text:
Customary to offer a fellow academic a chance to rebut criticism in a paper?
If I write I paper in which I criticise a view or argument expressed by another author, is it considered polite or customary to offer the author an advanced/draft copy of my paper?
My criticisms are of course at an academic rather than personal level.

I wonder in which field this is. As a mathematician, if I find a serious mistake in another paper (like, the main result being false), I contact the author quite immediately and confront them. But again, the "right and wrong" is much clearer for us than for other branches. That's why I wonder...

This seems very field-specific.  In some fields -- e.g. philosophy -- "criticizing the work of others" is more than business as usual: it's a substantial part of what all papers in the subject do.  (Philosophy is probably the extreme case: though I am far from an expert in this area, I do have some familiarity with it, and my understanding is that a truly correct and unassailable philosophical argument would in most cases serve to show that the problem was not really philosophical at all!  This is a field in which the rank and file philosophers of today criticize the golden gods of the past two thousand years as well as each other...and everyone seems pretty happy about it.)  In certain other fields there is the sense -- and this can only be meant sociologically without opening up some truly deep cans of worms -- that "right" and "wrong" work is not a matter of individual opinion or belief: it is something that the community as whole must come to an agreement on.  For instance, two scholars can happily present rival theories on the meaning of Hamlet or even on its authorship.  Two scholars who report inconsistent physical experiments cannot coexist so happily: the community as a whole has a strong feeling that at least one of the experiments must be wrong.
If you are just presenting a rival theory to someone else's in the sense of philosophy or the humanities -- i.e., the community as a whole will have no a priori problem with allowing the two theories to exist and each gain their own adherents -- then it seems to me that this is business as usual and everyone can read about it in the paper.  But if you are working in a scientific, mathematical or other field in which the two works cannot coexist simultaneously in the community as a whole, then you are doing something that is potentially much more destructive to the other person.  This doesn't mean that you shouldn't do it -- on the contrary, if anything you are more obligated to bring the issue to light -- but I think it would be at least courteous to personally contact the person whose work would be specifically invalidated by yours.  On the other hand, whether something is "courteous" is clearly a matter of culture.  I think that scientific fields vary widely on whether and how discourteous this practice is.  For instance, there are some fields -- e.g. string theory -- in which large numbers of people are working within a very small and rapidly moving space.  In this kind of situation, it is my understanding that you just take a good, rapid shot and see how everyone else reacts to it.  If on Wednesday two contradictory string theory papers show up on the arxiv, then you know what people will be doing on Thursday: in other words, the community is so automatically and rapidly self-correcting that people think in terms of "good ideas that didn't pan out" rather
than "wrong papers".  Or so is my understanding anyway: string theory is quite an amazing field to me because it is technically so similar but sociologically so different from my own.
In my field -- mathematics -- the culture regards my publishing a paper saying "Your paper is wrong" as an extreme act to be avoided at many costs.  Much better would be for you to publish an erratum/corrigendum/retraction saying "Unfortunately the result I stated before is wrong; I thank [you] for bringing this to my attention."  Publishing a paper -- or even circulating a preprint, say on the arxiv -- saying that Author X's work without making any attempt to contact Author X would be regarded by some as being discourteous to Author X.  It could also be a strategically poor decision in some circumstances: when this happens, very likely some part of the community will mobilize to figure out "as a whole" who is right, you or Author X (or neither!).  This mobilization will probably involve several people having conversations with both you and Author X, to the extent that you may end up talking to each other through other people.  It could be more efficient and more seemly to have that conversation directly and privately with Author X.  In particular, for better or for worse (and I think it is somewhat for worse) if you publish a paper saying "Author X is wrong" and you turn out to be wrong, then you may acquire a reputation for being a bit of a troublemaker.
Finally, in very technical fields, it is often the case that the unique person who is maximally well equipped to resolve the discrepancy between your work and Author X's is...Author X.  So unless you have some reason to think otherwise, availing yourself of this resource sooner rather than later is probably a good idea.

By the way, I agree with Alexandros's answer that whether and how well you know the person whose work you're contradicting is in practice a key consideration.  If you are at all friendly with this person then I would say definitely send them an email.  If you don't know the person even by reputation that makes it harder.

While I definitely agree that in math you should contact the author directly if you think their work is incorrect, perhaps one should also be cautioned that such discussions do not always go smoothly.  So you should try to approach this as politely and nonconfrontationally as possible.  (I remember one time I didn't believe an author's proof about the second part of his main theorem, so I politely emailed him about how he came to this conclusion, and after looking at it again, he agreed he had not proved that result.)

@Kimball: I agree completely; you catch more mathematicians with honey.  I believe this "maximal politeness" approach has been discussed elsewhere on this site (e.g. by me).

In the environmental sciences, papers that explicitly criticise other papers (and the inevitable rejoinders) are sometimes published, but are unusual and often an indication that the two authors have some personal issues between them. The rest of us sit back and watch it as a blood sport.

No, you don't have to provide a copy in advance to this individual. It is customary within most scholarly works to point out in the literature review which theories you do and don't agree with, and why. You are not expected to agree with everyone; in fact, agreeing with everyone would indicate a serious lack of critical thinking on your end. It's good that you don't agree, as long as you are able to express it professionally and support your disagreement with a strong counter argument buttressed by sturdy methodology and data.
Finally, it's likely that this individual will be asked to review your article when you submit it for peer review. You can be assured that he/she will rebut your criticisms during the review process, so by the time your paper does manage (if it does) to pass review, you'll have likely had to rework a significant portion of the paper.
If you are submitting this to a non-scholarly publication, then it is likely that the publication itself will provide the author a chance to respond to your criticisms.

+1 for the point about the likely reviewer. This happens a lot, so addressing their existing and likely future arguments, methods, and theories head on in your article is important.

You are right that "rival" was poorly chosen. I did indeed simply mean someone I disagreed with on a particular issue. I am replacing rival with "fellow academic"

Is there a particular reason my response was edited?

@Jacob If you click on the "edited" link, you'll see the whole revision history, where D.W. explained why they made the edit.

Ah! Fair enough :)

If I write I paper in which I criticise a view or argument expressed
  by another author, is it considered polite or customary to offer the
  author an advanced/draft copy of my paper?

Most certainly not. The other author will have a copy of the paper when it is available after publishing. Contacting him just to show him your published "opposite" paper (especially if you do not know the guy personally) will probably seem weird if not unfriendly. People on one scientific area know when there are other papers a) citing them or b) contradict their previous papers (Google scholar notifications are excellent for this). So, there really is no need for sending a special "reminder" about your paper.
On the other hand, if you know these people personally an email saying "This is my new paper building on your previous work" and "...tell me what you think about it" might not be that bad. Still, it might be better to wait for them contacting you about your work, especially if those guys are more famous and established than you.

I think this depends on both the customs in your field and on you as an individual. I doubt that there is any "unwritten rule" either way. You should do what you think is most beneficial to you.
I myself do always send out manuscripts to people whose ideas I criticize in my paper, and I do this before submitting them anywhere else. My main reason for doing this is to give them the chance to correct me if I have misunderstood their arguments. It would be in no one's interest if I publish a paper with such mistakes - not in their interest, since I would be misrepresenting their research, and not in my interest, since I would be making a vacuous counter-argument. I have also experienced other people sending me their manuscripts for the same reason.
Another reason I send them out is because I have good reasons to think they would care about my paper. After all, they have written about the very same thing.

interesting! you contradict a few other answers though. perhaps this depends very much on your field. do you also receive advanced copies of papers that criticize your work?

@innisfree What are "advanced copies"? One reason we do this in my field (or rather, in my subfield) might be because we're overall quite amicable with each other. We can get along even though we disagree. I've learned that this is not the case in some fields.

