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What should you do if you spotted a non-trivial error in a highly cited paper?
I have seen question on here regarding a citation error in a paper here:
What should I do if I found a citation error in a published paper?, but the nature of this problem is very different.
Basically, I came across an error in a paper (call this error 2).
I have previously contacted the author before regarding a different problem (call this error 1, say) in this paper, and I got no response. (That was what I still believe to be an unproven proposition, and is actually also related to this problem.)
The reason I decided to ask here this time is the following:

I am highly confident about error 2.
Its correctness has a direct impact on my current research.
The mistake cannot be easily fixed. (At least it appears to me, for the time being). I have spent months on a related problem before revisiting this paper and realised that I have tried this same technique in problem, which did not work in my problem, which led me to check why it worked in his paper - and it turned out, it did not.
The result was probably the first/the only result of its kind in the literature and the paper is fairly important with 150+ citations.

What should I do here? I have previously contacted the author and I have no reason to believe he would respond this time. I want it to be correct/easily patched because of reason 2. This paper was published in 1997 so it has been a while....
EDIT: Precisely for reason 2, I would much prefer some way of getting the author to respond.
EDIT: I had a discussion with my supervisor. He immediately agreed with me it was a mistake. The thing is when we tried to use a similar technique for a different problem, we fell down the same trap about 10 times. At the moment, we have no fix and the mistake is serious enough that it takes away a lot of credit from the paper.

Can you link the other question? Also, it is at times difficult to understand which error you are referring to.

If it is a substantial correction of an important paper (that you can also prove / clearly show), you may just want to write an answer paper yourself. This paper would start off by summarizing the core message of the original paper (plus reference, of course), then you would explain what is wrong, and conclude with what the important implications of the error are.

It also seems to me like you assume that papers work like books, where you contact the author or editor about any errors, and they will fix them in the next edition. Research papers are usually written once and never updated.

@xLeitix I very much doubt it would be worthy a publication on its own because a correction would mean I can do my own research and just put a note in this paper to point out the mistake - what do you think about this? Anyhow, I would much prefer getting some type of response from the author because it'd save me a lot of trouble because of reason 2.

Write up your own paper. Seriously.

Contact the journal and tell them about your finding, and if they don't respond then enquire regarding it, and try to push the journal for a correction.  Is there any benefit to keeping it a secret? If not then perhaps you could even ask on a stackexchange site related to your discipline.  You could even contact some authors that cited it, and see what they think

Can you patch the problem yourself ?

I would say: 1. clearly show the error(s) 2. fix the error(s) -if you can- 3. Upload it to Arxiv titled: "On the X of Y". where X is the error name and Y is the problem. Then email him/her a link of the paper.

You say that the paper got 150 citations. Any sign of someone spotting the problem you're talking about in those papers?

Also, if you don't succeed in contacting the author directly, you can try to put together the formal written understanding you have as others recommend, have your supervisor approve it and then maybe contact the editor of the journal explaining that you have difficulties to follow the argument (see attached paper) and politely ask them whether they could put you in contact with the author as you did not succeed in doing so.

In geometric topology, Thurston, Gromov, Perelman all were notorious for giving sketchy/occasionaly incorrect proofs of correct ideas. They knew the right method and didn't always bther with details. Many times it is just known in the community that the original paper had a flaw, but that there is an easy fix.

@PeteL.Clark I disagree with the addition of the mathematics tag - the question itself is general (even if the OP is in mathematics), and the answers represent a broad spectrum of fields (and I think that's how it should be. We don't want to answer this question again for CS, and again for physics, and again for biology, when there is a nice range of answers right here.)

@ff524: I was asked to add the tag by Piotr Migdal.  Perhaps it was a mistake.  However, I think that asking the question again for different fields would actually be a positive development, since the answers will be different in different fields.  Some of the answers here do not specify what fields they apply to, and thus seem to be bad advice for the OP in particular.  So if adding the mathematics tag means that answerers will clarify the scope of their answers, that seems like it would be a positive development.

@PeteL.Clark I think the answers to this question cover a broad range of fields; if someone feels none of these answers covers their field, they could offer a bounty on this question and specify what they are looking for. I also think the new tag makes the answers that are not about mathematics look like they don't address the question, which is unfair to people who wrote those answers.

@ff524: "[I]f someone feels none of these answers covers their field" What concerns me is that an inexperienced student may well have trouble understanding whether the answer applies to their field or not: that's much of the point of asking this kind of question.  When the standards vary so wildly from field to field, I don't think an answer which does not identify the applicable fields could possibly be a good answer to this question.

Do you think that including the tag "mathematics" means that only answers about mathematics are relevant or desired?  I don't interpret it that way; I interpret tags as clarifying areas of particular interest to the OP rather than excluding other answers.  But maybe others see it differently.  Anyway, at this point I believe the OP has seen the tag change on the question so I would prefer to leave it up to him/her.  Perhaps you could inquire as to the OP's intent...

@PeteL.Clark It's good that your answer does specify the field it applies to. But I don't think the way to address this concern is to add a tag to a question, effectively changing its meaning after it already has many answers. It might be better to comment on the other answers, indicating that they should specify what field they apply to, and take the "mathematics" tag off.

@PeteL.Clark I think the OP's intent is not necessarily relevant at this point - once a question has answers, the OP shouldn't edit the question in a way that changes its content, either. Even if the OP's original intent was to ask about mathematics, that wasn't the question that was asked (use of the work "proposition" notwithstanding)

@ff524: I'm not sure I agree, but I don't really have strong feelings about it.  It is not my intent to be exclusionary, so I removed the tag.

@Lost1, so, any update about the status of the error? Was it really an error? How was it fixed?

The main answer to your question is easy: talk to your advisor.
I find it a little curious that you have not done this already.  As a graduate student, you read a very famous paper (in mathematics, more than 150 citations is a very large number) that was written a while ago, and at the first sign of trouble you contacted the author of the paper.  That is already a little strange: although both are possible, the probability that you, a relatively young graduate student, have misunderstood something in the paper (or are applying standards that are different from those of the field you will be working in, or some other similar issue related to the fact that you probably do not yet have expert level knowledge and experience in this field) is higher than that the author has made a serious mistake.  Writing to someone that you don't know at all and who is much more senior than yourself and pointing out a mistake is not without risk: the risk is that you will be wrong and they will dismiss you in the future as a less than serious person.
Your advisor is there exactly for such things: she is the person who is helping you transition from a neophyte to a journeyman to an expert, and she needs to see your mistakes and flawed reasoning in order to do this properly.  Some outside expert really does not: they can wait to see the finished product that you become.  Moreover, you are presumably reading the paper because your advisor wants you to, perhaps even because she directly told you to read it.  Therefore a mistake in the paper is your advisor's problem as well as yours.  Why are you holding that information back from her?  You shouldn't.
Having said that, I feel like the OP is getting a fair amount of advice that would be more appropriate in other fields than mathematics.  Especially:

In mathematics it is very difficult to write a paper whose sole or even primary purpose is to point out a mistake (even if it includes a correction) in someone else's work.

This is a cultural reality of the field; it is certainly not entirely positive.  In many other academic fields, one can "score points" by pointing out others' mistakes, and in some fields this is one of the best ways to score points.  Mathematics is not like this: if you can get such a paper published it will "take points away" from the author and give you a certain amount of notoriety, but if this is for instance your first published paper then many people will look at you strangely, almost as if they expect you to make further trouble.  (Again, I'm not endorsing this cultural practice; I'm just describing it.)
Similarly, I would say that contacting the editor of the journal in question is maybe step 10 of a procedure that is mostly designed to terminate after one of the first 9 steps.  You should do this only after you have exhausted every other possible avenue.

In mathematics -- very much unlike in some other fields -- it is prohibitively unlikely that an editor will publish any "commentary/correction/erratum" by you unless she believes that you are mathematically correct in the point you're making, and convincing someone with standing in the field like a journal editor that you are mathematically correct is largely what you're trying to do anyway.

Finally, while I barely know what a white paper is and to the extent that I do I'm not sure it's the appropriate terminology here -- in content I do agree with @eykanal's suggestion: it will certainly help your advisor if along with communicating the surprising news that Famous Paper X is wrong, you can supply a written version of your arguments.  This can be hard to do: explaining why a difficult argument is subtly wrong is one of the sternest expository challenges in mathematics that I can think of.  It takes a lot to go from "I don't understand the argument and find it rather unclear" to "I am convinced that it is wrong."  By the way, in writing to an author it is a good strategy to err on the side of the former quotation.

