal to publish proofs of major open problems like Collatz or Goldbach: such papers should be out of scope of the journal.  As @Corvus points out, submitting a paper claiming a proof of something like Goldbach to a journal like this just doesn't make any sense: such a paper should be published not only in a math journal but in one of the very top math journals, first because a correct proof of Goldbach merits publication there (such a proof would rank among the great mathematical achievements of all time!) and second because a top journal can get the top experts in the field to the vet the paper, which is needed in order for the community to accept the result.
When the editorial board of a journal like IJMEST receives a paper claiming a proof of a major conjecture, they should (I think) do one of the following things:
(i) Bounce the paper back immediately as being out of scope for the journal, or
(ii) Engage in a preliminary refereeing job to see if the paper looks serious.  If so, they should reach out to the editorial board at an appropriate journal -- i.e., a top mathematics journal -- and try to do a handover of some kind.
I've thought it over for a while now (slow internet connection...), and although in general I believe strongly that any interested party can contact editors and try to get published results corrected, in this case I just don't see why that would be a helpful thing to do.  I realize that I now believe that publishing short, fallacious proofs of two major conjectures in the same year is enough to irreparably damage the reputability of a mathematics education  journal in my eyes.  Either they are so far outside of the mathematical community that they don't understand the significance of problems like Goldbach to the mathematical community and how they have to be handled or they know and don't care: in particular, they don't really care whether the mathematics they publish is correct.  I don't see how to fix either of those problems.

It is somewhat odd. I looked at the journal on MathSciNet and it seems to have some of its papers indexed (not all, unless it publishes a very irregular number of papers per issue), but the page for the journal has no indexing information, which I do not think I have encountered before.

Here's some context: https://www.jcturner.co.nz/paul-s-bruckman-and-number-theory/three-papers-by-paul-s-bruckman/

I would not recommend contacting the author, as

The people who put together the disproofs probably already have done so, and
You're likely to end up wasting time in futile argument.

I know a researcher who claimed to have solved P=NP.  This researcher has done some nice work in other places, but this particular piece of work is based on hubris and naivete.  Like many who have a personal area of blindness (as often happens with such famous problems), this researcher is pretty much impossible to talk to rationally about their pet subject.  Thus, people basically just ignore it (which is easy since it's only ever been informally published as a preprint).
With something that has been published, you can contact the editors and see if they'll act, but if they don't I would recommend the policy of simply ignoring the article rather than making it a crusade.
I recognize that this suggestion may be controversial: it just feels wrong, given scientific ideals, to let an incorrect result stand.  The edges of science always have been and always will be cluttered with junk work that is wrong but not worth anybody's time to get retracted or corrected.
I find that this is best understood by the fact that significant results generally imply more than just the result itself.  If a result both correct and meaningful, then there should be a great deal of intellectual productivity that can expand out from either the result or the machinery used to obtain it.  If not, then an incorrect result is much like all the other numerous dead-ends of scientific inquiry that have resulted in true but apparently useless results.  That changes, of course, if an incorrect paper is likely to mislead experts or to cause public harm, in which case it's worth fighting, but that doesn't seem to be the case to me here.
If possible, it's nice to be able to lay a retraction marker down so that nobody ends up wasting their time on it. That's really all that getting the retraction would mean, however: just decreasing the likelihood of people stumbling across it and wasting their time.  The ultimate fate of these papers will change little, whether retracted or not.

"it just feels wrong, given scientific ideals, to let an incorrect result stand" -- in effect, "someone's wrong in an 8-year-old article" is a stronger version of "someone's wrong on the internet". Either one can easily stop you getting to bed by a reasonable time.

It seems that Paul Bruckman was an active mathematician with some non-retracted publications, but towards the end of his life he published "proofs" of Riemann, Goldbach, Collatz, you name it. He died in 2003.

Out of curiosity, I clicked through to the original articles, and noticed that both were retracted by the journal's editor-in-chief.

Retraction notice for the Collatz paper: https://www.tandfonline.com/doi/full/10.1080/0020739X.2019.1703070

Retraction for the Goldbach paper: https://www.tandfonline.com/doi/full/10.1080/0020739X.2019.1703071

Both notices refer to negative reviews and (unsuccessful) corrections elsewhere; neither mentions what initially brought this to the editor's attention.

I've dealt with this sort of thing in the past. I would begin by contacting the authors, explaining the problem and asking them to issue a retraction (while avoiding the temptation to ask why, if they really believed they had proven the Goldbach conjecture, they published the proof in an education journal!!).
If that fails, I would move on to the editorial board of the journal in question with the same request.

I have reason to believe the author is deceased.  Anyway, in general I hesitate to engage with people who think they have proved the Goldbach conjecture - conventional wisdom is that such interactions are rarely productive and sometimes lead to continuing and unwanted correspondence.  I agree that contacting the editor is a good idea; my question is how to phrase it.

That makes sense regarding engagement with Goldbach-provers. I suppose I might write the editor and explain that by virtue of its public visibility the Goldbach conjecture attracts a great deal of attention from aspiring mathematicians [that's the nicest phrase I can think of for "crackpot"; you may have something better]. I'd go on to explain that if it  had been proven, it would be a massive breakthrough in mathematics and a cause for massive international excitement. But instead, what they've published is a flawed proof; moreover a detailed explication of the flaw has been published...