In my experience, the expectations depend on the nature of your criticism, and probably on the field you are in.  At a broad level, based on what I've seen in my field, I can separate this into two different kinds of situations:

A factual dispute.  Here, I'm referring to a situation where there is an objective truth.  In my field, if I write a paper that says that a technical claim in a prior paper is wrong -- say, an alleged proof had a technical error -- it is considered polite to send an advance draft to the author of the prior paper.  This is a situation where there is an objective truth: either the proof was correct, or it was flawed.
Why is informing the prior author customary, in this kind of situation?  First, it's polite to the author of the prior paper; it's a nice courtesy to them, so they aren't surprised and don't feel personally attacked.  Second, and perhaps more importantly, it helps get at the truth more efficiently -- which is supposed to be our motivation for doing the science in the first place.  For instance, suppose your criticism is wrong and you simply misunderstood or have a mistake in your reasoning; then the prior author may be able to point this out and save you some embarassment.  Or, suppose they agree with your criticism and had actually already issued a correction to their paper which corrects the error.  Then you can cite their correction.  Finally, suppose they feel your criticism misrepresents their views or is not a fair characterization of what their paper was claiming.  Then this is an opportunity for you to review whether your criticism is valid (taking into account their perspective) and possibly revise or refine your argument.  In each of these cases, everyone benefits: you benefit from having a stronger argument, the prior author benefits from avoiding surprise or invalid criticism appear in print, and the scientific community benefits from getting to the truth of the matter more efficiently.  So it's not that you are somehow obligated to inform the prior author, but it benefits you and it is considered polite to let them know as a courtesy and give them a chance to respond.
Of course, this might well vary from field to field.
A matter of opinion.  It's a different story when reasonable people could disagree.  Perhaps it is a matter of professional opinion or judgement; perhaps we are trying to draw conclusions based on imperfect information; perhaps there are multiple possible answers with complex tradeoffs; perhaps we are making a case for a particular conclusion, but the problem is complex and one could plausibly make a case for the opposite conclusion.  This kind of situation might be more common in the humanities, in philosophy, in law and public policy, and other fields than in mathematics and the core sciences, but it can arise in any field.
In these situations, I would not expect any clear custom or expectation about whether you share an advance draft of your paper with the authors of the prior paper.  At least in my field, there is no expectation to share a copy of your paper with the prior authors.  Here debate and counter-debate is expected and part of the norm in the published literature.
So, in this kind of situation I would suggest that you evaluate what to do based on what you think makes sense in your particular situation, without feeling constrained by politeness norms.  If you think the authors of the prior paper might give you valuable feedback, you could share an advance draft with them.  If you feel that is unlikely to be useful, you could skip it (and you can still share a copy of the paper with them once the paper is published).  It's entirely up to you.

At least, this is my experience, in my field.  Norms and expectations may vary from field to field, so I encourage you to talk to your advisor, a mentor, or someone senior in your field who you trust.


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Should I address a "Charge de Recherche" or "Directeur de recherche" in France as "Prof."?
In France, the following are two of the main ways people get promoted in academic positions:

Maître de Conférences (assistant professor whose responsibilities include teaching as well as research) -> professeur (professor)

and

Chargé de recherche (in charge of research) -> Directeur de recherche (director of research).

Note that in the second sequence of academic promotions, one doesn't have to teach and the positions are mostly dedicated to research (although one can opt to teach if s/he wants to).
My question is: while applying to a position (postdoc/permanent) in the team of a chargé de recherche where s/he is the PI of the project, should one address her/him as a professor ("Prof."), say in the cover letter? It's technically incorrect it seems, but perhaps no harm is done because their positions are equivalent to those of professors anyway.
I'd like to know the viewpoint(s) of someone(s) who's familiar with the French system!

If you're going to communicate in English, go for "Dear Prof. X", if it's in French, go for "Monsieur" or "Madame". By the way, if you communicate with a UK prof, you would write "Dear Prof. X" only if they are literally a full professor, otherwise it goes down to "Dear Dr X" or "Dear Mr". In the US I noticed T.V. anchors addressing Nobel prize winners as "Dr X" rather than "Professor X", because for some the perception is that Dr is higher. But not in the UK. Table manners also differ quite a bit (hands on top in France, hands on lap in the UK, no rule in the US). Ah ah.

This depends upon your definition of academic position. Is CEA -my employer- an academic organization?

@BasileStarynkevitch No it's INRIA.

I think you should clarify what the language of the communication that you are talking about is.

You could send me an email (in French) to basile@starynkevitch.net

@BasileStarynkevitch Thanks, will do, describing my (somewhat difficult) situation.

I didn't got any email. Mention the URL of your question

@BasileStarynkevitch Will do, but I'm not sure what's the point of this email and why do you want me to send the URL of this question where you can access it here? And if I may ask, why do you want me to write in French (my French is intermediate so I'll use Google translate if I do write an email.)

You can also email me in English -or even  in Russian; and I prefer some URL because "Science Man" is a pseudo, not a real name

@BasileStarynkevitch Just sent you the email!

French academia is not big on titles. Whether it's by students, colleagues, or the administration, people are rarely if ever addressed by their titles. I'm a "maître de conférences" myself, and nobody addresses me as anything other than "Monsieur", and my colleagues of another gender are addressed as "Madame". That's it, no fluff, no "Prof Dr", no "Maître" -- which wouldn't be appropriate as this is how you address attorneys and notaries, not even "Dr".
If you want to err on the side of the formality, which is perhaps better until you know more about the person in question and how they like to be addressed, you can call them "Prof". It's inaccurate, yes, but we are used to the outside world wanting to impose American title norms on us. You can take comfort in the fact that many institutions have "research professors", so a chargé de recherches could be viewed as a "junior/associate research professor", that you would address as "Prof", indeed.
Personally I wouldn't care if a foreign applicant started an email with "Dear Mr. XYZ" (or Ms. as appropriate), and I doubt (m)any of my colleagues would. But I hesitate to give this advice, as it's possible that in some French academic subcultures some people give more importance to titles. I'm thinking of law and medicine, especially.
However, do not ever address someone as "Dear Chargé de recherches Dupont" or "Dear CR Dupont". That's just not used as a salutation, even if it's the title used by that person on their website.

There is an American joke: Call me anything you like, but call me MISTER. It leads to funny results. Not all printable.

I believe it was Pratchett who observed that such distinctions are most important to those near the bottom of the ladder.

I'd like to add that (i) using Prof rather than Professeur(e) would be considered familiar or rude by most recipients, as "le prof" is a item used by students and others outside the professor's hearing and (ii) the only domain where Professeur keeps being used as a title is in medicine, as in "Laurence Ferrari a interviewé le professeur Didier Raoult"...

+1; the only thing you should probably avoid is calling them by their first name in your first email, before somehow being invited to do so.

@PeterWone With respect, Sir Terry probably never met a Prof. Dr. Dr. at a German Uni. I'd also say that he probably never met the Queen, but, uuh…

If you want to be formal you can also use Dr. . Pr as you noted is a specific title in France that do not have the same meaning as American one. You can check if one is a Pr by searching the web.

@KonradRudolph the Queen would never acknowledge a breach of protocol. If the PM arrived with his underpants on his head she would finish the meeting without a word about it and not so much as a smile. The German insistence on precision and correctness is not limited to social hierarchy. Certainly you have found an exception, but do look up "humour".

@PeterWone “do look up ‘humour’” — My comment was, in fact, an attempt at just that.

@KonradRudolph -- I deserve this. Dry, understated humour is my own métier. Live by the sword...

As stated in a previous answer, the French academia does not use any title. The terms like "maître de conférences", "professeur des universités" are just the position you hold but not the title you have.
If you write an email in French, the best way is to start by "Bonjour" or "Bonjour Monsieur, "Bonjour Madame".
To be honest, since I am not a Ph.D. student anymore, I avoid using "Monsieur" or "Madame" because I think it can put a sort of hierarchy in the relationship. In most cases, you will receive an email starting by only "Bonjour". By the way, in the French system, it is not unusual to start an email by "Bonjour".
In some cases, the person you contact can just call you by your first name "Bonjour X" and use "vous" which is the formal "you" in French. It is also very usual to call somebody by his/her first name and use the formal "vous". Then, it can become weird if somebody calls you by your first name and you call him/her Madame/Monsieur.
I just use Monsieur/Madame part for formal administration-related emails. The same story for the hierarchy applies because when the administration contacts you, the most cases, the email you receive is very formal and uses "Madame/Monsieur". Then, to avoid any hierarchic context, maybe it is better to start this kind of mail by "Madame/Monsieur".
If you write your email in English, then you can just call Dear Professor X. It is not strange to receive this kind of email. You can use the same international norms used in the academia.

When you say "call you by your name", do you mean first or last name?

I mean the first name. It is very common in the French system.

Then, it can become weird if somebody calls you by your first name and you call him/her Madame/Monsieur. Weird but not unheard of. When I met, as a grown up adult, my teacher from primary school, he called me by my first name and tu and I of course went for "Monsieur" and vous :) He was an old school teacher and an old man at that time. OP: the tu/vous relationship usually stops at high school level (everyone is a vous) and then turns into tu for both parties at the same time.

Use whatever title they use on their website. E.g.,

Use Dr Alpha Bravo or Professor Alpha Bravo, if they appear.

When titles aren't used, e.g.,

Their website uses Alpha Bravo, PhD, you can rightly use Dr Alpha Bravo, but may favour Alpha Bravo, since they're discrete about their title.

When no titles are used, you're probably safe with their name, e.g., Alpha Bravo. (Although, you may like to google their name, find and use the title that appears in the press.)
Don't assume an academic adopts national conventions/stereotypes, especially a non-native.

I had to downvote because that is not the French way at all, sorry.

@PatrickT Using a title that someone uses themselves isn't the French way?

As pointed out by user135767 in their answer, no, you wouldn't. Note that you wouldn't address the queen of England by the title on her website, "Dear Queen of England" would be "Madam"  instead, so it's not just in France.