Very well put. I'd reiterate the point(s) that a neophyte's not being able to follow an argument is not good evidence that the argument is wrong, or even that there's a gap, and that a neophyte should consider the very large possibility that by whatever "expert standards" the paper is fine. Or has known reparable errors. Or pointlessly mis-states things which are easily corrected by experts. So one should talk to an in-house, sympathetic expert.

what you said is really good to know. I have updated the question to include my discussion with my supervisor. The mistake is a blunt 1st year analysis error but there is no easy fix to make it correct. I am a little concerned about what you said after 'mathematics is not like this'. And oh when I contacted the author the first time round, I already had a discussion with my supervisor and he could not see why something the author claimed was true. While I had my doubts, this time I was pretty confident. (else I would not have written here)

@Lost1: I'm very glad to hear that you've discussed this with your supervisor.  If s/he agrees that there is a serious mistake in a very famous paper, then surely s/he will take the lead role in dealing with the problem?

we are trying to solve it. :) I think I will leave him to decide how we go around making this known...

@Lost1: Sounds good.

Personally, I'd run it by at least three experienced practitioners before assuming that there is an error. Occam's razor suggests that if you're the only one to notice it, the mistake is probably (but not necessarily) yours; repeating the test with others will help check that (a) it's real, (b) it's significant, and (c) it isn't just a printing problem but actually carries through remainder of the paper. AFTER making darned sure of that, by all means bring it forward.

There's quite a lot of unfounded doubt being directed at the OP here and relatively little at the problem the OP proposes to deal with. I agree that it's good to preach caution when considering a critical confrontation with another researcher, but there are ways to approach it that aren't designed to self-censor or "terminate before step 10" with no further action taken. Be careful not to preach self-doubt and tacit acceptance of the published status quo. There's too much self-doubt in academic culture already, and no shortage of reverence for the establishment regardless of its actual merits.

@NickStauner The thing is that we are speaking, almost surely, about a math paper, and math is different.. There are no shades of grey, and no place for interpretation. A proof is either true, or wrong. And if a proof in a paper is wrong, it is extremely unlikely that 100+ people which are doing research in that area read it and don't find the mistake... Not to mention that math research is like building a house of cards, most of the times if something goes wrong, everything above falls down fast... 150 citations means 100+ pieces of research build over it, chances are not that great ...

that so much research was build over shady foundations and nothing went wrong. Yes, it is not impossible. But don't forget that math research is different than all the other areas, which also means that the rules are different... Last but not least, because math is different in this way, if something is wrong, you can easily prove it wrong. Again, there is no shade of grey, and no interpretation.Which means that the moment one goes confrontational, one of the two parties is made a fool. So a little caution doesn't hurt, and  one should make first sure he doesn't end the fool before starting.

Good points Nick S! (I wish I had more opportunities to say that without sounding boastful and loony.)

@Nick Stauner: I am not suggesting in any way that the OP censor himself or accept the status quo!  My answer gives the best strategy I know for (i) determining whether the error is genuine and (ii) if so, getting it publicly acknowledged and, if possible, fixed.  I also I did not "preach self-doubt": I advised self-vetting, which is an entirely different and more productive thing.  Your comment seems to miss the point of my answer.

Okay, that sits well enough with me. Just concerned about perceived implications; glad to be told they were misperceived. Cheers!

@Nick: OK, no worries.

Writing comments papers (I have written a few) is not (or at least should not) be about "scoring points", it is a fundamental part of the self-correcting mechanism of science.  The point of it is to prevent others from being mislead by mistakes in existing papers.  Highly cited papers (or papers that get interest from the general public) that contain serious flaws need to be discussed and corrected.  Note that new researchers may not have the experience to see the error for themselves and waste their time following a flawed idea.

@Dikran: Everything you wrote is consistent with what I advised, except: in mathematics the corrigendum/erratum is written by the author of the erroneous paper, not by the person who pointed out the error.  So when you speak of "writing comments papers", I am guessing that you are referring to papers written in a field other than mathematics.  Is that correct?

Yes, I was principally thinking of subjects other than maths, however viewing this activity as being about "point scoring" has negative connotations that are unhealthy to science (and mathematics).  At the end of the day it ought to be about getting the science/mathematics right.  I'm not sure the idea that the original author writes the corrigendum is such a good idea either!  In my experience there are no points for anybody in writing comments papers, it is just something that is necessary where incorrect papers generate substantial attention.

@Dikran: Thanks for your answer.  You say that you were "principally thinking of subjects other than maths", but you didn't directly address whether any of the "comments papers" you have written were in mathematics.  I agree that viewing error correction as being "point scoring" is a potentially unhealthy practice.  However there are definitely some fields in which points are gained this way: this is especially common in the humanities.  In philosophy, if you are famous enough you get entire books of "comments papers" about your work...to which you get the chance to comment in return.

Viewing "comments papers" as valuable research in its own right does at least create an incentive for errors to be revealed, which is a positive thing.  In some ways the prevalent mathematical culture is not so positive...."I'm not sure the idea that the original author writes the corrigendum is such a good idea either!" I agree, and I hope my answer made that clear.

The statement I was referring to was " In many other academic fields, one can "score points" by pointing out others' mistakes", so my comment did not pick out mathematics as being any different.  My comments papers are in Machine Learning, Chemistry and Paleontology (statistical aspects of).  There doesn't need to be an incentive for writing comments papers, it ought to be just an everyday scientific activity in the same way that peer review is.  Both are important elements of quality control in science.  The real problem is that journal practices and pressures on scientists to publish ...

... mean that more bad papers get published and we have less time to spend writing comments papers than used to be the case.  Add that to the proliferation of low quality journals and we have a system where comments papers are very badly needed!  I've often suggested (tongue in cheek) that it ought to be a requirement of PhD students to write a comment paper as part of their scientific training.

@NickS "if something is wrong, you can easily prove it wrong,"  not at all.  Falsifying a proof can be at least as difficult as the (allegedly) failed proof, which can be notoriously difficult--difficult enough that many experts for many years fail to notice and acknowledge a flaw.  I've known cases--which sadly I now forget details of the specific authors/results--where possibly decades after  a major paper is published, someone comes out and publishes a claimed counterexample.  And for many years nobody can figure out which one of them is actually wrong!

I would do the following:

Write up a rigorous white paper demonstrating the issue. This should be your first step, as putting the idea to paper will help you think of aspects you may not have thought of yet. If you can successfully convince yourself in a written paper that this issue is valid, then...
Present the white paper to your advisor. This has numerous benefits:

Your advisor will critique your writing, which is always a good thing; you will become a better scientific writer.
Your advisor can provide specific feedback on specific aspects of your argument by simply referencing what you wrote and providing counterexamples. This will make the process of convincing him that there is a problem much easier.

If you can sucessfully convince your advisor that the problem exists, then it's time for..
Work with your advisor to reach out to the author. Working with your advisor will significantly increase your chances of success. You may also be able to progress to
Write up your findings in a letter or article of your own, depending on the nature of the issue.

Do note that you state that this paper has been reviewed and cited many times. While it is possible that you have found something everyone else has missed, your ideas will need to be iron-clad before anyone will even listen to you. I would spend the most time right now making sure you haven't made a mistake before reaching out to the author.

Related: What is a white paper? (i.e., don't assume everyone knows this).

Ask someone else - your age listed in your profile suggests that you're a grad student. Have you talked to your supervisor about this? Even better, do you know someone in your own department that has collaborated with the paper's author?
Put yourself in the author's shoes. He's probably bombarded with emails all the time from grad students he's never heard of, so unless you've collaborated before then he may not even read your email. An email from your supervisor or one of the author's collaborators is much more likely to get serious attention.

I will talk to my supervisor today. I actually thought about asking this after this the meeting. Your suggestion is helpful. I am not sure if anyone in my department collaborated with him before but there might be someone who knows him.

After talking to your supervisor, you might want to do some research on the authors.  It's common in some fields for the last author to have supervised the first author, who may have moved on. It's perfectly possible that the first/corresponding author's email address as listed, or even as looked up online still exists but isn't used any more.  Some fields have statements about which authors did what in the paper. It may then be worth contacting the supervising author if there is one.  You may get further with them anyway - if it's 1 of many papers for them, the top paper for the lead author.