...at MathSciNet. This is a potentially embarrassing state of affairs for the journal, all the more so because of the prominence of the problem in question. I'd urge the editor to either retract the paper or obtain further review in light of the MathSciNet posting and, based on the outcome of that review, consider retraction at that stage. Most likely the editor will do nothing;  "Internat. J. Math. Ed. Sci. Tech. retracts paper that should obviously never have been accepted" is hardly desirable press. But you can try.
Likely the editor will do nothing. "Journal of

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Keeping track of bibliography references for an entire research group
This is a related question to my previous one about keeping advisees aware of literature.
Given the relatively large number of papers that are out there, it's inadvisable to force every student to start from ground zero in building up a reference library. To me, this suggests that there should be some centralized ways of keeping track of bibliography references.
The low-cost but high-maintenance route to me would be to have an SVN repository to which people can update their own personal bibliography files. Are there other more time-efficient routes to manage this process when:

people have different computing platforms and workflows (Windows with Office, OS X with iWork, Linux with TeX, etc.)?
working with collaborators at other institutes?
it's important (according to university/workplace regulations) not to have data stored "in the cloud"?

http://citeulike.org http://wiki.citeulike.org/index.php/Groups or http://www.mendeley.com/ http://www.mendeley.com/groups/

Thanks for the links. I should also mention that I'm interested in solutions that don't involve storage "in the cloud," as it's frowned on by my institute. I've revised the question accordingly.

Which data shouldn't be stored in the cloud?  Your bibtex file?  Or just actual PDFs?  If your institution frowns on sharing your bibtex file, I'm disappointed (see http://scienceinthesands.blogspot.com/2011/11/up-until-googles-recent-catastrophic.html)

@DavidKetcheson: The prohibition is definitely not on sharing data, it's about where the data "lives." The idea is that our data shouldn't be subject to external usage control and privacy policies. But we're certainly free to share BibTeX files and other data via university-owned media. (And obviously PDF's runs into a whole other issue.)

I don't understand the issue, but...Mendeley's privacy policy says: Your data and your content is owned by you.
Whatever personal data and original content you upload to your Mendeley account is owned by you. We do not claim any ownership rights over your research. Of course, you can delete your data at any time.  Does that make your institution happy?

@David, seems like a reasonable restriction to me, if you don't want the world to be able to see your stuff it doesn't matter whether you own the data or not! Can you restrict the desktop version of Mendeley to not upload the bibliography to the internet?

@AndyW, aeismail says letting the world see it is not the problem.

What do you mean by "reference library", in terms of files? A bib file? A bunch of pdfs?

I accomplish this using the groups feature of Mendeley.  It works on all three major OS's, allows you to share bibliographies easily with both your group and external collaborators.  It also allows something that I think is very important -- lots of bibliographies on particular topics within the realm of what my group does.  See, for example

http://www.mendeley.com/groups/1045561/runge-kutta-stability-regions/papers/
http://www.mendeley.com/groups/1070421/nonlinear-hyperbolic-pde-solvers-on-gpus/papers/

I should mention that Mendeley's web interface to bibliographies is awful.  But the desktop interface is quite nice and (most importantly) can export Bibtex.
Mendeley does store your data in the cloud (if you consider a bibliography to be "your data").
Update: I stopped using Mendeley when it was bought by Elsevier.  I haven't found a satisfactory replacement.

If you're using LaTeX, you can set up a .bib file on a shared drive and everyone can reference and add to it as necessary using whatever program they like. I'm a fan of BibDesk, personally.

I recommend to put this file under version control, to reduce the risk of people accidentally permanently deleting anything.

We used to maintain our own list on our (sadly now defunct) group website when I was a PhD student. The sources for the group website are in a shared (internal) version control repository to which we all have access. We maintained three shared bibtex-files:

one for internal references — everything any of us ever published

one for external references — anything not internal any of us has ever cited or found otherwise useful

one for new references; we go through them at our weekly meetings, then merge them into (2).

Simple, but works very well.

Neat! That is the kind of working routine I would wish for my group.

If you want to sync refs across multiple users but don't want to host in the cloud, you should check out sparkleshare. You'd set up a git repo on a local server to host a bibtex file, then have your users install sparkleshare on their computers and connect to the git repo. You would then use Mendeley, which has a bibtex syncing option. This will achieve a system that will distribute new refs added by any user.

hm, I take that back; it appears that Mendeley's bibtex sync is only one-way (mendeley->bibtex), so the system I described would simply leave all users constantly overwriting the shared file and never picking up the changes made by others.

For small scale projects, such as you and a few other authors working on paper(s), I would just consider plain text file (with standardized fields) in a location you can all access (plus version control). Bibtext would be an obvious solution (and most reference software that I know of can import bibtext files). Easy and minamalist to implement and update. Mike's answer seems like a better solution than this, but this is dependent upon all the members of the group utilizing such software, which sometimes isn't worth the effort to get people to convert.
For large scale operations (like you need to enter in over 1,000 papers for a lab) I would consider rolling your own database + user forms to enter in data. Fields you want from papers are fairly easy to delineate, so setting up the initial database is not too dificult. Here are a few other reasons this is nice;

You can have flexibility to put what you want in the database. For instance if you were conducting a meta analysis you may want to extend forms to include relevant statistics.
Querying on a variety of characteristics becomes trivially easy.
If you are saavy enough with the database, you can write some scripts to export the data in whatever format you want. For instance, I use the one statistical software I am most proficient in (so not a true database, but several seperate tables) to write my bibtext library, plain text citations in approximate APA format, and VBA code to find-and-replace latex like citations in word documents.

Alot of flexibility with your own database, and if you are doing a very large project it might be worth the upfront effort to develop and customize to suit your own needs.

The solution is the open source I, librarian server. It manages bibliography for groups. You can try it out online here: http://www.bioinformatics.org/librarian/
Look for "demo"

Why not just use vanilla git ? Everyone sets up their private repo and you can use github for shared syncing as needed.

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What should advisors do if one of their PhD students has to withdraw?
Unfortunately, there are circumstances when not everything goes right in a student's PhD career, or there can be personal circumstances that require doctoral candidates to withdraw from a PhD program before they have completed the requirements.
However, what is not clear to me is how to handle this situation from the advisor's perspective. What should an advisor do to:

Help the candidate, should she wish to apply elsewhere?
Discuss the situation with the group, to maintain morale?
Handle the "transition" process (during which the student is still officially on the payroll)?