@PatrickT I've edited for clarity. (Dignitaries are irrelevant, they don't maintain websites, academics do, when they have them.)

@PatrickT: while I completely agree with you on the French part, I think that for HMQ it would rather be "Your Majesty". I find these titles completely ridiculous BTW, including our "Maître" when talking to a lawyer....

'Madam" is explained here: https://www.royal.uk/contact, if you open with Your Majesty she'll never reply ;-)

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Is it OK for an MSc Student to Review a Scientific Paper?
I am an MSc Student of Computer Science at a department that is considered to be in the top ten CS departments in the world (QS Rankings here). I am telling this, just to let you know, that I have some good enough (I guess) general background in Computer Science. However, I am just an MSc student, not somebody who is a specialist, knows a lot of things including the current research conducted in a specific field.
I was asked today, from an editor of a journal, to review a paper. I would loved to do that, but I will probably respond negatively, as I can understand the danger of saying yes to a paper that does not actually show a good amount of research just because I am unaware of the current research and/or expertise on that field.
However, I can understand most of the papers in Computer Science and I found mistakes some times that were reported to their authors, who admitted that their papers had some mistakes. Therefore, I may be able to find some errors, but I am afraid that I may be unable to say whether a paper fully justifies and in a correct way what the authors want to show.
My question is: What should I respond to the editor provided the above?

I think the quality of the journal might be suspect. Ignore the mail. I have received such mails before.

@sriisking: If so, this earlier question I asked could be relevant.

I think Msc is sometimes research based anyway but I was also kind of wondering about this as an undergraduate. Any chance you could include undergrads in the question so I can find that one out too?

This is a good question: at what point in one's academic career should one begin refereeing papers?
I think the first order of business is to make sure that the editor knows you are an MSc student.  In fact, inquiring into why you were chosen to referee the paper seems reasonable to me: the answer may help you determine whether you are qualified.  Perhaps for instance your thesis advisor got the request and passed it along to you.  That's a good situation for you: you can read the paper for correctness (in my experience, assuming the requisite base level of competence and understanding, the younger the referee, the more likely she is to conscientiously read and check a paper for correctness) and then solicit your advisor's help in determining the appropriateness for the journal.
In fact, no matter what this is a good opportunity to talk to your advisor: she will be the best person (aside from you) to help you determine whether or not you are "ready" to competently referee the paper.  If she says no, you should probably turn down the request.  If she says yes, see if you can get her help on the higher level issues that you are rightly concerned about.
Let me also say that you have to start refereeing papers sometime (or you become someone who never referees papers even into the later stages of their career: I know such people, and although so far as I know they landed in that situation through no fault of their own, it is clearly an undesirable state of affairs for the community at large), and no matter what age or rank you start, you will still have to wrestle with the issues of knowing what standards to impose.  (For that matter, sometimes I get a referee request from a journal that I have never read or even heard of before.  I try to ask the editor for more information but have sometimes just been told things which amount to "Use your best judgment."  So I did.) There is a lot of subjectivity in the refereeing process, and though you may feel less confident about your opinion as a very junior academic, in reality it is far from clear that what you do will be worse than what some more experienced person would do!
Shorter Version: You need to get a sense of whether this is a job that you can handle competently in a reasonable amount of time.  Don't be afraid to ask for guidance in determining the answer to this.   Being a master's student does not disqualify you in any obvious way.  If you can do it -- without interfering too much with your other responsibilities, of course -- then you probably should.  It will be a valuable learning experience.

Thanks a lot Dr Pete. I will follow your advices, as they seem very good and reasonable to me. Thanks again.

I don't think it directly matters what point you are in your education or what university you are studying at. It is more important that you have written and published some papers yourself in the field. You need to have had the experience of having your own papers reviewed before you can review someone else's, just so that you know first hand what is expected of you. It is not common for someone at MSc level to have that experience but if you have then that's fine.

I reviewed at least one paper before I had published myself.  I don't remember the exact details, but roughly, the editor asked me to review it on the understanding that my advisor would give a lot of guidance; which he did, and it was a helpful experience.

(Just to add a point that’s not yet been mentioned.)
One thing you can do is to explicitly mention you your own level of knowledge in the review.  I recently began one review something like "This work is correct and interesting, and as far as I know it's new, but I don't know the literature on the topic thoroughly enough to be certain of that."
Indeed, in my field, most reviews come with a field on the score-sheet to give your own level of confidence, usually on a scale of 0 (null) to 4 (expert).  I would be uncomfortable reviewing anything where I’d rate myself 0 or 1, and for a 2, I would want to check with the editor before accepting the review, and see if they would prefer to ask another reviewer.  But from an editor's point of view, a well-thought out review from someone inexperienced but conscientious — especially when that inexperience is known, and can be allowed for — may well be better than a hurried review from an expert, and is certainly better than no review at all.

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text:
Creating compound alerts with Google Scholar
In Google Scholar, I want to create a compound alert, which returns papers that are relevant to two concepts. Concept 1 is all about a branch of machine learning, which can be triggered by the words "deep learning" and "neural network". Concept 2 is all about a branch of robotics, which can be triggered by the words "navigation" and "localisation". Furthermore, the article must definitely include the word "robot".
How should I express this as a single alert?
I know that an AND is implicit, such that:
"navigation" "localisation"

will only return articles which contain both those words.
I also know that an OR can be define, for example:
"navigation" OR "localisation"

will return articles which have either of these words.
But in my case, it is more complex. I basically want to say:
("deep learning" OR "neural network") AND ("navigation" OR "localisation")  AND "robot"

These brackets are just to illustrate what I want to achieve, but I'm sure that they're not interpreted in this way by Google Scholar.
Any ideas? Thanks!

Edit: My current solution is to just have four separate alerts:
"deep learning" AND "navigation" AND "robot"
"deep learning" AND "localisation" AND "robot"
"neural network" AND "navigation" AND "robot"
"neural network" AND "localisation" AND "robot"

However, most of these papers are triggered by three or four of the conditions, and it is very frustrating getting several emails for each one! So I am hoping that there is a way to express this all with a single alert.

Would this question be better on a Google support forum? Off-topic here?

Have you actually tried your sample query? As far as I can tell, it should work.

I think what you're looking for is a Google Scholar Alert for

+"robot" +("deep learning" OR "neural network") +("navigation" OR "localisation")

Google search operators include "OR", "-" and "+", and permit brackets, but do not use "AND".
Fun fact: The order of the terms will change the order of results (and content of previews). That matters if the hits exceed the number permitted by your alert.

Run the following search:
https://scholar.google.com/scholar?as_ylo=2016&q=%22deep+learning%22+OR+%22neural+network%22+AND+%22navigation%22+OR+%22localisation%22++AND+%22robot%22
I tuned it to include results only since 2016, and specifically scholarly articles.
Google advanced search also lets you play around with a fair few options.

If you have an academic access, I recommend Scopus. It will let you do searches as complicated as you want, sorts results by new (default, so you might not even need an alert) and lets you set up alerts or an RSS feed. Its search feature is much more advanced and thorough than google scholar's!
It has two main downsides: you need an academic access, and downloading pdfs is more cumbersome than with google scholar.

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Ethical grounds of letting supervisor hear recorded interviews with research subjects
I have collected a lot of data in the form of audio recorded interviews. My supervisor is asking if they can listen to them, however, I feel this goes against the consent stipulated to the participants under the data protection section. As such, I feel uncomfortable letting other people listen to it under ethical grounds.
Can a university or its staff demand to listen to private data collected which the participants understood would only be heard by myself for transcription purposes?

Has your design been approved by an IRB or equivalent?

The answer to this question depends upon the laws of your country or other jurisdiction (e.g., state), your universities policies, and your specific IRB approval.

As other people have stated, this depends on laws, policies, and IRBs, and of course, what the consent form states. No, any random part of the university or its staff can't demand to listen to it, however, it would not be odd for the project supervisor to listen to recordings recorded in her group. The consent form usually states the relevant staff may access private data as necessary/appropriate (what would happen if you left, could no one access the data?).

Can you add the section of the consent form you feel means only you may listen to the recordings?

I would find it ethically questionable if recordings of interviews were only ever reviewed, or even available to be reviewed, by a single person. That screams unreliable and untrustworthy findings. I have never heard of a consent form or IRB that specified such an odd requirement, so you would have to have a compelling reason as to why other members of a research team, especially a supervisor, should not be given access to research work product.

Aside from just the content of the data agreement, what also matters is whether this agreement is between the participants and you (unlikely), or the participants and the university (more likely).  In the latter case, it is the university that is being given access-consent, and it would then be natural for your supervisor to have access as an appropriate staff member supervising the research in the university.