Let me share my personal experience in a vaguely similar situation: Back in 2007 and within a couple of months of publication I spotted a huge mistake in a paper published in a journal that used to be A class but is more like B class these days. I wrote a proof of the error, showed how to correct it, and sent it to the journal. It took over one year of back and forth between the editor and I to get him to admit he had published a profoundly incorrect paper and to publish my "Comment": but I'll say that I probably got lucky that he admitted his error, got lucky that he cared to correct it, got lucky that he read my correspondence, etc.. If my experience is any indication, it will be very difficult to get across to the editor(s). At some point, about 6 months into the exchange, when it was clear that the editor was assuming I was in the wrong (he never read the math bits), I wrote to another editor and asked him if he thought I could damage my reputation by insisting so much, and he told me not to worry and go ahead on the quest for truth (but there was nothing he could do to help). The bottom line is you will hurt several people's pride and could make some enemies. I personally couldn't care less, but I'm atypical. And if you looked at my career, you'd probably think twice about upsetting the editors of an influential journal. Whatever you do, all the best!

I agree with Moriarty entirely. The first step is to get independent confirmation that there is an error.
The second is to judge its severity and how it impacts on the conclusions of the paper.
The third is to contact the authors directly and perhaps ask them to list or fix the errata on their homepage and on any pre-prints.
Mainly my answer is to introduce the fourth option. Many journals allow for publishing reviews, comments or corrections on papers that have already been published. Here's an example of this in a reputable computer science journal (TKDE). Particularly if the paper is highly cited and the error underlines grave concerns about its contributions, this option is recommendable.
If the journal does not allow corrections, you may consider writing your own independent "correction" paper instead (as others have suggested), but this way, you may be expected to present new results, not just pointing out errors.

But again, like Moriarty, I would highly recommend that you get the advice of a more experienced researcher, in particular before engaging in the fourth or fifth option.

The answer may be field-dependent, but in theoretical physics it is: write your paper. If the error is non-trivial, showing why something not works (or an counterexample) may be valuable. The same thing if the error is relatively simple, but most people are not aware of it.
Sometimes a critical flaw in one paper gives raise to a new field - see How the No-Cloning Theorem Got its Name
by Asher Peres (or for a longer story, How the Hippies Saved Physics by David Kaiser).
An erroneous paper (with an error being non-trivial at this time) resulted in the non-cloning theorem, and later - quantum cryptography, quantum information etc. The error (assumption that a machine could copy any quantum state) could be addressed by a few lines of an elementary  proof there no such machine could exist.

Did the OP say that he was writing a paper?

@PeteL.Clark No. So here is a recommendation to write a paper pointing the error.

In my answer, I specifically explained why it is difficult for such a paper to get published in a mathematical journal.  The OP will almost certainly get no "credit" for identifying the error.  If the error is genuine, then it is likely that the journal will publish an acknowledgement of this written by the original author.  Setting this process in motion is much easier for someone with experience in the field and contacts with the editorial board, such as the OP's supervisor.

In view of all this I don't understand your recommendation that the author try to publish a paper pointing out the error.  Have you ever published such a math paper yourself, or do you know someone who has?

@PeteL.Clark The question, as it stands, is not explicitly about mathematics (and I am not a mathematician). Is the example I cite not sound enough? Your answer starts with "The main answer to your question is easy: talk to your advisor." while OP explicitly says that he is in contact with his advisor (I totally agree that for a newcomer it is harder both to identify the error and react accordingly). Sure, usually there is little credit for it.

The example that you cite is with respect to a different field from the OP.  If your recommendation is meant to apply to someone with the same general question of the OP but not specifically to the OP, it would be helpful to indicate that, because in this instance what you recommend could actually be detrimental to the OP specifically.

@PeteL.Clark: There are plenty of statistical publications that point out others' errors. Have you never seen such an article in mathematics? Here's one in mathematical statistics, in case you haven't. Close enough, no? (It's a good read BTW, not just a handy example.) Another precaution: encouraging someone early in his/her career to hand off major project responsibilities to others without strong justification can be just as detrimental to career advancement as taking chances by critiquing others. What if he's got a genuinely good critique?

@Nick Stauner: To answer your question: no, I do not regard the paper you cite as a mathematical paper.  I just checked and it is not archived in MathReviews/MathSciNet, the online repository of all math papers.  Statistics is a different field, very close to and sometimes overlapping with mathematics, but with different cultural practices, so the answer to your question "Close enough, no?" seems to be "No".

"Another precaution: encouraging someone early in his/her career to hand off major project responsibilities to others without strong justification can be just as detrimental to career advancement as taking chances by critiquing others."  Nothing that I advised the OP to do is evading responsibility in any way.  I asked him to talk to his advisor which he did, and to check in to see that the advisor helps to get the problem identified.

If the error turns out to be genuine (this is still not clear, of course) then some kind of erratum will be published, and the OP will get acknowledged and thanked in it for pointing out the error.  Compare: http://www.integers-ejcnt.org/j32/j32.errata.pdf.  But note that I am not the author in the above link: that's how mathematics works.

To answer your question more directly: no, I have never seen a published article in a high-quality mathematical journal whose sole goal is to point out an error in someone else's work.  Very occasionally I have seen preprints uploaded to the arxiv doing so: the implication here is certainly that the author of the preprint tried and exhausted more conventional avenues first.  So you should be aware that you are recommending something that I (a 2003 math PhD) have really never seen done in my field.

@PeteL.Clark Interesting; thanks for the elaboration.

@Nick: I agree by the way that the paper you linked is unusually interesting.  It is written by some eminent people (including mathematicians, yes) for a rather noble purpose: more like public service / debunking than any attempt to garner "academic credit" in the conventional sense.  I would be interested to hear from a statistician whether this is in any way a typical statistics paper.  I would guess that it is not.

@PeteL.Clark OP's field is irrelevant for answers as it is not included in this questions (I know that looking up OP's profile says mathematics; but even the direct link from question's content leads to an example in... biology).

@Piotr: The question refers to an "unproven proposition", which is a big clue as to the field.  I agree that the question makes sense when applied to other fields, and I agree that appropriate answers may be very different.  To me, all this suggests that one should include information about the field in one's answer to the question: when the answers are not field-independent, it is worthless (or worse) to pretend they are.  In particular, the first sentence of your answer is written as an imperative to the OP.  The actual field of the person whom you are commanding is highly relevant, I think.

@PeteL.Clark I agree that answer may be field-relevant, and should not be too general. But physicist also do prove things, so unless word mathematics is in note of title, content and tags, it's confusing. So to make this thread useful for others (not only OP) I suggest adding in title and tags "mathematics" (could you edit they question accordingly?). While all of links in my answer are directly related to physics, I can make it more specific (see the edit).

@PiotrMigdal I disagree with adding the mathematics tag - the OP did not ask a mathematics-specific question (although it's reasonable that the mathematics-specific answer was most relevant to OP) and I think it's good that the answers cover a range of fields.

@ff524 It is a tricky thing on Academia.SE - sometimes answer is discipline-specific, sometimes - is not (and OP usually does not know). If it is, I strongly suggest editing questions accordingly. Otherwise it is hard to make it usable to others (e.g. having the same issue in other fields), both in terms of reading this thread and asking a new question (which may be easily closed because they are duplicates, supposedly).

@PiotrMigdal I agree before there are answers. But now that we already have answers for a range of fields I disagree with making the question more math-specific than it was as originally stated.

@ff524 I agree that now it will make more, not less, confusion. But it this case I shouldn't be criticized by Pete L. Clark for providing an answer for a different field.

@PiotrMigdal I agree with that, too, and I think you should ignore Pete's criticism in this case :)

(Added later: I upvoted this answer.)

My advice is pretty much the same as everyone else's: talk to your advisor, go over the suspected problem point with him; if there is no resolution, reach out to others in the department (your advisor should do this).
Having said this, I'd like to relate a few incidents from my own experience. As a graduate student, I independently discovered a result in number theory that did not appear in the literature. I was unaware of the significance of the result, but it came up in discussion with my advisor. He informed me that Professor X had found this result, but had never published it, and that I should not publish it, thereby "scooping" the (world-famous) expert.
While working with my second advisor, in a different area, I read a paper by a major player in that area who had developed a widely used technique. I mantioned to my advisor that there was a point in the proof of that technique that I didn't understand and he told me that no one understood the proof, but all assumed it worked.
Many years later, I now work in a different area. But while I was getting started in it I ran across a theorem in a book by a well-known expert in the field. What it said contradicted other things I had read. Not fully trusting myself, I reached out to the author who acknowledged that what he had written was not correct. He was very grateful for the correction and saved it against the advent of a second edition of his book.
Finally, I wrote a paper which contained an error, an error I should not have made because I was familiar with a counterexample to the statement I made. No referee caught the mistake, and only one person ever wrote to me about it, and I am very grateful to that person. Everyone reacts to these things differently, but I did not take offense at the correction. Granted this situation is a bit different than yours, because the correction came from a well-known source, and not from a graduate student. I would like to think I would have been equally accepting if the correction came from a student. I was embarrassed to be corrected by an expert, whereas I might have been peeved to be corrected by a student. However, were it you who wrote to me, you would never have known my reaction. I would have thanked you for pointing out the error, and perhaps have apologized for making it. But that's just me, and I'm far from well-known in the field. So, I have no idea of what my more famous colleagues have to deal with on a daily basis. The paper in question has never been corrected to my knowledge.
As I said, everyone reacts differently in these cases. Work with your advisor. The most important thing for you is to determine if there is indeed an error in the paper, and, if not, to understand why the paper is correct so that you can move forward with a correct grasp of what the paper established.