Without additional details, it will be impossible to provide very detailed answers so from a general point, each case has its own solutions. The first question I would ask is, what is my part in this and how can I best help out (best may be = nothing). In general I would try to help out as much as I can unless the problem lies in the realm of a conflict or personal problems. Then there is not much you can do except suggest professional help. If the candidate is a good student then I would certainly support with any letter of recommendation I could. Since you mention morale issues in the group, it suggests some form of non-trivial problem. In some cases too much help makes people fall into a false sense of security so to be shaken can be useful as long as the reasons are very clear.
So without trying to read too much into what is between the lines, I think the degree of help depends on to what extent help can or should be given (seen from an objective point).
Probably not the most satisfactory answer but being responsible for the research education at my dept., I have seen how difficult these matters can be. In our case, I would also be a resource to help out, if nothing else just to discuss the matter. (This does not mean I run a research group completely without problems myself!)

It depends on the circumstances, but I certainly help the student if I'm able. We had one student who wanted to transfer to a Ph.D. program closer to home, and another who wanted to take a crack at programs better than ours. I was happy to support them both, including writing rec letters. I put a third student in touch with some people who worked at a software company.
Some students blow us off, in which case general well wishes and respectful silence seem to be what is called for.
A Ph.D. is 5+ years of backbreaking work, during which you make poverty-level wages, with uncertain job prospects at the other end. I can hardly blame a student for leaving, if his/her heart is not in it.

Handle the "transition" process (during which the student is still officially on the payroll)?

Support would be great.
On the other hand:
If you are talking about a PhD student who was employed at an institute, then maybe the advisor should think what he/she has made wrong concerning advising.
From my point of view, a retrospective would be worth for both - student and advisor. For instance, can you remember the first time when an expectation and an actual state of the student's work was rather different. Talked the advisor with the student regarding publications and interesting conferences? Which intervals were scheduled for meetings? Did their meetings worked out? If not, why not? (agenda, interruptions during the meeting). Which method was used by the student to assess his/her progress? Were these "story points" observed a little bit by the advisor?

Discuss the situation with the group, to maintain morale?

Yes, but firstly the advisor needs to know the actual reason concerning the end of the student's work. Talking in front of a group about a reason which was not the actual reason could be not the best when having persons in the group who are friends of the student who ends his study and work.

Help the candidate, should she wish to apply elsewhere?

If she has achieved a certain level within her scientific field, why not?

I'm not talking about cases where the PhD advising relationship has fallen apart. I'm talking about situations like visa problems, family emergencies, failing required coursework, and other non-research issues.

@aeismail the situations you mention could easily fall under the category of private information that you should not be sharing with the group. At the very least you should give the student the chance to explain to group members (if they choose to). If not, you have to leave it at "personal decision" and not go any further.

From my experience, most advisors seem to simply shake hands and part ways; I've seen a number of students leave, and in no case did the advisor do anything for the student. I view this as appropriate. Consider a work relationship, where an employee decides to leave because they (got married/got sick/won the lottery/will likely be fired for poor performance/dislike their job/dislike their boss/etc.). It's almost unheard of for the employer to assist the quitting employee to find new employment. (Note I'm not talking about firing someone, where local laws may require some sort of employment help.)
It's a similar situation here. You have a student who decides to leave for whatever reason. At that point, your work relationship is simply terminated. You can continue to interact as professionals, but you are under no obligation to assist in future endeavors.
That being said, I don't think any grad student would turn you down if you offer to help. It would definitely be a nice professional gesture. Just realize that you are under no obligation to offer such help.

Hmmm.  I really have to disagree.  When I agree to be a student's advisor, I'm making a commitment to their professional development, even if they decide to leave.  I've helped my students find other advisors, and I've written recommendation letters for my students to join other PhD programs, because I believed that was part of my job.  My first PhD advisor did the same for me when I changed PhD programs.

@JeffE Couldn't agree with you more!

If you treat students and colleagues instrumentally, and if you have no compunction exploiting the time and energy of others for professional gain, then of course, you must never offer to assist  students who are no longer working on your projects or to whom you have assigned low academic-value work to benefit you but not them. Terminate the relationship and find a replacement.

@Jeff - Interesting, I didn't expect this to be so controversial. I guess all I can say is that many of the professors I know don't share your view. I know mine didn't :)

Your analogy with other workplaces is false in one aspect: in academia, if you don't write your student a letter of recommendation, their career is probably done.  If the student's work has been acceptable and you believe they have the potential to succeed elsewhere, I believe you have an obligation, both to your student and to your discipline, to write the letter.  Other forms of assistance (calling contacts, etc) are good if you have the time, but I would think of writing a letter as an absolute requirement.


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How to encourage administration to handle plagiarism?
I obtained my PhD about five years ago and immediately took up a postdoctoral position at a national lab in Japan to continue my research in computer engineering.
Over those five years I worked with the person who is now my supervisor, and trusted him in the same way I would trust any ordinary person, only to learn (too late!) that my trust was misplaced.
After working on a large project of his for about two full-time years, he forced
me to "leave the project". Now that the large project is nearing completion, I have since discovered that he has started to present my ideas and my work as his own.
The administration vacillates between feigning ignorance and admitting there is a problem but then claiming that they are powerless to do anything about it.
What can I do? What should I do - and why?

As JeffE would say, Run, don't walk.

@DaveClarke: if only I had known that earlier!

@Charles Morisset: Because leaving would entail relocating my entire family, etc. Not impossible but hardly a walk in the park!

Has he published your work, or just presented it?

@DaveClarke: Until now, just presented it. For him, this means there is less of a paper trail, and there are no pesky editors or the like to be found. I suspect he knows that if he publishes my work, especially somewhere reputable, I am probably going to be able to handle things by working with the editorial staff.

This can be solved. As suggested below, the way could be to talk with him. Another is to write the work up and try to publish it, probably with him as co-author.