Ordinarily, when research involving human subjects is conducted, it needs to go through an ethics clearance with the university, and that should involve stipulation of which staff members will have access to the data, and what protections are imposed on the data.  Usually the scope of this access would be broad enough to allow access for anyone on the research team (researcher, supervisor, relevant administrators, etc.), so long as they comply with the relevant data protections and only access the data for legitimate purposes.  These matters really should have been stipulated clearly in the ethics application for the research, and it is an oversight if they were not.  (You should think about this for next time.)
You mention your concern that giving access to your supervisor goes beyond the consent stipulated to the participants under the data protection section of your project, but you have not stated the content of that section, or the parties to that document.  (If you can elaborate on the specifics, they may help.)  Usually a data-agreement for research will be made between the research participants and the university, rather than being an agreement between the participants and the specific researcher.  Members of the public who consent to participate in research through a university usually expect that they are giving consent to the institution to record and access their data, rather than giving consent to specific researchers.  They will therefore expect that various professionals in the university will have access to their data, for the purposes of conducting or supervising the research, and the university will ensure that access is only done for a proper purpose.
Now, obviously, if your data agreement has a section that stipulates an access restriction, then you should obey that restriction.  However, in the absence of any clear stipulation that access is restricted to specific researchers, the more natural interpretation would be that the university has consent to record and access the data, and this would usually be expected to extend to a supervisor with a duty to supervise the research of a student researcher.
As to whether your supervisor can "demand" access to the data, if the research agreement with the participants is between them and the university, then your supervisor can probably legitimately demand access, and the university will almost certainly grant him access.  If you are a PhD student at the university, and this person is your graduate supervisor, then your supervisor has a duty to supervise your research.  In any case, if you are not sure of the access rules here, just send an inquiry back to the ethics board that approved your application, and ask for their guidance.

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


text:
How to change to Mathematics PhD program following M.S. in Computer Science?
I wonder if anyone can give me some advice about how a computer science graduate shifts career to mathematics? I'm currently doing a Master's degree in computer science and i was thinking about doing a PhD in pure mathematics? so I was thinking is this transition feasible? how can I make this leap of faith?
Kindly note that currently -after graduation- I nearly don't do mathematics anymore, currently all what I am doing is writing software and administrating open source operating systems. In undergrad levels I took an introductory course in discrete mathematics and some calculus courses.
someone told me: Yes, the transition is feasible but it requires I take some courses and attend some math classes even as a special student (no degrees, no exams). But I thought I can get other opinions and views.

Did you have a specific country in mind where you want to do your PhD?

Take a look at Is it easy to change your major after starting your PhD or masters, if it is necessary?, which is somewhat similar.
In particular, unfortunately, it sounds like your current mathematics background is very far from what would be needed to enter a math PhD program - it's maybe 1/4 of the coursework that would be expected. You would need to have preparation equivalent to that of a BS in mathematics, and that sounds like it would be the equivalent of 2-3 more years of full time coursework for you.
To be honest, I don't think that the coursework you describe can even have given you much of a sense of what pure mathematics is, much less what it is like to do research in the area.  One needs rigorous proof-based classes such as real analysis and abstract algebra.
I would not really advise you, or anyone, to even think about grad school in mathematics before they have enough of a background to reasonably understand what it involves.

It's always possible to go into another field, especially ones that are somewhat related (i.e., you'll have an easier time going to mathematics with CS than if you had a Psychology degree, for example).
The Bad

In undergrad levels I took an introductory course in discrete mathematics and some calculus courses.

That's about one or two classes more than even most humanities majors have to take. I'm assuming you've taken at most integral calculus (Calculus II in the US).
You're going to need to take quite a few courses to be prepared for a PhD program, and have a chance at doing some useful research afterwards, considering you want to do pure math.
Undergrad math majors usually take (to prepare for grad school) courses such as:

Real Analysis (at least two semesters)
Modern/Abstract Algebra
Vector and/or Complex Analysis
Geometry and/or Topology
Combinatorics/Graph Theory
Number Theory

Many schools also require a course on proofs/logic/set theory before you can do many of those, as well. It could behoove you to also know about functional analysis, and differential geometry/riemann surfaces before you enter as well, though you may be able to take those as graduate coursework.
So you're looking at a good amount of time and effort before you can even competitively apply.
The Good
Having a master's in CS is a very useful thing. After all is said and done, you will be a very big asset in industry and R&D. A computer scientist who knows mathematics is a very dangerous person ;^)
Good luck, and I'll be cheering for you.

Remember that graduate schools vary a lot in the material that they require for incoming students. For almost every school, a background in real analysis and abstract algebra is mandatory, along with mathematical maturity and proof ability. But topics like combinatorics, Riemann surfaces, and number theory are more specialized, and only a minority of schools would have those as part of their qualifying examinations.

Sure, that's why I put that many math students 'usually' take courses like them. I probably should have not lumped them together

The easiest transition is probably to focus on mathematics programs where you can study topics closely related to computer science. You didn't mention in the question which areas of mathematics you are interested in studying. There is a significant amount of overlap between "theoretical" computer science and mathematics, although you have to take time to find the schools where this is studied in the mathematics department.
Even at such schools, though, a mathematics PhD includes a significant amount of "general" coursework. For my PhD in mathematical logic and computability theory -- which is one of the closest mathematical topics to computer science - I passed exams in abstract algebra and real and complex analysis.  The exact topics you would need to study vary by school.
One option that has not been mentioned -- which has advantages as well as disadvantages -- would be to take a master's degree in mathematics first. This would certainly give you the background needed to be prepared for PhD studies. The main disadvantages are that it takes a year or two of your life, and that the funding for master's programs is not as generous as for PhD programs.

Ah, i was going to mention taking a master's first, but I have no idea what Shazly's time frame looks like !


text:
Have I embarassed my supervisors by solving a problem that a PhD student in my group was working on without success?
I'm a bachelor student in mathematics writing my thesis at a small university in the US. A PhD student that has the same supervisor has spent a very significant amount of time working exclusively on a theorem which he hasn't been able to prove, so the supervisor offered me a thesis on the topic. No one was really expecting me to make any real progress, but everyone was very nice and enthusiastic.
It turned out that I was able to prove the theorem essentially straight away using a different approach to what they've tried. After this happened I've felt a distinct change in attitude towards me. There is no excitement, there is no discussion on how to strengthen or generalize the result and I generally get the feeling that they are pretty embarrassed about the whole situation.
The PhD student has a severe lack of publications and is probably feeling quite stressed because further progress on this problem seems unlikely. So what is my best plan of action here? Keep in mind that stepping on toes is the last thing I want to do given that I was hoping to pursue a PhD in this very department. How do I act diplomatically while at the same time making sure I get due credit for my achievements? Is it possible they will try to bully me out of first-authorship to protect the reputation of the PhD student?

Are you sure that is indeed the cause? Causation != correlation (and kudos to xkcd reference)

"hoping to pursue a PhD in this very department"?  Why, if you're producing graduate-level results, would you miss the opportunity to do research in another institution?  So-called "Cross-pollination" of research groups is the normal and desirable thing.  Now this is not to say that you should try to make yourself unwelcome.

I'd still need letters and references, not to mention the ability to prove that I was the originator of the result.

Wait, the supervisor offered you the same thesis topic, or a related topic? Did you solve the same problem or a related one?

Essentially, he wanted me to investigate special cases of a problem, while PhD worked on the general case. I got an idea that turned out to be general enough to solve the general case. I suppose supervisor did not assign this event any significant probability but IMO he really should have.

It's not your fault... But it's a tender situation overall. I suggest talking to your advisor 1-on-1 over lunch or coffee. Ask advising on how to proceed. Express your excitement at the discovery but also the realization about the social and professional implications to with the PhD student. You absolutely deserve credit for your work, but it would be nice if everyone walked away gaining something here. Keep humble and communicate.

Hooray! The struggling grad student gets a publication with an undergraduate coauthor! Everybody wins!

Is there a way that the main problem here is that the grad student and faculty now, with your quick proof, understand that this problem is just not as interesting as they thought it would be?

Consider letting the grad student have the theorem 'for free' (with you keeping the special case for an undergrad thesis if you need it). Offer this as a solution to the professor and and say you understand the embarrassment caused and are willing to give up credit in return for being accepted as a PhD student yourself.

Do not give credit to others, if it is your idea you should be the first author. Accepting an offer to trade credit suggest a possible significant level of corruption and misconduct in the department.

@xLeitix Very good point.

@TheMathemagician It is basically cheating isn't it? I would guess it is highly problematic to publish someone else's results as your own.

first thing you should do is congratulate yourself. you've done something great and have done absolutely nothing wrong.

@TheMathemagician Suggesting rolling over and giving away the achievement for free is terrible advice.

@MikeyMike's advice is spot-on. Frankly, you have an ethical obligation not to negotiate your credit away! Credit is partly a badge of honor in academia, but it is also taking responsibility for your published work. For example, if your proof were later shown to be wrong, as the person who created the proof, you're the one who should primarily have to face the music (which isn't the worst thing in the world if you act in good faith), not the grad student or your advisor.