Chris, you are describing a real dark side of our profession.  The fact that you can, if you are sufficiently famous or connected, somehow "get credit" for merely announcing the proof of a certain result (or sometimes even a program for proving a certain result) has always been maddening to me.  When the manuscript appears a year or more after the original announcement, I really worry about the ethics involved, and I think this is bad for the profession.

Pete, as far as I know, the result never saw the light of day. I'm not even sure it passed into the folklore, but I've been out of that loop for some time. What galled me most is that it is not uncommon to see things like "this result was established independently by X and Y." A citation like that could have had consequences for my career and confidence. What was also disconcerting was that my advisor knew the expert, and even invited him to our school for a colloquium. I got to meet him. He was a genuinely nice person. A little mediation on my advisor's part could have helped. Oh well.

Since I happen to be a number theorist, I am curious about the result.  I would understand if you didn't want to disclose it publicly, but if you don't mind...

Pete, This is going back almost 40 years. I don't remember what it was with any specificity. I was working on trying to find minimal models of Hilbert modular surfaces at the time. I believe I still have the notes on it. Next time I get to my office, April 23-24, I'll try to remember to look it up (I'm on sabbatical this semester). I know how to get in touch with you.

If you can give all the relevant details in a reasonably concise way, then it may be appropriate to ask a question on mathoverflow.net.  I would strongly recommend that:

You prepare your question very carefully, and review and revise it several times before posting to ensure that it is as clear and complete as possible and correct in all details.
You phrase your question as "I do not see how this can be correct, please explain what I am missing" (even if you feel very sure that you are not missing anything).

If your problem is in an area that is well covered by mathoverflow, then this should be effective.  Either someone will explain what you are missing, or the relevant experts will become aware that you have uncovered a genuine problem.

I think this could be a very efficient way to resolve the issue.  Let me say though I that I think the OP and/or his advisor should at least try to write to the author first.  The OP mentions that he wrote to the author once before about an "unproved proposition" in the same paper.  To me that sounds very different from a serious error.  I think the author deserves to hear about the mistake first.  If s/he is unresponsive, than MO sounds good.


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How to deal with different stylistic advice from two professors/institutions
I'll start by sketching my situation. I first studied a couple of years at institution A where we were taught a couple of things concerning academic writing. (E.g. don't use passives, distance yourself from your work.) After that I did another bachelor's at another institution B (same field, same country, other city). Even though we didn't have a course dedicated to academic writing there, the promoter of my bachelor paper taught me not to distance myself from my work:

You did the research, and not some leprechauns, right? People should
  know that you did all this -- it didn't happen magically.

However, after my bachelor's I returned to institution A where I am currently going for my master's. The thing is: even though my grades for the first semester were good, I received feedback from different tutors and professors that my work is too personal and that I should use more passives to distance myself. This is completely the opposite advise my promoter at institution B gave me. Normally I would just go with the advise of the current institution, as that's where I am studying now and I don't want to challenge their style. The problem is that the promoter of my master thesis is the same professor as the one who promoted my bachelor paper. He changed institutions the same year that I went from institution B to A and of course he wants me to write from a personal viewpoint - whereas his (new) colleagues advised against that.
Tl;dr: promoter tells me to follow one specific (personal) style of writing, but his colleagues and other of my professor seem to like a non-personal approach better.
Note that this question isn't restricted to the distinction between personal vs. distanced/distant academic writing. I am interested more in the situation itself: what should one do when his or her promoter advises for A when the institution's approach is the contrary?
A promoter here in Belgium is a professor who is your supervisor when writing your bachelor paper or master's thesis. He or she is typically very knowledgeable about the topic you are writing in. In the process of writing your bachelor paper or master's thesis you can ask him or her questions related to your topic. Not only that, I have found that you can basically ask him or her anything related to academics - as long as it's morally and socially acceptable. He will also be the one will grade your thesis at the end of the year - possible together with a jury. The problem thus occurs that in my case this person gives me advice for something, whereas other authorities in the same institution seem to give advice against that. Since he is the one who will have to grade my work at the end of the year, I'm not sure whose advice I should follow.

Sorry, cultural context question: what is a "promoter adviser" and what do they do? I'm in the US and have never heard of this title.

What style is used in publications by top researchers in your field?

@Penguin_Knight I appended a clarifying paragraph.

Is there any work which you should write which is judged from both professors?

The first thing you need to do is determine if there is an underlying issue with your writing that A and B are trying to get at. If there is, fix that problem and the style issues may be ignored. If it truly is a style thing, you need to talk to them and explain the issue. If one supervisor demands that you never use the passive voice and instead write in the 1st/3rd person and the other supervisor demands that you never use 1st/3rd person and prefers everything in the passive voice, then somebody is going to have to give.
Once you determine it is purely stylistic, you need to decide which style you want to write in. This should probably be influenced by the recommended style of whatever journal/publisher you are targeting and/or any archaic rules your department has about theses. Then approach whoever you are agreeing with, get them on your side and finally explain to the other person the approach you are going to take. They might have a good counter argument or they might give up.

As far as I know, the promoter is the principal supervisor of your research. Hence, it wouldn't be a good idea to go against his advice. On the other hand, every institution has it's own style and norms which you are expected to follow. since your promoter is new to this institution , it is possible that he is not yet well-versed with these norms. One idea is to very mildly and casually inform him that you have got this kind of feedback and see what his response is. If you wish to play safe, you could perhaps choose a middle ground and use a balanced approach, neither too personal, nor too distanced.

It sounds like you are getting contradictory advice about whether you should write in the passive voice or the active voice.  This is a perennial issue in scientific writing.  In my opinion, it does not really matter which voice you use.  Since the goal of academic writing is typically to publish in a journal, I recommend looking at the journal's style guide or editorials for advice.  For example, PRL clearly advises writing in the active voice.  If the journal does not give advice, check some recent papers in the journal to see what common practice is.  Sometimes, I change the voice based on the goal.  For example, in the introduction to a paper, I want to show that I have significant results, so I write in the active voice to show what I did.  In the methods section, it does not matter who performed the experiment so I write in passive voice.
You also have an interpersonal issue here where two people have given you contradictory advice.  I suggest informing the faculty that they are in disagreement and asking them how you should handle the disagreement.  Most likely you will find they do not care very much.

"Since the goal of academic writing is typically to publish in a journal" - As the question is about a master thesis, I am not sure the very text being written by the OP is supposed to end up in a journal.

"Since the goal of academic writing is typically to publish in a journal, ..." Damn. I thought it was something about communicating ideas and sharing information.

On the one hand, you should inform the supervisors of the disagreement—in particular, the promoter, who hopefully can navigate the disagreement and the review system. You might have to stick to different styles in different contexts, though that's hard.
Unlike others have said, this is not just a matter of convention. I'd say that, given certain assumptions, your promoter is right and the others are wrong (but I don't care about other assumptions). I don't suggest you present things this way to your professors though ;-)
Banally using passive to distance yourself typically removes information and
confuses the content: "A program was written to evaluate claim X"
contains less information than "I wrote a program to evaluate claim
X" (who did the work?), and is clumsier. "A program was written by me..." seems clumsy and not distant at the same time.

More in general, this is just one example of a wider conflict between different goals in writing. You can show off you're smart by writing hard-to-read texts: this can be easy or not, and requires more work for the reader. Passive fits there. Or you can show off what you did by actually explaining it well (which isn't easy): this requires more work from you, saves work for the reader, and it might prevent misunderstanding. Since readers live in information overload, the second can be more effective to have people read what you did.
In English you have a choice, also depending on the discipline, but good writing advice suggests reducing work for the readers — that's especially true in Computer Science research (at least at top publication venues). Other languages have different traditions and underlying values.
My recommended writing guide is Williams's Style: Toward Clarity and Grace — the first chapter discusses the conflict, the others teach writing and revising for clarity.