@DaveClarke: I can't talk to him - he has literally locked me out of the office, won't answer e-mail, and even pretends he can't see or hear me on the rare occasions we bump into each other and I try to put in a "hello?". It's quite remarkable.

@DaveClarke: regarding pre-emptive publication, that is an interesting idea, but might not be easy for a number of reasons. To give just one example, the work in question is (part of) the design of a computer system, but now I'm not allowed to use that very system.

It is harder to deal with plagiarism in oriental countries than in the western world. It's even harder when your employer is a national lab.
To answer your question, how to encourage the administration to handle plagiarism?
There is something you need to know (I suspect you already know it to some extent), orientals tend to treat their faces much more seriously than anything else. This is the key.
Things may not be that serious as you would think. So far, he only presented the idea and the work as if they were his. But I agree that it's a bad sign. You need to deal with it as soon as possible before he goes any further.
Edit (I would like to argue that we do not have sufficient information to tell if plagiarism will happen or already happened.)
 End of Edit
From what you described in the comments, your supervisor seems to have personal issue with you. You might have some conflicts with him without you even knowing it. The key word face is the most probable reason I could think of. There is probably some cultural thing buried somewhere you would need to figure out if you want to resolve it. It may not be that serious as you think, could be just misunderstanding.
There is some different thinkings between oriental and western world. In the western world, people take individual ownership for what they think and do. In the oriental world, some tend to think the ideas and the works are products of the whole team/group. Thus, the head of the group would present the idea and the work as the head of the group. This could be construed as plagiarism in the western world
You said they are powerless to do anything about it. This is probably due to that thinking. I must say that changing a culture takes huge efforts and long time. If you want to talk to them to encourage them to handle plagiarism, you need to

Talk to them politely, professionally and discreetly.

Wow, just wow. Thank you for this answer, is is completely orthogonal to anything I had imagined. Having said that, I am not sure I fully understand what you are talking about - at least, I'm not confident I know how to deal with the issue! I have, thus far, been dealing with people as politely, professionally and discreetly as I know how, but it hasn't gotten me far.

@Lostintranslation I rewrote my answer quite a bit.

As you've mentioned, a paper trail is always harder to deal with in presentations—and taking credit is a lot harder to define than on a paper.
Right now, you have a few key challenges: you will first need to find a new job as soon as possible. Secondly, you will need to establish the paper trail that shows that the ideas and results that you have obtained are in fact yours. This requires having a clear email trail, plus any relevant lab notebooks and supporting evidence that shows such work was in fact yours.
Beyond that, you have already done due diligence in that you have alerted the administration to the possibility of academic dishonesty on the part of your advisor, and you have also informed him of your intentions in this matter (by email, which he has received).
If you have done both of these things, then you should be able, as you suggested, to work directly with the editors of any journals in which your advisor chooses to publish this work without you.
However, one other thing that you could do is write up your work independently. Presumably, you are much more knowledgeable about the specifics of the methods and techniques that you've performed, and would be able to write a better paper on this topic than he can by himself (which he would need to do in order to publish without you). You could then offer him to publish those manuscripts. (Before sending him such a manuscript, however, I would be sure to watermark the PDF, and lock it down so that it can't be printed, edited, or copied. Alternatively, I'd only send part of the paper—by withholding the methodologies and conclusions sections, for instance.)

Let me start with plagiarism/academic dishonesty is a serious offense and it should always be dealt with. You said, "After working on a large project of his for about two full-time years..." this immediately puts us into a gray area. Did you discuss authorship at the start of the project and if so what was agreed then?
When I employ someone to work on a grant, that doesn't guarantee them co-authorship on everything they work on. Often I need someone to turn a crank and there just isn't the opportunity to make a contribution worthy of authorship. Other times I may not trust the person enough to do anything independently enough and therefore spoon feed them. In my opinion the extent to which supervisors "steal" the work of their advisees is often overrated by advisees, especially ones who have had a falling out with their supervisors.
You have a sour relationship with your former advisor and the first thing you need to do is to repair the relationship. Accusing a former supervisor of academic dishonesty by brandishing words like plagiarism is not helpful in this regards. Talking to him and explaining that you need to publish the work is useful.
I would suggest creating a list of all the projects that you worked on while in his group. From this list, you need to identify the publications that you can generate without needing any resources from him (i.e., access to HIS computer/software) and ones that you need to collaborate with him on. The goal is to identify all potential publications and establish authorship (i.e., what should have been done at the outset).
For each publication that does not need any additional resources, write a short description/abstract about the key findings, propose an author list and order, provide a time line until submission. For these publications, you should be the only one responsible for anything on the time line (apart from providing feedback on drafts). Ask him to provide feedback on the key findings, author list, and time line so that you can tailor them to better fit his needs.
For each publication that requires additional resources, you need to remember, he can ignore your previous work and just regenerate it and write the publications on his own. What you are offering is a collaboration. Again, you need to write a short description/abstract about the key findings and the additional work required, propose an author list and order, and provide a time line until submission. For these publications, the more you expect of other and the more resources you need, the less enticing the collaboration is.


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Thesis project outside of advisor's expertise
I'm working on a project outside of my advisor's experise. He doesn't have background in this area (he's not familiar with both the big picture nor the basic detail). For example, it's a machine learning project, and while the first critical thing is training data, he told me to focus on finding features. Also he's not consistent with the design of solution: sometimes he want it to be unsupervised, and when I mention training data he switched to supervised system.
I managed to do the work on my own, but without the advisor's guidance I couldn't go further. I can only go to the point of reimplemeting state of the art papers and add small modification to them. Whenever I present a new idea/working solution, he couldn't criticize it since he's not familiar with the field.
How should I resolve this situation ( ask for a coadvisor etc)? I absolutely love this project and am capable of working out the solution, just need better guidance from professor.
P/S: This project is one of the main project of my advisor since he gets funding from that.