@Kevin: doesn't that depend what else the paper contains? If it's "proof of a known conjecture" then sure, the questioner could potentially be sole author. But the more other material is included, the more was contributed by the PhD student or the supervisor. Or not? Anyway, as xLeitix says, the problem here might be that they've realised the whole topic isn't paper-worthy, and the dirty looks are because they are restraining themselves from throttling the messenger. In which case one hopes they'll get over it ;-)

Starting a credit war for a small theorem is a terrible advice. JeffE's advice is good: co-author the paper with the grad student. It doesn't hurt you in any way.

@MikeyMike in mathematics, the order of authors is alphabetical.

The thing I love most about situations like this is that through all of our moral and cultural beliefs, if we ever expected there to be one area of society where results took precedence over petty politics it would be academia. But No!!! A culture developed by the most highly educated mankind has to offer, that prides itself as the flag bearer of science and having no dogma. Yet someone who did nothing but his job has to worry about diplomacy. There's is something really wrong with this model of research academia. Unfortunately, it's the only one left now.

Don't give up an ounce of your due credit.  But consider this, did any of their work help frame the question when it was presented to you in a way that helped your chances beyond if you'd come to the problem cold?  At the very least they picked the special case for you to start work on.  A lot of this world's answers were only found once we asked the right questions.  Work that eliminates dead ends might not get a lot of press but it's still work.

It sounds like you've put your finger on a bad situation, but I'm not sure if the bad situation actually has anything to do with you. There seems to be some doubt about this grad student's viability, and maybe you coming up with this quick solution made those doubts stronger, but it's not really your fault, and you're still not really involved. I think the issue of what to do with your result is pretty separate from the social / academic issue that the professor and student are going through and I don't think you'll find any conflicts.

It is easy to get excited if you manage to do something that other people haven't, but please try and remain calm. It is very easy to unintentionally hurt peoples pride if your excitement spins out of control.

@MikeyMike The question is: how much credit goes to the supervisor and PhD student for formulating the question? Sometimes especially unexperienced young researchers underestimate that the clear formulation of a question is as important as being able to answer it. Quite possibly that's not the case here - but I'd like to remind of the Taniyama-Shimura conjecture. Credit-grabbing can cut both ways. It depends on the complexity of finding the question formulation and the complexity of finding the proof.

So @horsestaplebattery got the answer correct? Great, you've ruined my secret password...

@horsestaplebattery Since you solved his PhD thesis for him by your method of proving the general case (or one that covers much of it) of a problem I imagine that he cannot use your method for his thesis. Because of this he may try another method or change the topic of his thesis. Then why can't you use it for your own PhD thesis? You already proved that you can do original work to add to the knowledge base. Although you may also need to take some courses along with other rigorous requirements it may turn out to be one of the easiest PhD's ever earned.

Interesting that this answer by Moishe Kohan https://academia.stackexchange.com/a/194816/108687 about sharing the credit was so warmly received, whereas here there's significant pushback against the idea of sharing credit unduly (to the point of calling it corruption and misconduct)!

First, if you haven't already, I suggest you have a discussion with your advisor about what to do with the result.  Is it worth writing up?  Is it worth trying to publish or try to go further?  If so, you should write it up and make sure there are no errors, and hopefully your advisor will be willing to help check over this.

Is it possible they will try to bully me out of first-authorship to protect the reputation of the PhD student?

Anything it possible, but nothing you have said gives any indication anyone else thinks they should be a co-author for this result, assuming it is publishable.  It's common in math that a problem seems difficult from one perspective, but is easy from another.  This can always be a little embarrassing, but usually it's no big deal if you're dealing with reasonable mathematicians.  However, it may mean (for a variety of possible reasons) that the problem is less interesting to them than originally thought, and this could be part of what you're sensing.  I've often gotten excited about discovering things, only to realize later that they weren't so novel, or been interested in problems because I thought my methods could solve them then lost interest when I found out other methods are much better.
Anyway, hopefully an open chat with your advisor about this will clear things up.  I would not mention the PhD student in this discussion, just focus on the questions in my first paragraph.
Edit: I forgot to say, your situation may indicate that this department might not be your best option for a PhD (there may be a trend of weak grad students or not-on-the-ball advisors).

From my experience as a math grad student myself, I agree with the suggestion that it is not that the PhD student (say Paul) is particularly slow, but that the problem itself was easier than Paul or your advisor anticipated. When you are acquainted with a larger collection of techniques, it is easy to start throwing everything you know at the problem, thereby making the problem actually seem much harder than it is.

For example I attempted a naive 2D extension of a method that had worked in 1D for a certain problem on a lattice. Superficially it seemed that nothing should be different, but in fact there was more room in 2D for nonphysical effects, which were present but minor in the 1D case, to propagate and thereby persist. This essentially killed the idea of directly extending that method...which my advisor thought would likely work.

I suggest you to publish it immediately

BAD IDEA @AlexeyVesnin ! If the work the OP did is in any way based on any quantity of research done by others in his department he will be accused of taking credit for other's work. Even the grad student's failed approaches are valid parts of the research that must be given credit. If he publishes without the university on board it is the END of his career. What he needs to do is establish evidence that he is the originator of the proof and then approach the team and the uni to see what they plan or want to do. Maybe they will all be cool but he needs to be ready for the worst.

@O.M.Y. I didn't even presumed any form of plagiarism, you've got me wrong. As far as I understood the OP's situation, he'vr done it on it's own, so there's no problem of any kind in publishing his very own research/work as an article. Plagiarism is not just an END of career - it's a punishable crime in almost all developed countries. If someone has been researched the same subject, but failed - he can publish his fail on his own.

@AlexeyVesnin OP says in their question that they used an approach that hadn't been used yet by the PhD student. This implies that OP had working knowledge of the work that had already been done on the problem. If OP didn't have that knowledge, they may have redone the exact same work as the PhD student, thereby taking just as long or longer, and the PhD may have completed before OP. By leveraging failures, OP completed the problem faster. That is to say, it could and likely would be considered plagiarism. O.M.Y and Kimball are right. OP should speak with advisor pronto.

How do I act diplomatically while at the same time making sure I get due credit for my achievements?

Follow JeffE's advice: You have at least three people who contributed to the proof of the theorem. The advisor who suggested the problem. The grad student who worked out several ways that don't work. And you who produced a proof. So it is perfectly valid to write a joint paper. In mathematics it is pretty important to figure out ways how not to prove something. (There are papers and blog posts by renowned mathematicians starting with "How not to prove…", e.g  a paper called "How not to prove the Poincare conjecture", the blog post "How not to prove that P is not equal to NP", the paper "How not to prove Fermat's last theorem".)
Very often it is the case that a proof is discovered by somebody only because he already had seen enough attempts that don't work. It is really common to try two different ways to prove something, see how each one fails at a different point and then see that some third way will succeed. In addition the grad student may well be able to write a good introduction on the background and context of the theorem.

Is it possible they will try to bully me out of first-authorship to protect the reputation of the PhD student?

There is not such thing as "first-authorship" in mathematics, see here: https://mathoverflow.net/questions/19987/math-paper-authors-order

Could you provide the authoritative links for your references?

Added  links. I could not find a digital version of the  paper on the Poincare conjecture, however.

I think this is by far the best answer. Don't focus on the problem, focus on the solution. And here there is a very clear one, which should make everybody happy and transform this from a sad success disaster into a fruitful collaboration.

In math, neither suggesting a problem nor failing to solve it usually merits co-authorship.  The "How not to prove..." links you gave are not typical research articles.

I agree with @xLeitix but I also see the point Kimball made, and surely there are many avenues in which the result could be tweaked, generalized, strengthened (even if only by an epsilon amount), etc. This is an aspect on which the supervisor should be able to provide numerous suggestions. I realize the OP should not reveal precisely what the result is, and I am certainly not asking for any details, but I find it very difficult to think of anything in mathematics (that I know anything at all about) that I couldn't easily come up with all sorts of possible ways to tweak.

Does that mean Perelman would have had to add Poincaré as a co-author?

There is no such thing as "first-authorship" in mathematics One less opportunity for bullying.

If the horsestaplebattery was aware of the PhD students attempts and avoided using the same approach because those attempts had failed, then I would include that PhD student on the paper.  Even the simple knowledge that there was a PhD student working on it could have helped him find the answer quickly if he purposely avoid the more obvious approaches because he assumed the PhD student had already tried those.

There's nothing here that suggests that the advisor's name should be on the paper (if the result is publishable), nor that the advisor would want coauthorship.  Math publishing conventions are different than many fields, and most student papers are not coauthored with the advisor.  A joint paper with the grad student may be appropriate, since the graduate student may have worked out closely related results, examples, or applications, and the prior failures of the grad student may have helped in finding this proof.  (Though, depending on circumstances solo authorship might be most appropriate.)