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What kind of design freedom can you permit yourself in academic writing?
In scholarly journals, or publicising in certain magazines you are expected to hold true to a certain design pattern and citation style. However, when publishing your own work independently you are free from those constraints, or are you?
I am a designer by heart and every couple of years I create a new template that I use for future academic papers, following contemporary design patterns. In my opinion, my templates look nice. Not too strict, though flirting with kittenish. I am convinced that a nice design leads to a fruitful first impression. However, I am aware that this might be very subjective.
My question is, then, do academics generally look down on "design hippies" and should all retain a strict - possibly even chippy - style? Or does all of this matter not as long as everything is legible and well-formatted?
I use hand-written, cursive fonts in informal paperwork all the time. That's why I posted this question: even though certain fonts are well-suited for distinguished forms of design and publicity (such as magazines or webdesign), how does a formal academic world react to such patterns. On a (possibly less formal) website, for instance, Pacifico would be used without question. Of course, an academic audience is an 'ole other bunch all together. That's where my inner designer and outer academic struggle with one another. Should we stick to the trusted, formal (and, let's be fair, boring) style, or can we go a little (just a tad!) crazy? Note that I'm not strictly talking about fonts. It can be anything, going from structure (column layout), to colours and highlights, to bold face and font families. Heck, maybe even illustrations!
Update: people in the comments seem to focus a lot on the fact that I mentioned Pacifico, a cursive font. First of all I should clarify that I only brought it up as an example. Secondly, I only considered that font as a candidate for large headings with a font size of 24pt or larger - which increases readability. I did not imply to use this particular font as the main typography for my text, but merely as a means for catching titles. I'd also like the emphasise - again - that I am aware that certain fonts are not formally applicable and would annoy rather than refresh an academic reader's mindset. But as said, I am a big fan of design trends (focusing on, but not restricted to, fonts) and innovation, and I am simply curious to know how academics think about this: how far can one go. How different is an academic design style from for instance web, advertising, magazines and newspapers.

I was assuming the main reason for academic writing to use "boring" fonts is legibility. It's annoying to read less than fully legible fonts when your main aim is to understand the paper as fast as possible.

You seriously want to use something that you define as "border-line legible"? The whole idea of a good design is to make something easily readable not the contrary.

@Matteo I use the font (and similar handwriting fonts) in  informal paperwork all the time. That's why I posted this question: even though certain fonts are well-suited for distinguished forms of design and publicity, how does a formal academic world react to such patterns. On a website, for instance, Pacifico would be used without question. Of course, an academic audience is an 'ole other bunch all together. That's where my inner designer and outer academic struggle with one another. I wouldn't ask it, if I already knew the answer.

On a website, for instance, Pacifico would be used without question. — [citation needed]

@JeffE Just do a quick Google search for the most popular handwritten web fonts in 2014. It'll be up there somewhere. No need to be this sarcastic.

Readability above all. Go creative, but stay conservative.
That Pacifico font is simply unacceptable imho.

@BramVanroy: "Just do a quick Google search for the most popular handwritten web fonts in 2014." I have never seen a paper written in a handwritten font, ever. I have also never seen an academic website typefaced in a handwritten font. JeffE was not trying to be sarcastic or offensive, he was actually being serious when asking for a citation.

Also, cursive of any type is basically dead nowadays, and is best avoided; cursive is objectively inferior to printed characters, and only very old people use it at this point. It's probably a good choice for websites and adverts targeting specific audiences, but it should be avoided in a professional publication.

A similar question I have asked: Why shouldn't I take a risk to make my thesis have better design?

@DumpsterDoofus I have added an explanatory paragraph that might clarify things a bit. I was only considering Pacifico as a style for headings, not for plain text. Also cursive fonts aren't dead at all! They are very much alive, and will grow in number the following years - yet again. There's been whispers in the woods of a new typeset tred. Cursive has returned. You are right, though, in mentioning that it's almost exclusively used in informal publication.

@Ooker Your question is hardly similar, only in that it considers design. My question focuses on freedom in design in academic and formal writing as a whole, whereas your question implies defying your university in order to make a statement. (Which I do not necessarily disapprove of, but it seems more like something an undergraduate would do - not a PhD student! An undergraduate can be a rebel without too much serious consequence, at least that's my experience, but as a PhD the jury might not be as gentle.)

The catching should optimally be achieved by good content. Using extraordinary (fancy) fonts will most likely result in readers not taking you as seriously as your content may deserve.

Read Robert Bringhurst's Elements of Typographical Style first, then ask yourself whether your design choices match the subject material.

@DumpsterDoofus "[O]nly very old people use it at this point" is a rather strange statement to make … I am 21 years old and I use cursive extensively. It's definitely less common than it use to be, but by no means totally obsolete.

I read papers, I don't hang them on my wall. That is the main objective, and your design should subdue to it. I enjoy a well crafted book, but I get extremely annoyed when some unnecessary decoration gets in the way of usage.
In your case, the font of the titles requires a mental effort from my part to read them, which I find unacceptable, and thus, annoying. When reading a paper, I usually skim through the sections to get a broad picture of it; with Pacifico, I need to waste neurons in deciphering it while constructing my mental idea. I also find that the numbers in the text stand out a lot, probably more than they should, as they are not information I would like to get while skimming.
On the other hand, I have encountered a few unique and very nicely crafted documents, and those made a more long lasting impression. If not for anything else, I remember the general image of the article.
Bottomline is, if your design is good, it will be welcomed; but if it has flaws, some picky people like me* may get displeased and cause a worse first impression. A standard template is a safer option; but more difficult to stand out.

*To give you an idea of how much, I find several citation styles to be rather annoying because they are clearly inferior to others. For example, anything without DOI in the modern times.

I agree. Good designing should have a goal, and the primary goal in academic writing should always be promoting understanding. It's not that good design isn't appreciated in academic writing, it's that anything that detracts from that goal, which includes some elements of the example, is bad design.

I think if one wanted to be truly revolutionary, they would publish papers in a format like tex and simultaneously distribute style sheet so the people who like numbers can have them and the people who don't won't.  While we are at it, at least one style sheet should be friendly to the vision impaired - either producing a paper that works well with text readers or perhaps produces an audio publication.

This seems to bring up culture-specific issues, and a "plain" font might be the most culture-independently legible one. I am saying this because I personally absolutely disagree with your statement "the font of the titles requires a mental effort from my part to read them", though on the other hand, that is because the font of the titles is more or less exactly the font that I was taught (and, by some teachers, even required) to use during all of my school life, hence this experience is obviously country-specific.

+1 for style without DOI. 30 seconds of googling per citation is nontrivial considering the amount of people who will look them up.

@MarchHo and even worse, without DOI and without titles!

As March Ho mentioned in the comments, one important factor is legibility.  This is true both at the level of fonts and more broadly in design/structure: if your most important goal is to communicate your ideas, then it's worth optimizing for ease of reading and comprehension.  Unfamiliarity is itself an obstacle, so even if your design would be superior if widely adopted, it might prove inferior in practice.
Another issue is demonstrating membership in the community of scholars.  Choosing an unconventional design amounts to announcing "I am an outsider," and although being an outsider is not a bad thing in itself, it can come across to readers as a terrible sign.  For example, when I see mathematics papers with highly nonstandard formatting, they are almost always crackpot papers of no value whatsoever.  That's not company you should voluntarily join.  I wouldn't consciously ignore a paper just because of the formatting, but I can't help approaching it with a strong prejudice.  Unless your papers are really exceptional, unconventional design is likely to decrease your readership.
The fundamental issue here is whether you are writing for yourself or others, which is a common tension within academia.  You can take the position that you are creating a work of art and aren't willing to compromise on your vision even if it will hurt the work's reception, or you can try to do what's necessary to increase your work's impact on the scholarly community.  Different authors end up balancing these concerns in different ways.

I agree with the point about labelling yourself as an outsider. I think I would probably treat something that is substantially different from the norm as 'suspicious until proved innocent'.

If you are self-publishing, then you are free to format your work however you please. However, as the others have already pointed out, the harder your work is to read, the less it's going to be read, and the more trouble you will have getting others to take your work seriously.
As you mentioned in your question, you yourself find the font "borderline legible." That's already a huge strike against its use: why would anyone else want to read it if you, the designer, find it only marginally legible?
As someone who greatly appreciates good page design, I have to admit that I find it too "cute" for its own good. There are many fonts that could serve your design purposes of being "original" without sacrificing legibility. Pacifico is not one of them. Also, the bold numbering in the text is probably not good unless those are going to be hyperlinks.