Is the advisor the same in your previous question Not enough guidance from advisor that you asked in March, 2013 ?

Yes. This is the new project, supposed to be my thesis project.

Why does your advisor get funding for a project that's outside his expertise?

without the advisor's guidance I couldn't go further — Then, obviously, you need to find someone who can give you expert guidance.  Your advisor should be able to help find such a person.  (Yes, this means telling your advisor that he is not such a person.)

@Kimball Good point but I would add the question HOW he got the money without expertise as well.

Step 1:
Figure out if your professor is actually not capable of advising this project, or if you are just not communicating well. For instance, oftentimes when I hear that advisors are giving inconsistent advice, it just happens that the student often misunderstands what the advisor is trying to say (or the advisor is just throwing out ideas in a brainstorming style, which almost by definition means that some of those ideas will be conflicting - that does not necessarily mean that he does not know what he is talking about). For instance:

it's a machine learning project, and while the first critical thing is training data, he told me to focus on finding features.

Focusing on the features first does not seem entirely crazy to me. Of course you'll need to find good training data for supervised learning at some point, but identifying the potential features is indeed usually a very early step in the process, afaik.

sometimes he want it to be unsupervised, and when I mention training data he switched to supervised system.

It's a research project, he probably does not have a 100% clear vision of what exactly you need to do to make it work (nor should he). Maybe he is just throwing out ideas, and you are taking his words too seriously?
Critically question whether he or you are not understanding the project correctly. If this is the "main project he gets funding from", chances are that actually you are not understanding correctly.
Step 2:
If you decide that he actually cannot advise the project, and you can't do it alone, you can either get help or get out.
Getting help may include finding a co-advisor, but this may be difficult for various reasons (one being that most faculty are not overly interested in joining in ongoing, troubled projects of other professors for the dubious honor of being a co-advisor). Usually, it is easier to get the help of other persons in your lab more senior than you (postdocs, or even older PhD students), who have the necessary skills, and collaborate with them on your project. For this to work, you need to figure out what is "in it" for your collaborator (joined papers? something useful for their own dissertation / projects?).
If you are unable to get help, I see no other way than to get out, that is, change your project.


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Is it ethical/legal to use the University's resources for a personal project?
I am currently pursuing a PhD at Technion (Israel). My area of study lies in computational fluid dynamics (CFD), which involves high performance computing. My research requires me to develop/use complex code on large clusters (hundreds of CPUs) made available for me by my university.
I have a few projects (which might one day be monetized) on which I am working on my personal time. One of them involves using code very similar to that I am already using for my research. Is it OK (from an ethical standpoint) for me to use my university's resources (both solvers and actual hardware) for my own projects? Note that I always make sure that these projects do not affect my research, and only work on them once I am ahead of schedule.
Would it be legal for me to do so in the United States? Or can the University be entitled to a piece of the company if it found out I had been using their resources for my projects? Note that the Israeli law system is also based on common law, so I am interested in knowing if it would be legal in the US.
Note that about 70% of the cluster's processors are never used since we are currently understaffed. Also, my own solver would use at most 10% of those unused processors.

I think "which MIGHT on day be monetized" is key, they MIGHT also lead to a research paper, or you just learning something.

But what effect does you using the "actual hardware" have on other people?

@ChrisWhite the university has given our lab a lot more processors than we currently need. About 70% of them remain unused (the lab is new, new students/post docs should be joining us in the next months/year). Running my own solver on the cluster would use about 10% of those unused processors.

@ChrisWhite ahead of schedule just means that I have already more than exceeded my professors' expectation of productivity in a given amount of time (or my own that matter)

@Ian check edit

This might be a silly question, but have you asked the person/body that manages your cluster? They might have a policy on exactly this.

Every university I have ever worked at has had an explicit policy about what one may or may not use the university's computing resources for. Since many academics do consulting work, this is something that most universities should have well-thought-out policy on. Read the policy. If you're not certain how it applies to you, ask the people who are responsible for your university's policy.

It's unethical to use your university's hardware resources and then not share with them the eventual proceeds of that research. If the work you do were to produce papers, then they would share in the reputational advantage for employing you and being affiliated with your work. If it would produce a patent or a product, then employment rules at my university in the US would have us split ownership and royalties. At the very least, the university bought the equipment, paid the power bill, and paid someone to administer it. Ethically they deserve to benefit, too.
Now, I have no idea what the laws of Israel or the regulations of your university have to say about this, so you should check before you do anything.
When it comes to software (the solvers in your question), things may be different. If the software is open source under a usual license, you may generally use it for any purpose you like. Open source licenses typically do not regulate use at all, and only cover redistribution. If the software is not open source, then, in the US at least, regulation of use is generally left to the copyright holder. Any permissions that you have to use that software flow through some sort of explicit (written down) or implicit license. If someone at your university gave you software owned by the university and told you to use it for your project, then generally speaking you may use it in the course of your employment as directed by your supervisor. You probably cannot use such software for a side project without permission from the copyright holder.
Your employment agreement, contract, or university regulations will govern whether or not personal projects somehow become property of the university, shared property, or are kept entirely separate due to your use of university resources. Most universities actually want their researchers to pursue interesting ideas, but if you use their property, they want a cut of the resulting profits or an ownership interest in any intellectual property. In the US, the Bayh-Dole Act guarantees that inventions made through federally funded research can be owned by the grantee rather than the US government, and most universities pursue this ownership. I don't know if Israel has an equivalent law.
The ethics here are pretty clear to me. Don't use other people's property to make a profit without sharing the profit with them. The laws and regulations are local, so ask your boss, administration, etc. about the local rules.

by split ownership you mean 50-50? Because I agree that ethically the university deserves a share of the company / profits, but to what degree? Is it judged on a case-by-case basis or are there some general guidelines, to your knowledge? :-)

@Ant, patent ownership is the only thing I know anything about at my university, and that's a negotiated thing, but the default is 50/50.