Regarding first authorship not really existing in math, I don't think this is universally true (which is very bad for people who are following the alphabetical convention). Consider the conference SPARS in France, they have a call for submissions for a "Best Student Paper Contest" and in the guidelines they write, "Papers co-authored by a student (who must be the first author) may enter the Best Student Paper contest."

Of course I can't say anything definitive based on the limited information in your question, but one possibility is that you may have inadvertently committed a faux pas.  Your advisor may be upset that he/she didn't anticipate this possibility and head it off.
One of the basic rules of the mathematical community is that you don't compete with graduate students by working on their thesis problems.  This rule isn't always followed, but exceptions are rare and they look terrible unless you have an awfully good excuse.  The reason is that grad students are generally inexperienced and slow compared with faculty, which makes it unfair to compete with them.  There's little glory in winning, and you can do an awful lot of damage if you swoop in and ruin someone's thesis.
Of course this rule is not really aimed at undergraduates, and you aren't in nearly as awkward a situation as a faculty member would be.  However, the fact that you could prove the theorem indicates that you are unusually talented, in which case it could still look bad if you screw things up for a less talented student.
I don't mean to suggest that you are primarily to blame.  It sounds like you were put in a delicate situation without being warned about potential pitfalls, and your advisor should not have let this come about.  However, when you started trying to prove the theorem, what did you think was going to happen to this graduate student if you succeeded?  There are various possibilities (restarting work on a different problem, hoping to find extensions substantive enough for a thesis before you prove them, dropping out of grad school), but they aren't terribly appealing.
It comes across as callous to be more concerned with getting credit yourself than the repercussions for this graduate student.  You deserve credit and should get it, but I'd recommend having a discussion with your advisor (in private) about how to avoid causing problems for the grad student.  For example, maybe there are directions for follow-up work that you could leave to him to explore.  This could help relieve the tension by showing that you realize it's an awkward situation and want to make sure the other student has a viable path forward.

I appreciate this answer very much. In hindsight, the only outcomes of me joining this project was me not producing anything of worth, or the PhD student getting embarrassed. Clearly I did not consider any of this at the time, I was just excited to prove stuff. Maybe I should consider sacrificing credit for the sake of diplomacy. There are always new ideas to explore.

Excellent response. It is a major problem if you succeed whether others have failed and you were not expected to make them "look bad". But it's not your fault. A highly diplomatic approach is required to avoid them losing face. But frankly, if latent rancour develops or persists, this is a good reason to see that you change department (if there are other good departments in your field), because they may feel threatened. You need a place where your superiors are not afraid of you.

I read the question as the supervisor and PhD student had already given up on the problem and moved to other things.  Otherwise, I agree the advisor should not have given the OP this problem.  Maybe @horsestaplebattery can clarify?

It sounds like you're saying, in so many words, that the mathematical community is very anti-meritocratic.  Is that what you intended to convey?

Downvoted because the idea that an undergraduate can take any blame for taking an assignment, and performing it too well for diplomatic niceties, is beyond my ability to accept.

The posting explicitly says "the supervisor offered me a thesis on the topic".  That being the case, it seems absurd to suggest a rule was violated.  "you don't compete with graduate students by working on their thesis problems" seems like a rule for faculty.  A student who is "offered" "a thesis on the topic" cannot be considered to be violating such a rule because he succeeds.

I understand that a faculty should not swoop in and steal a PhD student's thunder. I even understand that a fellow PhD student should not do that. But assigning (even partial) blame to the undergrad because he solved the problem too well seems super odd to me.

@xLeitix: AnonymousMathematician isn't blaming the OP here; I think there's a misunderstanding. He's doing the equivalent of asking a pedestrian who got hit by a car, "Did you look both ways before crossing after you saw your green light?" That's not putting blame on the pedestrian (the car driver would still be at fault); that's just giving advice to prevent accidents caused by others' mistakes.

@Mehrdad I guess we are arguing semantics here, but for me "giving advice to prevent accidents" is at least close to assigning partial blame. Also, there are definitely parts in AnonymousMathematician's answer that suggest to me that he sees some part of the blame on the OP.

@xLeitix: Sure, so let's get the semantics of "blame" cleared up. He's not "blaming" the OP in sense of holding him responsible (which is the first definition my dictionary tells me, incidentally). He's only "blaming" him in the sense of criticizing him (which is the second definition my dictionary tells me). Does that clear it up?

when you started trying to prove the theorem, what did you think was going to happen to this graduate student if you succeeded? is holding the OP responsible for not thinking carefully. I strongly disagree with this sentence. What is the OP supposed to think? Why should he think what is going to happen? He just took the topic from his advisor and worked on it. What did he do wrong? What else can an undergrad do when he is given a thesis topic to work on?

"It comes across as callous to be more concerned with getting credit yourself than the repercussions for this graduate student." It's not his job to be concerned about the grad student's progress; if anyone, the advisor has been negligent here. Downvoted because this answer in effect discourages excellence.

@DanielR.Collins "I don't do favors. I accumulate debts." This may be the most profitable approach in the long term.

Downvoted for -this should be science, not politics!!!

@MikeyMike When dealing with people, everything is politics.

I don't understand at all why a sucess of some undergraduate student in solving a problem is considered as a shame for him ?! Besides, it is the supervisor who offered this problem as a thesis to OP... Weird that mathematics community behaves in this way...

I think the last paragraph is of great value: showing to the supervisor that you care about the grad student may help relieving the tension.

@scaaahu: The OP is not being "held responsible" for the problem though. He's just being told that he could have potentially prevented someone else's problem. "What is the OP supposed to think? Why should he think what is going to happen?", well, a super-cautious student could have told the adviser, "I'd love to work on that, but wouldn't that overlap with his work...? Do you expect the solution for the special case to be necessarily different than for the general case?" Of course, you wouldn't expect any undergrad to have the experience to do this; it's just advice for the future.

The situation is unfortunate, but/and I think AnonymousMath'n has captured the reality of the situation, and the contemporary conventions in mathematics. That is, while it's not an undergrad's "fault", and the advisor should be blamed for bad advice and more, the latter is not sufficient for the undergrad to just go ahead... That is, there is a general tradition of not "poaching" on other peoples' projects... (unless it's something really juicy, I suppose, in which case it's amoral carnage?) It's one thing to "hijack" the project of someone one doesn't know, but worse if you know them.

I strongly object to this entire post but especially with @paulgarrett 's use of the word "hijack" in this context! An undergrad was assigned a legitimate task to work on one or more special case solutions as a subset of a larger research project, the UG did the task he was assigned, and in the process stumbled across a general solution. End of story. The OP did absolutely nothing wrong and the advisor is the only person who should feel any level of guilt in this matter. Did the advisor even bother to pre-discuss the task assignment with the grad student so he would be aware of it?

I think Paul is spot on, actually.
academia.stackexchange continually conflates expectations with reality. How should this play out is entirely different to how will this play out, and a downvote for this was not a helpful answer is entirely different to a downvote for I don't like this. Ironically, those who downvote because the answer contains an element of injustice are frequently being unfair themselves..

It's really shocking to me that the one answer that actually explains what's happening is heavily downvoted.  Probably mostly by people who aren't mathematicians and have no idea what they're talking about.

@NoahSnyder I might not downvote this answer but especially "However, when you started trying to prove the theorem, what did you think was going to happen to this graduate student if you succeeded?" is in my opinion an odd thing to ask and does come off as accusatory. Especially as it does not become  quite clear (to me) what exactly OP should have thought and done in A.M.'s opinion.

Just publish it. You are the "kid" in this business and all you did was to do what was asked of you. You just happen to do better than what was expected of you. Hardly anything to be worried about! So be humble and thankful but grab the credit that you deserve and let the others worry about their own ego frailty. Those are not your problems.
Spread your wings and look elsewhere for graduate work.

Totally agree !

BAD IDEA! A publisher will almost always contact the university to ask about the author's credentials while vetting the paper. If the supervisor is either unethical or just plain embarrassed this could backfire badly on the OP. Unless the OP has created evidence that he is the true originator of the mathematical proof, publishing without any in-house discussion is a very dangerous game.

I disagree completely with O.M.Y.'s comment. I have never heard of a publisher contacting an author's university; in any case, it is certainly not true that this "almost always" happens. Moreover, even if they did, there is nothing inappropriate here that the publisher might discover; the OP does not need any supervisor's permission to publish a paper!

Tom's right, I have no idea what O.M.Y. is talking about.  You're well within your rights to go ahead and publish without talking to anyone.  But writing a math paper is its own kind of skill, and you're likely to have a stronger paper published in a better journal if you get advice from someone more experienced when writing that paper.  That's why you should talk to your advisor, not because it's mandatory, but because it will help you.