+1.  Using a font that isn't easily readable doesn't make sense.

I believe the guidelines can be stated fairly briefly.
The typography should convey the message without providing resistance to the reader. Selecting good type faces and setting the text according to typographical guidelines regarding line spacing and line length (number of characters) is key. Remember many journals are set to conserve space rather than readability as a prime target.
The illustrations should as show (in Edward Tufte's terminology) graphical excellence, that is give the viewer the most ideas in the shortest amount of time with as little "ink" as possible.
Just remember that if the main point is communicating science, then the ease with which the reader can access the information is more important than personal design ideas. The challenge thus lies in achieving "excellence". Fortunately, excellence usually also is beautiful (my personal note)
References
Edward E. Tufte, The Visual Display of Quantitative Information. Graphics Press.
(e.g.) Robert Bringhurst, 2012. The Elements of Typographic Style Fourth Editions (vesion 4.0). Hartley & Marks.

Academia should be in part about the transfer of existing knowledge, and in part about pushing the boundaries and discovering new things. For the former, being a little bit formal and traditional is OK - although it's also good to bring a new and personal style to the way you convey the information (think of Richard Feynman's incomparable physics lectures that brought a new clarity to a traditional subject).
I like it when people try different things - as long as these things contribute to the over all purpose of the paper. For example, I was very impressed the first time I read an internal report in which the author used pull-quotes to help in the process of following the narrative - very powerful, but rarely used in scientific publications. That kind of experiment - specifically aimed at aiding in the understanding of the document - is laudable. Just tinkering with fonts - especially fonts that are not so legible - is something I appreciate less. I'm OK with showing individuality of thought, and in the expression of the individuality in any form: but it has to support the main aim of the publication.
Some people publish to show how clever they are: they use long words, complicated structure, difficult mathematical derivations... this can indeed give the impression that they are "a notch above the rest of us mortals". But it does not provide access to their thoughts, and limits the dissemination of their ideas and contributions. And that, ultimately, is what publishing ought to be about.

There certainly is room for improvement of scientific writing. The question is, are you trying to convey your work in a more efficient way, or are you just adding noise?
I can think of several examples of positive attempts at improvement: Don Knuth's TeX project, the special fonts created for his book Concrete Math. Or the work of Tufte on graphics and page layout. Even though these can at times be annoying, inasmuch as novelty often is, they do help and some of their stuff gets picked up and ends up going mainstream.
Sometimes, reading older research (say, 50+years old) can be rather refreshing as well.
On the other hand, you have to be extra careful and really ask yourself if your design really helps. If you, and several others you will show your work to, are convinced of the improvement, then definitely go for it. You may even suggest to your readers that you are open to comments and feedback.

In my experience, academic culture seems to be of two radically different minds when it comes to design:

For papers, there is virtually no appreciation for design innovation, qua innovation.  I suspect that the cultural focus on content makes a glitzy presentation seem "suspicious."  In practice, there actually can be a good bit of innovation, especially in the design and presentation of figures, but it needs to be within some indefinable bound of scientific "good taste," whatever that means.
For presentations, on the other hand, the sky is the limit, and innovation in communication seems to be highly appreciated.  For example, I've seen a number of talks using Prezi in the last few years, which are definitely following a trendy new tool and playing with its capability.

Perhaps a good way to think of the differences is like the differences between forms of poetry: papers are like a sonnet where you can make beautiful art within a absolutely rigid form, while presentations are free verse where there is much more freedom of choice for both good and ill.

I think the best outlet for such creative yearnings is presentations, and perhaps posters. In these there is so much heterogeneity to begin with that you will not experience much prejudice due to simply being different.
Another good candidate is figures. Here, there are 3 chief cases particularly suited to creativity that I know of:

Diagrams, especially flowcharts showing steps of a project
"Soft data" where precision is less important. For instance, when you have a graph of number of PhDs over time not to present it as data, but to make the point that it is increasing, you can get away with some fancy colorful designs such as the default Word chart themes.
In complex and unusual datasets, where no good way of visualizing them has been agreed on. For example, in genetics, with heatmaps showing various signal levels across the genome you have some latitude in picking colors and adding little icons and so forth.

For publications, you couldn't easily mess around with the typography because most journals precisely specify their visual style, and they have some uniform theme across all the papers in their issue and across different issue they want to maintain. They won't let you choose your own font.
For informal texts, you do have an advantage: 90% of scientists use either Times New Roman, Arial or Calibri (the Word default). Another 9% use whatever came with their Mac or Linux system. If your font is slightly different, but largely similar to these (Pacifico doesn't work, Lato is fine) most people won't notice, and those that do notice would appreciate a good font (assuming you made good design decisions).
When I use Latex to type my own informal writing, it ends up in Computer Modern. Granted, this is a very good font, but although being vaguely similar to Times New Roman, it clearly isn't even to an untrained eye. Because of this, I doubt anyone is bothered that I used a different font, and the comments I got tended to be favorable.
So for your informal texts I'm sure you can get away with taking some liberty in your font choice. It's still worth erring on the side of being conservative, though: First, don't make it too weird. For instance, writing a report in Comic Sans (I'm sure it is obvious) is a bad idea. Writing it in Helvetica instead of Arial - the rare person who notices will think better of you for it. Second, don't change it too often - if every other letter you send to a collaborator is a different font, I imagine the charm will quickly wear away.

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How to motivate students you supervise to produce high-quality research when other graduate students in the program don't?
I have a good friend who is in his first year as an assistant professor right now, having earned his PhD last year.
He is frustrated because in his new department, standards for graduate student research seem to be lower than what he was used to in his PhD department. Some PhD students in his new department graduate without ever publishing anything (which is not usual in our field). The theses that students in his new department produce would be considered at the level of a good bachelor's thesis in his old department. The graduate students all work fewer hours and are less productive during their working time than what he is used to.
I suspect this is a common problem, since many people who land tenure-track academic jobs end up in a department that's ranked lower than the one where they earned their PhD.
Assuming the graduate students he supervises are actually capable of more, how can he motivate his students to work harder and produce better work when other students in the program don't? Is it realistic to even try?

This can also be a recruiting problem.

Replace this with "employees" and you'll find it's one of the age-old questions of performance management. How do I maximize productivity from my employees?

@corsiKa Except the threat of being fired is much more real in that scenario.

Not really. If someone is only working out of fear of getting fired, they're going to be producing the bare minimum productivity to avoid getting fired. People in the corporate jungle don't get fired because they aren't the top performers at their firm, only for being at the absolute bottom of the scale. Maximizing their productivity has the same challenges as described here, and as maximizing that of a typical worker.

This is, as you say, a common problem. It certainly is realistic to try to get more out of your students than the other faculty. However, depending on how substantial the gap is between the norm and your expectations, getting into a better school may turn out to be the only realistic and sustainable way of aligning goals and reality. If the statement that the PhD theses in the new school are like bachelor theses in the old school is not just hyperbole, this may certainly turn out to be the case for your friend.

how can he motivate his students to work harder and produce better work when other students in the program don't?

Step 1 is certainly to figure out why they should work harder than their peers (who still graduate!) in the first place. It's likely that your friend never really gave this much thought, because in his old school, working your ass off was simply what PhD students do. Here it isn't, so he needs to find a motivator that works for them. The two solutions offered by Brian (tell them that they won't find an academic job if they don't publish, and show them what cool things they could be doing) are good, but they will work only if they actually have aspirations to stay in academia, or respectively have substantial internal drive to do good research. Both may have been a given in the old school, but not necessarily so in the new one. Other potential motivators may include:

Getting to see nice conference venues (don't laugh - this works much better than you think as a motivator)
Serving as a stepping stone for a cool industry internship, e.g., at Microsoft.
Finding a problem that they personally really want to solve, i.e., real curiosity-driven research.
Bonuses! Most likely difficult to implement in  many universities, but depending on his financial capabilities, there should be some goodies that he can offer in exchange for going beyond the work of peers. It does not need to be a super-formal, but knowing that the students that work hard and get published are also the ones that get new laptops first is certainly a motivator for some students.