Hi Bill, your reply answers a lot of the legal implications of something like this. Does your ethical viewpoint remain the same if you are an undergrad that pays money to use university facilities and does not partake in "official" research?

@Conor, my answer was in the context of employees and student-employees (grad students) who are under employment rules or contracts. My feelings on the ethics for non-employee students are more nuanced. At public universities in the US, tuition only covers part of the costs, so the taxpayer has probably contributed, too. I don't know how deeply to follow this idea (subsidized loans?). Universities typically have rules that cover students' work products too and are typically permissive. I'm certainly OK with that. Lots of startups come from uni projects. How much of Google did Stanford get?

Beside the concrete suggestions Bill made in his answer, which also specifically explain the situation in the U.S., you should discuss this with your head of department.
I know professors in Europe who actively encourage the use of university resources in certain cases where fresh doctoral degree holders create startups, for instance, or other creative somewhat professional uses, without trying to get any portion of the ownership or revenue. Expected benefits for the university in such cases include:

an increased visibility of the department's research
possible future opportunities for more research
simply the knowledge that the theoretical research is used in marketable products (which in turn can be presented as a showcase for the success of one's research when acquiring more funding)

Note that the respective universities generally do not try to "create products" or generate revenue from selling things. Their mission is to provide education, not to act as a business. As such, while lucrative activities are definitely welcome, there is little to no pressure that financial gain must necessarily be drawn out of each and every activity of the people at the university.
In general, though, do not use such resources without asking the person who is responsible for granting these resources in the first place. You may not negatively influence your own research, but, for instance, using resources of department-wide servers may still mean there is less capacity on those servers for other researchers.

This one is on-spot: (whether this is a printer, cluster or anything)

http://www.phdcomics.com/comics.php?f=1578
Bear in mind that many things which are accepted / ethical (or at least - not too unethical) may still be officially illegal (perhaps even printing directions to parties).

It seems this graphic largely misses the point. The graphic talks about clearly private, leisure-related uses. The question, on the other hand, talks about professional uses that are just not the primary research topic. As I've pointed out in my answer, I know department heads who are completely supportive of activities that could serve to broaden the professional horizon of their employees, even if they do not directly lead to research publications.

Also note that in some legislations, minor activities that do not overly impact work can be legally assumed to be permitted if they are "usual among the staff" and not explicitly forbidden. Not sure to what extent this applies to the target cultures the OP is inquiring about, though.

@O.R.Mapper Verbatim quote from the picture "Printing stuff for your side business". When it comes to the legal side - it varies a lot with contract, country, etc. BTW: My answer is by no means comprehensive - rather a short, humours (though not nonsensical) answer.

You're right, I must have missed that text. Though in that case I would argue that it is indeed the high volume (as indicated in the graph) that increases the risk of problems, whereas the fact that it is for one's own business can, depending on the arrangement, easily make it more legitimate to use the resources in that way than the private things such as directions to parties.


text:
How is a PhD student staying in their institution as a postdoc perceived by future employers?
I am finishing my Ph.D. very soon, with the only thing remaining is the thesis defence, which hopefully should go smoothly. My goal is to go into academia, so I started looking for postdoc opportunities. What I am looking for in this position is to have more publications so that I could eventually find a tenure-track position.
I recently got an offer from a university in a nearby city, and I was about to accept it. However, my advisor heard about this, and he suddenly wants to keep me as a postdoc himself after I finish. While I see some positives and negatives in both offers, I feel that there is a higher chance for me to produce publications if I stay with my current advisor. So I am considering staying.
I am just wondering that if I stay, will I be viewed in a negative light by future faculty selection committees, seeing that I stayed in the same place as a postdoc where I did my Ph.D. with the same advisor?

What is your country? In some countries (in small unis), it might be useful for faculty applications if you stayed all the time in the country (as you know local profs, language and procedures).

Did you change universities before your PhD? Other ways you've worked at several institutions?

I am in Canada, so that does not apply here.
Yes, I changed institutions three times in three different countries when I did each of the three degrees.

All bets are off in 2020. Whatever you do will be ok - you'll be able to explain anything away on the covid crisis

As someone hiring post-docs and staff members, I am leery of someone doing a long (defined as ~ >6 month) postdoc where they were a PhD student, particularly with their same advisor. Why? To me, the purpose of a post-doc is to have a clear demonstration that the new PhD can move into an at least slightly different area and rapidly come up to speed and be productive on something new. Staying where you are just means finishing up loose ends, whether correct or not. If in the 6+ month range, you've got some explaining to do to me in the interview.
I'm not upset by a few-month "postdoc" with their PhD advisor, finishing up things, as they are looking for the next position to come open. But a post-doc has to be something new - it is the time to show off your new-found abilities to learn and make progress. Why? Because that is what you are going to have to do for the rest of you career. You aren't going to keep doing your PhD project for the next 30+ years.
For my postdocs, what does showing off look like? We hand them a project, and expect that within ~3 months there should be progress sufficient for starting to submit abstracts to conferences. And then they get another new project to get going, with abstracts going out on it 3 months or so later. The point is that in the first year there should be conference presentations and papers heading out the door on the new work at my institution. They should have an interview talk based on that work. That is what a postdoc should look like, and what I look for out of their postdoc when hiring new staff members. And that does not seem to happen for a postdoc staying at their PhD institution under their PhD advisor - it is just too easy to wrap things up, not start new, well defined projects that are different.
I would like to add that for the next 2-5 years (or more based on what happens) I will be much more flexible with this. Clearly the pandemic is not going to help anybody's career trajectory, and the constraints on jobs, moving, and everything else will make life for grad students and postdocs far more complicated than usual (and everyone else, too). Still, choose wisely - what will make you better at what you want to do?