It's worth keeping in mind that in the long term the amount of "credit" that this result is worth to anyone is almost certainly very very small. Math is very hard, and it's very rare to find genuinely important questions that an undergraduate or a weak graduate student can solve.  Most of the value of undergraduate research is learning whether you enjoy the process of research and not in the result itself.  Most of the value in an average PhD thesis is the training in the process of research and not in the problem itself.  I feel like a lot of the answers and comments here are treating this like the amount of credit involved in your result is unrealistically large.  In the long run, people care about your research program, and this paper will fall outside of that program, and so won't be important in evaluating you.
That said, it's a great experience for you to solve an open problem!  Hopefully this has showed you that you're capable of getting a PhD and that you would enjoy it.  It also should be valuable to you in that it should show admissions committees these two facts!  It is also worth remembering that this "credit" to the admissions committee is at least as much in how your letters of recommendation talk about this result as it is in the publication itself (which may well not be through peer review when you apply for grad school).
So think about this more in terms of experience and less in terms of piling up formal credit.  Talk to your advisor and figure out what is best for you in terms of further experience.  Maybe there's a solution that will also allow you to learn valuable collaboration skills by working with the graduate student on related questions.  You will also learn valuable skills by writing up the paper (whether alone or in collaboration).  All of these things will make you a stronger graduate school candidate and a more prepared researcher.  A strong letter that says you're an excellent problem solver and an excellent collaborator and great to work with is how you get the most credit.  Generosity and credit are not enemies of each other.

+1 for "Most of the value of undergraduate research is learning whether you enjoy the process of research and not in the result itself. Most of the value in an average PhD thesis is the training in the process of research and not in the problem itself."

As an academic with three departments under my belt, I'd strongly advise you based on your experience here to take your skills elsewhere.  It is generally a bad idea for an undergrad to continue on to do graduate work in their same department: to the faculty, you will still appear to be the same undergrad, not "fresh meat" that everyone is excited to work with.  And there is also the general rule that first rate people seek other first rate people, second rate people seek third rate people, third rate seek fifth rate, etc.  If there is no excitement at your unexpected result -- you should seriously consider whether this is a department you wish to be affiliated with.
Under NO CIRCUMSTANCES should you grant the credit to others.  Not only does it do discredit to you, it does discredit to the entire field, and cements and institutionalizes the theft of credit.
In my experience, an undergraduate who achieves a significant theoretical result belongs in a place which can develop their abilities.  Such an achievement would go far towards a very strong graduate application.

"undergrad to continue on to do graduate work" this is about undergraduate research.

I disagree that you should never continue from undergrad to grad at the same uni (I did so myself along with a number of others, based on good advice that this was perfectly reasonable). Otherwise, there are some sensible points here, although they are not really answering the question that has been asked.

who seeks second and fourth rate people? Or in general 2n rate people (where n is an integer and n>0)? (yeah, I used to be a scientist too :))

(Too long for a comment.)
Worrying about potential consequences to some grad student is a task of their supervisor, yet this is not an ideal world. To a various degree, most of us frequently act with a wider context in mind, protecting others from their (usually) temporary stupidity. Note that in many countries some things are explicitly forbidden instead of only marked as dangerous. This is also one of the reasons why some people are great team players, while others aren't. Moreover, this is often far from easy, there are lot of factors the difference that matters might be slight, like saying that everybody is alright before that there was a car crash.
Doing math is a social activity, and we should consider other people feelings.
We should strive for an excellence, but that is no excuse for being a jerk.
I think @JeffE's solution (a joint publication) is the best one.
Do not accept giving away the result, but a joint paper should be ok (with an alphabetical order of authors). Be aware that although in math the author order does not matter, it might matter for some other things (scholarship rules, etc.). Perhaps the grad student can do some additional work to justify coauthorship if you are unsure. Talk it over.
As for the change in attitude, normally it would depend whether that was a change in attitude towards you, or towards the problem and situation in general, whether it was positive (more respect) or negative (you are a threat), permanent or temporary (it's normal for people to get grumpy for a few days). In your case however, unless you have some special circumstances, I advise you to pick a different place for your PhD.
I hope this helps ;-)

Whether you have embarrassed your adviser will depend on his/her personality. If the focus is on the maths or scientific progression, then he/she should be happy.  Moreover, he/she should have the graduate student build on your progress (if there are avenues for doing so).
I don't see why you should feel bad about proving the theorem.  You should celebrate!  Yes, you may have embarrassed the graduate student, but heck, that's is normal.  You came in with a fresh perspective so you have a better chance.  From your description, the graduate student seems weak academically.  There is nothing you can do about it.  His/her adviser on the other hand can maybe help out a bit more, but that is his/her problem.

I'd suggest you offer to go out for a couple of beers (you pay) - And after a few beers just be honest about your concerns. Be sure to give the PhD student a wealthy round of thanks for the "great" work that he has already done, as it certainly played a part in the solution you were able to come up with.  Above all, be humble!

I do not consider beer to be a professional solution, but it depends on the local culture.  The rest is good.

I agree with @AnonymousPhysicist. Awkward professional situations like this require whisky.

a wealthy round of thanks for the "great" work that he has already done - Dishonest flattery is not becoming.

Okay, so I overstated it a bit, and I don't suggest dishonest flattery either.  Acknowledging that someone else's work had some part in your success (if true) can never hurt the situation.  I guess my focus here with beer, encouragement, and humility is that we are talking about human relationships here.  Building someone else up is always a preferred to tearing them down.

All of this assumes your idea is indeed great.

It's unlikely they will try to steal your idea outright. If concerned, get your approach in public as much as possible (trace your original publication of it, email your group about it, post it in whichever online forum this is done, etc.). E.g., submit it to a conference, even if only for students, etc. Want to piss them off? Submit it to a regular conference.
Forget these fools if they act like they don't know you. Nourish relationships with those that matter; move on to somewhere else.
Catering to people's weaknesses is the real faux pas.

If you ever need to defend yourself against a charge of plagiarism you will want evidence/proof of originality. Before you do anything else I would create what is called a "Poor Man's Copyright" as such evidence. NOTICE: I am not a lawyer and this is not legal advice (this is just what I would do based on my experience) so use at your own risk:
Do the following but make every effort not to use campus-owned supplies (paper, blank DVDs, etc) or equipment (computers, copiers, etc) unless you have no choice (mainframe screen-grabs). Do not give anyone an excuse to say you were misusing University resources:

Write this up as quickly as you can, even if it is not perfect ... probably what you have already written is sufficient. Date it now if it does not already have a date on it.
Print a copy of the writeup and put it in a simple long envelope.
Take that long envelope mail it FROM a post office to your home address. Send it via "registered mail, signature required, and return receipt requested". Be sure the envelope is well sealed.
DO THIS TODAY!

The above is the essence of a poor-man's copyright and is the very least you can do (see the very last bullet paragraph below for how it is used) but you can expand on this by ALSO doing the following:

Print another copy of the write-up and all the supporting documentation that can be printed. If there is software code or data for documentation either make some screen-grabs (cell phones pics are ok) or burn it to a CD-ROM / DVD disc (or disc sets). Make 4 of these discs (or disc sets). WARNING: Do not copy any software code/data you did not create yourself.
Photocopy three sets of everything (use a copystore away from campus if you have a choice and get a receipt). Use a black & white copier except for any specific pages that would make no sense without color.
Copiers malfunction so double-check before you leave the store that all FOUR sets (including the original set) are complete AND legible. Did you get everything back on your originals? Do your three copy sets all have the same pages as the original set? In the same order?
Have four envelopes/folders/boxes (whatever you need for carrying each set in a single container). Once you have verified all is complete put each set in its own container then go home.
From this point on do not write anything on those originals or change that set in any way. Keep the original documents in their container and leave it alone. Hands off!
At home count the number of pages (count twice, double-check) then on the copies ONLY with a RED pen number every sheet with "X/Y" (or "X of Y" if you prefer). Also put "Copy A" or "Copy B" or "Copy C" as appropriate. Work slowly and carefully as all three sets must have matching sequence numbers. If you make a mistake put a line through it, initial it, and correct it. It is okay to write over the photocopied text if you must, that is why you are using a red pen.
Next type up a simple letter telling your story as you did here (but with all the names, dates, and problem description included) and closing the narrative with a declaration that you are the sole creator of the proof and also personally created "the attached documents".
In the header of the letter put "AFFIDAVIT OF EVENTS" centered across the top of each page and also be sure the letter formatting includes "page X of Y" in the footer.
On the same letter, immediately after your narrative, include an attachments inventory summarizing one set of everything you copied ("Item 001: 2 pages describing the proof", "Item 002: 14 pages of data representing XYZ", "Item 003: 1 screen grab from the department mainframe terminal", etc.). If you have any discs include them on the list last ("Item 29: 2 CD's containing R code used to demonstrate the proof.").
At the bottom of the letter include a statement that declares everything above to be true and affirm that you are the sole author of the letter.
Include a space for your signature but do not sign it yet. Also leave at least a half-page of space on the same page after your signature. Reformat/resize the text/font/margins/etc if you have to but that half-page space is important.
Take ONLY the original set of documents and the unsigned letter and go to a (NON-campus) notary public (ask your bank manager if you don't know where to find one). Be sure you have your official photo id (driver's license or passport) with you. Also note a "notary public" is NOT the same thing as a "notario publico" -- a sort of specialized lawyer from some Spanish speaking countries -- so don't confuse the two).
Tell the NP you have created a "personal affidavit" of events and wish to have it notarized. Take out your letter and IMMEDIATELY sign it in front of the notary THEN hand it over to them to read. Be sure you sign the letter's signature space in the presence of the notary using a BLUE ink pen, NOT a black one. That is important because most notaries use black ink for the areas they have you sign but when the letter is photocopied it is hard to decide which is the original if everything is black.
The notary is only going to glance at the letter to be sure it is in fact what you have described (an affidavit). It is unlikely they will spend more than about 30 seconds doing this. They may also ask about the attachments (since they are referenced in the letter) but it is unlikely, but if they do show them the originals. Again, their primary concern is that the document is what it says it is, not the contents per-Se.
They will have a form or imprint of some sort to attach to that letter (which is what the half-page space is for). Depending on what state you are in you may be asked to "swear or affirm an oath" that what you have written is true. There will be a little paperwork and some sort of thumbprint will be taken. You will be charged about $10 (ten dollars) for each signature required (which should be only one).
Take the notarized letter and go get at least FOUR additional copies made, but a couple extra above 4 is a good idea. Put the original letter in with the original documentation and close the container. With luck you will never open this container again.
Go home. Put the container with the originals somewhere safe. Next get the other 3 documentation containers and put one copy of the letter into each container. Put "Copy A" aside, that will become the one you show folks in general, if you need to.
Take one copy of the letter and put it in a simple long envelope.
Take that long envelope and also the "Copy B" container (with its own copy of the letter inside) and mail each of them (one letter by itself, one container with a letter & docs inside) FROM a post office to your home address. Send them both via "registered mail, signature required, and return receipt requested". Be sure and tell the Post Office if you have included any CD/DVD discs in the package as these may affect their security scanners.
Take the "Copy C" container with a letter inside and ship it FROM a Federal Express office (Kinko's copystores usually) to your home address. You may need to put it in one of their official envelopes/boxes. Send it "signature required". Be sure and tell FedEx if there are any CD/DVD discs in the package.
NOW THE MOST IMPORTANT STEP OF ALL: When the letters and containers arrive at your home, put them aside somewhere safe and NEVER OPEN them. Put the 3 packages (the Originals, Copy A and Copy B) in three different places so they are safe from fire/water damage/theft). These letters/packages should only be opened in a courtroom (with your lawyer present) since once the seal is broken the proof of the date of their contents is lost.

Hopefully this all resolves without any accusations or legal evidence required but at least you will have this if you need it. Good luck and be proud of the proof work you did.

I don't understand why someone downvoted this answer without bothering to comment. This is the only answer that addresses the question as a legal problem and provides a very specific course of action to protect the author from further unpleasant situations. Until now, other answers have provided suggestions on how to behave in a sociable and acceptable way without "stepping on toes", but that's not the real issue. If any/all of the involved decide to use the OP's proof for their own exclusive benefit, there's no way that the OP can prove to anyone else that the discovery was made by himself.

I think I failed to make clear that the "social" solutions (private and honest conversations with the people involved, etc) are certainly worth pursuing. But having evidence ready as a backup in case those strategies do not work is all that I am suggesting. As I said, hopefully the evidence never needs to be touched once it is created, but a charge of plagiarism could destroy a career unless you can successfully defend against it.

Apart from up-or-down votes, the reality of the situation, in contemporary mathematics, is that doing this sort of thing, if anyone else were to become aware, would be construed primarily as evidence of crackpottery... and nearly-perfect lack of awareness of the current conventions. In particular, probably whatever problem was solved is not of tooooo enormous consequence, so going to such measures to prove one's priority is wildly disproportionate. E.g., unless one presumes the gross dishonesty of one's co-workers and advisor, it is already well-known that one did the thing, etc. ... [cont'd]

... [continuation] Such quasi-legalistic priority games are not what one wants to do. It's not that anyone's trying to not give credit. Rather, it's that other people had estimated what would happen, without thinking too much, evidently, and screwed up. It's ugly when one's advisor screws up in a way that splatters the excrement around... and they're embarrassed, etc. And, yes, one should not have had to worry about it... but it would have been far better to have wondered a bit... and so on.

@paulgarrett, my field is words, not numbers, so it is true I may not know the "conventions" of the world of mathematics academia. In words and most other academic (and private sector fields) proof of originality is paramount, if for no other reason than establishing the provenance of idea developments. The entire concept of plagiarism, a central issue in all fields of academia, is firmly grounded in proof of originality as well. Establishing a court-provable dated papertrail is an extremely simple (no lawyers required) precaution to be used ONLY if you are accused of plagiarism.

@NajibIdrissi, you cannot copyright ANY kind of idea, only an expression of an idea. You also cannot copyright number sequences but you can copyright applications of those sequences. In this case the law grants OP the copyright for anything he created automatically, including research documents & reports that express the idea and show the work done so far. However the University may have contractual rights to his work. Ultimately however this is not about copyright at all, it is about being able to both publish and be ready to defend if accused of plagiarism if that happens.

Yes, I did read your link. I never said he should not widely publish, I only said that he should take 1 or 2 days to do a little C.Y.A. before he publishes. We do not even know what country the OP is a student in and we all know ethical standards vary widely by geography, by culture, and even by school. In a best case scenario the OP publishes and all is cool, the envelopes are never seen by anyone. In a worst case scenario the OP publishes and the Uni says he stole the ideas, but he can prove that accusation false because he was prepared.

Aside from the overall whiff of crackpottery / anachronism that this answer gives, this 25 step plan is based on a logical flaw: writing something down and keep signed / dated / notarized / whatever copies of it doesn't show in any way that others were not involved in the work.  Maybe this practice can be effective in a priority dispute between people who have minimal or no contact or affiliation.  But it is not convincing at all to show that the work was done independent of the advisor who told the student the problem and the PhD student who had previously worked on the problem.


text:
How to stay organized while conducting research?
Doing research, there are plenty of stuff we should take care of, different articles and notes, websites etc..
It is sometimes hard to stay ordered and not to get lost in too many pieces of information. How do you organize your work? Are there any helpful software tools to conduct research projects — in my case, a thesis?

Possible duplicate of Are there specific organizational processes or tools (not necessarily software) that can help in developing and structuring research ideas?

For me, it is difficult to give a fit-for-all answer. The best method is the method that you are most comfortable with. Different people use different tools. My M.Sc. thesis supervisor was a believer in taking notes in paper notebooks. I prefer to construct a set of structured folders in my PC and and use them for managing different aspects of a project (codes, texts, papers, notes, media, etc.).
Of course, there are software tools that can be helpful too. As Elad Den has answered, reference tools are very helpful (I have personally used Zotero but couldn't like it much and ultimately used plain BibTex files).
On the other hand, there are project management tools that some people are very comfortable with (after all, a thesis is a big project). Trello is a popular and free tool that is very simple to use (I have used it for non-research projects and was very comfortable with it and I believe that it has potentials for managing research projects). Evernote is also another tool that is great for taking notes and has some project management features.
Generally, and based on my personal observations, it mostly depends on your personal preferences and I believe that it is a good investment to spend some time on trying different methods and finding (and/or fine-tuning) your approach. Also, it is not a bad idea to have a talk with your supervisor and have his/her opinion.

I recommend working with reference tools such as the likes of Jabref (or Mendeley or Refworks or whatnot). They are bibliography tools, but they can also be used to orginise your references. You can add the abstracts and your own notes. The great advantage in using such tools is that when the day comes to use this information in your thesis your bibliographical database will be ready.

If you are familiar with Jabref, than a look on Docear (http://www.docear.org/) may be interesting.  It includes JabRef, bridges (back) to TeX and wordprocessors, yet additionally offers mindmapping to the literature already managed/annotated, and (optional, based on these maps) suggests further literature.

Outlook is good for organizing meetings, seminars and other events in calendar. Onenote is quite good as well, although I don't know if it is has project management features as MxNx said Evernote has. You can also consider online repositories as a way to inspire progress. Research-gate for example is not just a repository, but a way to update projects. Outlook is also the ideal way to manage your various mail accounts. You can add more than one email and also group categories, such as supervisory team, writing groups etc. You can even make a team in outlook, which allows you to send emails to select groups of people in one click.
Others have also mentioned tools such as Mendeley, personally I use Endnote to organize my references and annotated bibliographies. I don't upload my papers, so I didn't see the need to branch out into Mendeley. Instead I use separate folders for each task. You can use Mindmappers to conceptually organize your ideas. You an also use a tool such as Harzing's Publish or Perish to keep track of citations by researcher and other parameters, or simply use alerts in Google Scholar etc.