The most important step is really to start giving it a thought why they should be working hard in the first place, rather than lamenting why they don't.
Step 2, and strongly connected to Step 1, is then to find the right students. This was again something he has maybe not given too much thought, as in his old school most students were good to excellent. In his new school, there are almost certainly also people for which some of the above motivators will work and compel them  to produce good research, but he will need to identify and actively recruit them to his cause. The most important part of this is to make clear that things in his lab are different than in the rest of the department. Students are not graduating without papers. Students are expected to work on their research X hours a week, for whatever a realistic X is, and so on. If this is the message that your friend is communicating plausibly, most of the students will stay far away from working with him, but that is ok - he does not want those students anyway. However, even at a weaker school, there are likely going to be students who are dissatisfied with the status quo and who are actually going to be appealed by your friend's less lenient approach to PhD school, especially once he builds up a track record of students actually going beyond the norm in the school.
Step 3 is going to be the most difficult, but maybe the most important, step. He then needs to meet his students half-way. Despite all of the above, he is still not going to be working at a top-tier research university. That means he will need to re-evaluate his expectations on his students and the papers they produce. This may include both, quality and quantity of results. He needs to realise that it actually is much harder for his students to produce good work in this environment than what it was for him. He likely had a stimulating and high-competition environment to work in. They just have him, and maybe one or two other more ambitious students. All the other students (who plan to graduate without papers) are frankly more of a distraction than support for them. All the other faculty are simply of not much help. At the end, he may be ok with his students not, or not immediately, submitting to the very best venues. Instead, he needs to ease them into it (without teaching them bad practices). In computer science, a good way may be to initially submit to workshops at the top conferences. This is allows students to go to the top conferences and see what the work is like that is published there, but getting a paper accepted at those workshops is achievable for most students given a little supervision. Really, the core in  this step is to get away from the mindset that is common at top schools that only the very best publication venues are good enough.
What is also important in this step is the right kind of expectation management. Telling stories about your friend's old lab may be a good way to reframe the expectations his students have on how a PhD works, but he needs to pick his time and place. For instance, when his first student gets a paper in the major conference of the field, this is a big deal and should be celebrated as such. This is certainly not the right time to let everyone know that in his old lab they had papers in this conference every year for the last decade.
Finally, Step 4 is to make alliances within the faculty. It is  likely that there are other (younger?) faculty in the department that are also not happy with how the department currently operates. They won't be able to turn the department as a whole around, but it will certainly be easier to improve their own labs if they share their experiences. From a motivational point of view, it is also a good idea to try to socially align the labs of the higher-aspiration professors more tightly - if your students are friends primarily with the students of the other faculty who expect their students to actually work, it will be much easier for your students to keep up motivation. Ways to achieve this include joint  social events or retreats, joint talk series, and of course, if possible, joint research and publications.

Step 5, related to step 4: be careful not to tread on the toes of the other faculty, who apparently liked the status quo and may resent a newcomer upturning it and making them look bad.

@StephanKolassa Oh yes.

Where I did my PhD, the research group would get a bonus from the university per paper published (funded from overhead on research grants across the university) and the PhD student would get a bonus if finishing her/his PhD within the allocated time.

Even if the conference venue is not nice, the city that hosts the conference might be a nice place to visit, and the possibility of getting funded trips is a really hook-line-sinker for the wanderlust-prone.

Regarding Step 2, he could formalize his expectations into a written document.  For instance, on my website, I have a page explaining what my students should expect from me and what I will expect from them.  At least one student became interested in working with me in part because of reading that.

it actually is much harder for his students to produce good work in this environment can definitely be true. I went from starting a CS/IS degree at a school with an excellent mathematics and CS department to one with little in the way of either (due to health reasons) and have found myself constantly needing to re-adjust how I evaluate peers and juniors - who were simply not able to attend the level or types of classes I did before because they do not exist here.

It could also help to send the students on research visits to high-ranked institutions, to "absorb" some of the academic culture in those places. The professor could exploit his ties to his old institution in order to achieve that.

In my experience, one of the best ways consists in leading by example. He can try and publish excellent work on a regular basis, and he can require high standards for any publication from his team. He can say that it is a matter of reputation and even point out the importance of international competition in the field. After a while, I bet that there will be at least one student who would like to be part of this "excellence" group and show that his or her work is worthy of the requested high quality. This could become a positive upward spiral, since other students in the team won't like to be left behind.

Absolutely: make the research exciting, paint a picture of the relevance of research, give it meaning. Bonuses, future employability etc. are all nice and good, but the inner meaning of research is what actually gets good stuff done. Of course, the #1 criterion: be selective which students you pick.

I don't think "selectivity in picking students" is as important as "setting clear standards, starting from day 1". In my experience most "new starters" make an honest (and usually successful) attempt to do what they think is expected of them. I've learned from experience in industry that if you let some interns loose on a problem that "everybody knows" is unsolvable, but don't tell them it's unsolvable, you often get a solution, or something close enough to be useful in practice. But if you ask them to sort out the office filing, the most you will get is some tidier filing cabinets.

One strategy would be to explain to the students that their success on the job market after graduation will depend greatly on the quality of the research that they've done as graduate students.
Another strategy would be to  expose the students to high quality research being conducted by students at other universities (e.g. by taking them to conferences) so that they can see beyond the provincial confines of their department.

This does not work if the PHd is only needed to get a unrelated job.   E.g some companies like to have all the sales people being "Dr" as the clients then are more likely to talk to them.

I am providing this answer as a graduate student who is NOT in a program with perceived underachievers - in fact I am in a well-ranked biology-related program at a public university that vies with Ivy Leagues for students.  I am very impressed with my cohort, many of whom work long hours and are very passionate about their research.  So perhaps I can provide a graduate student's perspective.
I joined my lab with a great deal of enthusiasm, worked long hours, and found quite a lot of success immediately.  However, as time has worn on, I have realized that most of my lab mates are not quite as enthusiastic.  They do not always keep up with literature, they do the minimum that they are told, they are generally poor lab citizens, and can even be passive aggressive if not openly antagonistic.  My advisor is very hands off and rarely creates or enforces policies to ideally prevent but minimally remediate bad behavior. This has affected my productivity quite negatively.  The point of this anecdote is to highlight that the local environment can be just as important as the global climate.  I often feel intellectually isolated, and while my advisor is very capable of carrying stimulating discussions and cares a lot, he is not yet tenured, so he's very busy, and cannot be the only one in the group with a passion for science.
Thus, based on my perspective as a graduate student on the other side of this question, I will share what I think your friend can do, as well as open with the note that I am largely corroborating and elaborating the good suggestions that xLeitix provided above.
The goals:
1) Create a stimulating and organized local environment with lab/group members who care deeply and will support each other intellectually and culturally in spite of the global research climate.  The late nights, stress, and social isolation need to be offset if depression and/or absenteeism are to be avoided.  My own enthusiasm has suffered because of isolation, lack of organization, and lack of accountability.  Maybe this also means putting extra time into mentoring to make the student feel special.  If one does not want students to treat a PhD like a j.o.b., then it is necessary although maybe not sufficient that students not be treated like employees.
Your friend should also be honest with himself about whether he has the personality traits to create and maintain a stimulating environment that will not be corrupted by poor organization.  If he cannot do this, then he might hire someone who can.  In the experimental sciences, we have "lab managers" or "project scientists" who often play the role of "bad cop" and "foreman" since faculty do not have the time or will to wear these hats.  Perhaps there is something analogous in your friend's case.
2) Related to (1), without the right people, goal (1) is difficult to unattainable.  Therefore your friend should try to be as picky as possible with who he recruits, both in terms of students, but also any other members of the lab regardless of their role (e.g. post-doc, admin, technicians, etc...).  This can be difficult as a junior faculty member because there is little to no managerial training and little formal framework for more experienced faculty mentoring younger faculty.  Nothing in his career up to that point formally prepared him to essentially run a small intellectual business, identify early signs of high achievement based on a 1-2 hour meeting or email/call to a reference, or motivate humans to achieve.  This leads to (3).
3) He should seek the help and guidance of more experienced faculty where appropriate.  They would be more able to ferret out good recruits as well as provide advice on effective management strategies to motivate people.
To summarize, many PhD students have the requisite curiosity and intellect to do great research, but at a minimum the local culture needs to facilitate this as much as possible, especially if the overall culture in the program is one of underachievement, which your friend has limited power to alter.  In my case, I am surrounded by brilliant students, but am hampered by a crummy local environment.  I hope this helps, and maybe other students can support or counterpoint my arguments.  Good luck!

Adding to xLeitix answer; specifically step 3 "For instance, when his first student gets a paper in the major conference of the field, this is a big deal and should be celebrated as such." Find out how long it has been, if ever, for the department or even university and celebrate accordingly. If it is the first ever then throw a party with him/her as the guest of honour and after cutting the cake present him/her with a brand new laptop or similar gift. If the university wont fund this but does not object he may want to fully or partially fund the purchase.
He could also see if there are any suitable rivalries with other universities he could use as encouragement.