I appreciate the points you make and my point is about "ought" rather than "is", but I think that this view can be quite damaging for post-docs and PhD student (myself being one). The pressure for people to constantly move between cities and countries, uprooting their social support networks just to fufill some criteria set by senior academics who are likely very settled in their life frustrates me no end. Perhaps this should be considered more when people discuss the mental health crisis for early stage academics. This isn't a direct criticism to you btw, more at the system itself :)

@4galaxy7: I didn't see anything in this answer about constantly moving between cities and countries. The one move discussed in this answer is moving away from the influence of one's advisor and towards academic independence.

You are right - the poster answer didn't explicitly say it's necessary to move cities/countries, but a natural extension (at least in my country) of leaving your supervisor is that you need to at least switch cities, since it's unlikely someone else in the same institution will happen to have funding to hire a post-doc in the specific area. Anyway, this is just a rant and something I feel strongly about, and not suitable for comments, so I'll leave it there.

The numbers given are probably field-specific.

@4galaxy7 I see your point, but I don't think you should generalize your feelings to everyone. I'm also a beginning postdoc, and find the endless mobility is one of the nice features of academia and it also pushes one to grow as a person. Apparently, scientists can be either 'nerds' or 'adventurers' (https://www.nationalgeographic.com/science/phenomena/2011/07/19/the-four-types-of-scientists/) which is maybe what makes the difference. But anyway, the odds for tenure are so slim, that I wouln't make big decisions that jeopardize mental health to get there, if they weren't fun by their own.

I agree with the overall sentiment, but disagree with your numbers per my post below: https://academia.stackexchange.com/a/154723/22733

@Wouter Or maybe it's the stage in life of the postdoc. Postdocs are also asking their partners/families to move cities/countries every couple of years and partners of older postdocs are likely to have real careers. To say nothing of the massive visa and moving costs to take jobs that may be interesting and fun but don't really pay very well. Suggesting not to generalise goes both ways.

@JenB - indeed, I was single in grad school, so picking an overseas postdoc was attractive and exciting. Although, now as a (much) older married person taking a multi-year assignment overseas at some point is starting to look pretty attractive.

You aren't going to keep doing your PhD project for the next 30+ years.  At the same time, if you stick with a given research group, they're also not likely going to be doing the same things for the next 30 years.  The circumstances in each case will be important.  If you're staying on as postdoc with an institution because that gives you access to something like the LHC and your ambition is to continue to master that facility in anticipation of an opportunity at the upcoming FCC, then that could be a highly defensible choice.  Each situation will be different.

@JonCuster - for context, what field are you in?

@James - materials science, accelerators, pulsed power.

Publications

I feel that there is a higher chance for me to produce publications if I stay with my current advisor

One of the very best outcomes of a postdoc is publications. Academia is essentially built on publish or perish. All other things being equal, I would go where your chances of publication are the highest.
I would also explore options for collaborating with the PI overseeing the potential postdoc in the nearby city. Is there still an opportunity to broaden your network by doing some collaboration? Just a thought.
I have evaluated a few job candidates who have a postdoc. (I work in industry, not academia). I usually do not care where they did their postdoc. I care what they did. Generally speaking, I would much rather take a candidate with three publications with their old PhD advisor than someone with one publication at an institution different than their PhD granting institution.*
Network
One thing I will mention is the benefit of opening an entire new network of opportunities by going to a new institution for a postdoc. At my former PhD institution (call it U of X), most PhD grads end up in some low level academia position (community college, non-research teaching university, etc.) Networking was really tough at this university.
At U of X, I shared an office with a lady who had an opportunity to do a postdoc at U of X. She had published several papers with her advisor already and likely would have published many more. However, U of X has mediocre to poor faculty networking (a discussion for a different day. Long story short, when a department hires a bunch of their own PhDs as professors, it's not good for networking). She decided to leave to another institution for a postdoc. She only published one paper during her postdoc, it just happened to be a really good one. She now is a researcher at an Ivy League school. Her postdoc blew her networking wide open.
Be careful to examine where postdocs from both opportunities end up. Network matters a lot in getting your first "real" job. Do not compromise network for one or two extra publications.

*Do note that I would question a postdoc who did his or her BS+MS+PhD+Postdoc all at the same place. It might not be a deal breaker, but it would certainly make me wonder if there are some underlying issues.

"I would question a postdoc who did his or her BS+MS+PhD+Postdoc all at the same place" What if they were Ivy League, or some similarly prestigious school like MiT or Oxbridge?

@nick012000: Absolutely, and in fact perhaps more so, because I might wonder if the candidate was able to function outside a highly privileged environment.

General opinion: "Prestigious" has only a loose correlation with quality across many types of thing, but definitely for institutions.

@nick012000 If they were so great that they could do a PhD/Postdoc at Harvard, why not drive up the road to Princeton? It's not the quality of work I worry about here--it's the fact that they just spent the last decade plus at one institution with one way of thinking.

@Vladhagen what if they had family, friends and a house In Harvard and didn’t want to leave that behind them? It’s down to a lack of imagination that one could not find a better criteria to discriminate between candidates than whether or not they’ve stayed at an institution their whole career.

@4galaxy7 MIT is 2 miles from Harvard. Boston University is also right there. It's not like it's in the middle of Alaska or something. Sure, we can fabricate reasons for never moving. But what is this supposed candidate going to do when they don't get a job 1 mile from Boston? They'll move, just like all the rest of us when we get a job.

@Vladhagen "They'll move, just like all the rest of us when we get a job". A very American attitude to things like your center of living. Just beware that the same does very much not apply to large swaths of the rest of the world.

This is probably more a function of what you do and how you present it when applying later than anything. If someone stays because they have nowhere else to go it is a bit negative, but your description can be stated as a positive thing.
You are likely taking your current research further than you could otherwise. It isn't just the publication count, but the significance of what you can produce.
In a new position (in some fields) you will have constraints on what you can do, depending on the PI. Not so much in mathematics, perhaps, but more in some other fields.
I'd suggest that you can make it work either way, but think about how you present your choices when you move on.

People have lives, so hiring committees hiring tenure-track faculty should not be jerks about something like this. My mom stayed at the same institution for undergrad and PhD because she was a single parent (of me), and my father and soon-to-be-stepfather were there.
The point of a postdoc is to show that you can work more independently and establish your own research program. You can do that while staying at the same school. Just...do that.
It depends on the field, but in many fields there is no longer any expectation that you can do a single postdoc and then apply successfully for tenure-track jobs at research-oriented schools. (It shouldn't be that way, but it is.) In these fields, you'll probably be doing a second postdoc somewhere else anyway.
What matters is the quality of your work.

They should not be jerks..but are they? (In my experience, many are.)

+1 Even to an audience of jerks, the quality of your work may matter more than whether you moved for your postdoc.

This issue here is not staying at the same institution for a PhD after an undergraduate degree, it is staying at the same institution for a postdoc after a PhD.  The two cannot be compared.  And most people in academia don’t take “life got in the way” as an excuse.  Maybe they should but most don’t.

Clearly, there are some people in the community who will make judgements based purely on the fact that you have or have not moved institutions. However, I think that is not the real issue here. The more significant factor is that changing institution tends to provide opportunities to develop a broader academic profile and perspective. Thus, individuals who move around tend to gain a competitive advantage over those who do not, and come across as more impressive candidates in an interview situation.
Of course, this is a sweeping generalisation, and one can easily think of individuals who provide counter-examples in both directions. However, moving tends to provide a number of opportunities, including:

Change/evolution of research focus;
Exposure to new ideas, techniques and ways of working;
Exposure to different opinions on which problems are important in your field;
Access to a different set of resources;
An outsider's perspective on your former group's work, and its strengths and weaknesses;
Access to a wider pool of potential collaborators;
Opportunity to re-evaluate the projects and activities that occupy your time, and to have a 'fresh start'.

These will tend to have a positive impact on your overall academic profile, and help when you come to apply for jobs and grants. Thus, while there is certainly a short-term productivity cost associated with moving, in the medium/long term it pays off.
It is worth noting that most of the above benefits can be acquired without moving, if one makes a conscious effort to seek them out.

+1 to “ changing institution tends to provide opportunities to develop a broader academic profile and perspective”, which is what a good postdoc should provide.

I'll keep it short. At least in the UK I've never heard of it being seen negatively if you did a postdoc after your PhD in the same research group under the same supervisor. Most PhDs I know prefer to get a postdoc in the same group if they can. I also believe it's more efficient.

To bring a counterpoint to this perspective, in NA I've never heard of it being seen positively, although there some instances where it's not seen negatively.

It isn't necessarily seen negatively, but in many places it is seen as not having done a postdoc, just an extended phd. You may still manage to demonstrate the qualities an employer is looking for, but you need to be careful what you do during that "postdoc" so your application is convincing.

I am an example of somebody who did a postdoc in place, with the same professor and same grant.  In essence, I spent an extra year at my institution while I organized my job search.
Since the time leading up to one's thesis defense is often quite stressful and chaotic, a postdoc in place is a quite reasonable and normal option. Yes, it's preferable to be writing your thesis and searching for jobs at the same time, but that often just isn't an option for many and varied reasons. These are also often additional complicating factors, such as the timing of a partner's degree or other career steps.
Furthermore, since academia tends to work on an annual cycle, if your timing happens to not be well aligned with that cycle, it's easy to end up with a full year or so of gap.  For example, somebody who finishes and starts organizing their search just after the Spring hiring season completes could easily end up on 15 months of postdoc, from the end of the Spring semester to the beginning of the Fall semester a year later when a new position starts.
I would thus not be at all concerned about somebody who spends up to a year or so in a "transitional" postdoc.  Once I saw it stretching to two or three years, however, I would begin to be concerned about the ability of the person to be an independent researcher.

One of the most important things as a post-doc is to show the ability to work with different people and independence (both is best, either is good).
If at all possible, try to publish your papers which do not include your supervisor as an author -- these can be solo author, or with other people. It is OK if these are "lesser", the important thing is to avoid someone looking down your publication list and see one name which occurs as a co-author on every paper you have ever been involved in, which can set off alarm bells.

To my mind, it doesn't matter where you go but you do need to eventually demonstrate independence. Basically, it can be harder to do this with your own supervisor and it can also be quite difficult to shift from being a "student" to "collaborator" (for both of you actually). This said, I'm sure there are stacks of opportunities outside of the current supervisory sphere so if you stay then make sure your future network is not identical to theirs (overlap yes, but hanging off their coat-tails entirely as a postdoc will be viewed negatively). Are there small project funds or perhaps students you can supervise with someone else to demonstrate your broader network? My advice to PhD students is you need to work out the strengths and weaknesses in your CV. Then, pair with someone who compliments your research strengths (and hopefully compliments any research weakness - ie they are strong there) and have a frank conversation with someone you trust about how you make sure you are independent and your CV is as strong as it can be. This might be your PhD supervisor or another mentor (perhaps both).

I think it's important to remember that not all publications are equal, and your publication list is not just the sum of its parts.
You say that "there is a higher chance for me to produce publications if I stay with my current advisor". True, but the point is that hiring committees know that too, and may take it into account in deciding how much weight to give those publications, particularly if your advisor is also an author on them.
I'm not saying that moving is necessarily better, just that staying being the easier way to get publications isn't on its own a good reason to stay.
(By the way, I have never been on a hiring committee so don't speak from experience.)

It is difficult (but not impossible) to demonstrate that you are capable of independent research if you continue working exclusively or at least primarily with your former PhD advisor. It doesn’t mean you should burn the bridges with your old boss, but you should clearly establish that she or he is no longer in charge of your research agenda.
You could demonstrate independence by developing other collaborations, but then why stay in your original group?
A successful transition to another group or institution is always advantageous over continued success with your former PhD advisor.

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