I can agree with throwing a party and cutting a cake for celebration. But, a brand new laptop as a gift seems to be a big deal to me.

That's the point. If the current and past standard has not been great then a grand prise for the first to do so can inspire others to greatness as well. I have seen prises gifted to the best before but they were often poor and/or unrelated and provided little if any incentive to the students. Obviously this would not be handed out every time. The aim is to ignite the fire and encourage the student to raise the bar themselves.

To me, my name on the wall of the department office is more of a grand prize than a laptop. Your idea works in industry, but may or may not work in Academia.

But we are not talking about you we are talking about a group of people some will certainly be motivated by such a prise and then others will be motivated because they want to be the best, or because they don't want to be the worst. This is about shifting a groups perception rather than an individuals.

In my view as a supervisor, everything comes back to the supervisors. If the level of the students is lower than you, you should try harder in your courses and in the process of the supervision.
In my department, many colleagues are discussing this issue regularly and compare the current students to themselves. But the point I've seen is that if you have an average student and give a good idea and a correct milestone, He (she) surely succeeded in the research process.
The important fact is that many researchers are not great supervisors and just try to imitate the behaviours of their supervisors from the top universities (that is a different story).
My suggestion is to do following works to produce more research results even from average students,

Course planning carefully and beginning the research process from it by working on current research works and topics
The discipline in your programs and weekly or biweekly sessions with students are very important issues.
Begin with simple ideas with your students than the hard and difficult ones
You should study more than the students in the research and show them that you are courageous enough to the academics work.

I am a PhD student and thereby not qualified to answer the question in the intended spirit of the OP. Still I feel an urge to express my opinions in a general context since I find no logical explanation that negate the following. Assuming that the student is interested in the subject, I would advise an enthusiastic student that there are 3 major ways that you would loose your motivation.
1. Anxieties of the Past.
Thinking about something negative happened in the past and worrying that it will happen again. E.g. I had failed to understand General relativity even though I tried 3 times. I am going to fail again.
2. Anxieties of the Future.
Thinking of what to say in my Nobel prize speech in the middle of a Gaussian curve fit.
3. Anxieties of the Present.
Thinking of the numerous parameters to be given for the fitting function, leaving the data untouched from morning to afternoon. After noon, its lunch and I need some rest.
I would advise my student to block these while doing your work, think of what need to be done now, never lose your energy thinking of the results that are yet to come in the future and concentrate all your efforts for the single piece of work that you are doing and thus results will be excellent.

-1 I am sorry but this is a reasonable answer to a completely different question.

authors: فخَامه ألاقّْتِبَاسْ


text:
How to make my Thesis supervisor aware of my Visa issues?
I am finishing my Master in a foreign country on a student Visa. The Visa will expire in one and a half month, the exact time I was appointed to receive graduation, but my Thesis supervisor wants me to stay one additional month to "finish" the Thesis. Indeed, he says he won't accept it if I don't stay to include additional verification, rendering me unable to fulfil my graduation requirements.
I have asked for support at the International Office of my University, but it seems nothing can be done at this point to extend the Visa. I should have begun the process at the beginning of the semester if I needed an extension. Therefore, I am facing the imminence of being deported, not to mention that: 1. Without a valid student Visa the University can't award me my degree. 2. If I remain in the country, I will become homeless because my student's room contract will end at the same time that my Visa and, as a foreign student, I don't have enough money to rent a room on my own.
I had a tense relation with him after one month on my thesis. He wasn't particularly interested in my Thesis (poor communication, not interested in students benefit but on his project, disappeared for months and then reappeared totally disconnected, etc.), but I remained because of his prestige and fear of losing one complete year of preparation in the field. This is the worst moment in our relation. On his criteria, I have been lazy and put myself in this situation. Either way, I have to solve it now or lose two years of hard work and spent money.
How can I solve such situation? How can I make my a Professor aware that there is bureaucratic world beyond academia, that I don't have the same privileges as a national of his country? Maybe a foreign student had a similar problem and can give me advice or tell his/her experience...
Edit: I have to mention that my supervisor has a legal/financial obligation on the project I am part of henceforth comes his worry.

Is there a deadline for the submission of Master theses?
Do you know how many people will assess your theses?

@Dmitry Savostyanov There isn't an specific deadline, but I have to submit it in 15 days to get the degree in one month (originally my appropriate time of graduation). Students must submit the thesis in their last year and some ask for extension, but that can't be my case. Even if the thesis is assessed by other Professors, it must contain the approval of the thesis director.

Do I understand correctly that you told your supervisor clearly that you have to leave the country due to visa issues, and thus cannot finish your degree if it takes an extra month?

@Ana Yes, exactly.

Is it possible for you to finish the thesis remotely, in your own country? You could stay in touch with your supervisor via Skype and email.

@mhwombat I told him about that possibility, but he didn't agree. He says that physical presence in the laboratory is the only way to secure job quality.

Do not get deported. Whatever happens, make sure you are out of the country before your visa expires. If you are not, it is possible that you are never allowed back into the country.

Maybe the title is a little misleading to readers. It asks how to make him aware of your visa issue, but it sounds like you have successfully done this; what you want to know is how to convince him to accommodate you.

Have you tried talking to your department? The department chair, for example. Doing something at the University end would be much easier than the government end. It sounds like there is no major intrinsic problem as such, just your adviser being unhelpful and inflexible. Join the club. However, it is quite possible that if the department (read, this person's colleagues) intercedes, that this person could be persuaded to be more reasonable. I've been in not dissimilar situations before, (and heard and seen similar problems faced by other people) and while faculty don't really care much about students, they also aren't really interested in having disasters happen to their students, especially if they are easily preventable. For one thing, it is bad publicity.
I agree with others that you should definitely not overstay. If it comes to it, much better to upset your adviser (and possibly the university) than the govt. It might also be worth finding out if there is any student level organization that can intercede on your behalf. Other possibilities include the Graduate School itself. But your own department is clearly the best bet.
Without knowing more about your situation, and just based on what you have said, it sounds like finishing your degree requirements remotely is your best bet. And again, based on what you have said, the main obstacle to this is your adviser. Though it is not clear (to me at least) whether he is the only obstacle.
It sounds like you should have made sure that your visa status was in order before all this happened. While this was clearly a mistake, it clearly is unreasonable for the department and university to punish you for what was, at worst, an oversight on your part. And such bureaucratic issues are easily overlooked when one is busy trying to finish a degree. One could argue that someone at the university should have been taking some interest in your visa status, but I don't know if taking that line would do you any good.


text:
How can I secure funding for a PhD in the UK?
I am an international (non-EU) student got an offer from a professor from a UK university to supervise my PhD. I have applied for funding for research students within the university, but I couldn’t secure it probably because had lower grades than the requirement for the scholarship.
Now, my supervisor was promoted to the director of research of the same university. Does the director of research have the power to influence the funding committee in my favour, in spite of my low grades?
I need help, I am totally unable to understand the process of securing funds in the UK, and what role your supervisor plays in securing funds for you.

I would also recommend asking your supervisor about this, and ask them what you can do to get funding. You should not accept an unfunded PhD place.

Please take a look at: I accidentally created two accounts; how do I merge them? Please [edit] additional information into your question.

I was in a similar situation as you a few years ago. I have written a few answers on this SE on the topic:

General info about funding for PhDs in the UK
A bit more about the same topic
and Some information about why this is so difficult if you're not British or European

In the end, this depends on many factors, including your nationality, your field, and your institution. Funding for a PhD for a non-British and non-European person is rare, because it is the financial equivalent of 3 or so British students. You will be responsible for International Student tuition (at my old university this was about 17k£/year plus living expenses, all of which you need to have the first year prepared for in order to get your visa.
So we need more information, and your first point of enquiry should be the supervisor who wants to work with you.
To be quite honest, even with stellar grades, this would be extremely difficult unless you're very lucky. I had several PhD offers in the UK but in the end I gave up and went to Europe, and didn't look back. I would advise you consider doing a PhD in the EU - in many cases these are fully funded, with no discrimination based on nationality.
But: maybe there is something your prospective supervisor knows about. Maybe there are nationality-based scholarships. Maybe there are scholarships from your home country. The only way to know is to ask your supervisor, the International Office, and google. The remaining scholarships are very competitive (e.g. Fullbright) but worth a shot as well.

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