Have I embarassed my supervisors by solving a problem that a PhD student in my group was working on without success?

197

23

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?

horsestaplebattery

Posted 2016-04-12T23:42:58.247

Reputation: 813

13Are you sure that is indeed the cause? Causation != correlation (and kudos to xkcd reference) – Fábio Dias – 2016-04-12T23:48:57.027

89"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. – Ben Voigt – 2016-04-13T00:15:03.493

2I'd still need letters and references, not to mention the ability to prove that I was the originator of the result. – horsestaplebattery – 2016-04-13T00:19:15.280

1Wait, the supervisor offered you the same thesis topic, or a related topic? Did you solve the same problem or a related one? – StrongBad – 2016-04-13T01:11:03.303

28Essentially, 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. – horsestaplebattery – 2016-04-13T01:22:59.323

14@BenVoigt I agree, and also, this whole incident seems like evidence that OP is swimming in too small a pond for his abilities. – user37208 – 2016-04-13T01:53:43.537

8It'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. – zahbaz – 2016-04-13T02:19:38.737

87Hooray! The struggling grad student gets a publication with an undergraduate coauthor! Everybody wins! – JeffE – 2016-04-13T03:32:54.897

51Is 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? – xLeitix – 2016-04-13T06:00:15.830

2Consider 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. – TheMathemagician – 2016-04-13T11:54:17.887

96Do 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. – Mikey Mike – 2016-04-13T12:25:55.870

@xLeitix Very good point. – optimal control – 2016-04-13T13:44:16.007

14@TheMathemagician It is basically cheating isn't it? I would guess it is highly problematic to publish someone else's results as your own. – Honza Brabec – 2016-04-13T14:07:25.377

16Have I embarassed my supervisors by solving a problem that a PhD student in my group was working on without success? One hopes so. – None – 2016-04-13T14:22:55.140

6first thing you should do is congratulate yourself. you've done something great and have done absolutely nothing wrong. – sgroves – 2016-04-13T17:31:30.647

27@TheMathemagician Suggesting rolling over and giving away the achievement for free is terrible advice. – underscore_d – 2016-04-13T19:02:25.250

10@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 – 2016-04-13T20:59:04.693

11Welcome to the wacky world of Academia, where preserving people's feelings trumps actual results. – None – 2016-04-14T02:56:27.227

2@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 ;-) – Steve Jessop – 2016-04-14T10:50:15.547

4Starting 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. – Dilworth – 2016-04-14T16:32:53.343

12@MikeyMike in mathematics, the order of authors is alphabetical. – Sasho Nikolov – 2016-04-14T22:26:19.443

2The 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. – Saad Farooq – 2016-04-16T05:46:02.583

5Don'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. – CandiedOrange – 2016-04-17T05:00:14.627

2It 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. – Owen – 2016-04-18T03:51:43.227

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. – mathreadler – 2016-04-18T07:11:08.150

3@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. – Captain Emacs – 2016-04-18T16:01:51.073

1So @horsestaplebattery got the answer correct? Great, you've ruined my secret password... – Paul – 2016-04-18T19:18:31.333

@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. – Jules Manson – 2016-08-28T03:39:39.850

Answers

149

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).

Kimball

Posted 2016-04-12T23:42:58.247

Reputation: 22 129

27This is the most realistic take on the situation. OP is making a lot of assumptions here, like saying the PhD student has "a severe lack of publications" (lots of PhD students don't have any publications until right before they graduate) and assuming there's a major problem based on a perceived lack of enthusiasm from his supervisor (which could have nothing to do with this incident). – user37208 – 2016-04-13T06:00:32.213

9From 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. – Ian – 2016-04-13T14:10:20.910

2For 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. – Ian – 2016-04-13T14:12:14.317

1I suggest you to publish it immediately – Alexey Vesnin – 2016-04-13T18:14:20.477

7BAD 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. – 2016-04-17T11:36:59.000

1@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. – Alexey Vesnin – 2016-04-17T15:59:32.253

@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. – EvSunWoodard – 2016-10-12T17:42:45.773

93

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

Dirk

Posted 2016-04-12T23:42:58.247

Reputation: 28 198

Could you provide the authoritative links for your references? – l0b0 – 2016-04-13T06:48:50.073

Added links. I could not find a digital version of the paper on the Poincare conjecture, however. – Dirk – 2016-04-13T06:57:13.127

8I 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. – xLeitix – 2016-04-13T08:14:54.927

40In 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. – Kimball – 2016-04-13T13:15:32.027

1I 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. – Dave L Renfro – 2016-04-13T15:15:35.663

2Does that mean Perelman would have had to add Poincaré as a co-author? – phresnel – 2016-04-13T15:45:22.663

17There is no such thing as "first-authorship" in mathematics One less opportunity for bullying. – GEdgar – 2016-04-13T15:51:31.677

1If 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. – Readin – 2016-04-17T19:31:23.383

5There'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.) – Noah Snyder – 2016-04-18T15:11:45.950

23

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.

Anonymous Mathematician

Posted 2016-04-12T23:42:58.247

Reputation: 119 796

4I 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. – horsestaplebattery – 2016-04-13T01:16:14.983

9Excellent 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. – Captain Emacs – 2016-04-13T01:39:25.033

1I 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? – Kimball – 2016-04-13T04:12:41.243

2It sounds like you're saying, in so many words, that the mathematical community is very anti-meritocratic. Is that what you intended to convey? – Kevin Krumwiede – 2016-04-13T04:30:17.073

130Downvoted 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. – Daniel R. Collins – 2016-04-13T04:46:14.760

52The 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. – Michael Hardy – 2016-04-13T05:11:35.393

50I 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 – 2016-04-13T05:58:42.023

5@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 – 2016-04-13T07:37:27.303

4@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 – 2016-04-13T08:13:29.760

1@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? – Mehrdad – 2016-04-13T08:17:50.533

32when 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? – scaaahu – 2016-04-13T09:16:34.830

44"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. – G. Bach – 2016-04-13T11:11:47.550

1@DanielR.Collins "I don't do favors. I accumulate debts." This may be the most profitable approach in the long term. – TheMathemagician – 2016-04-13T11:57:18.497

5Downvoted for -this should be science, not politics!!! – Mikey Mike – 2016-04-13T12:29:14.190

10@MikeyMike When dealing with people, everything is politics. – cst1992 – 2016-04-13T13:11:55.453

8I 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... – optimal control – 2016-04-13T13:31:02.210

1I think the last paragraph is of great value: showing to the supervisor that you care about the grad student may help relieving the tension. – Davidmh – 2016-04-13T21:43:33.177

2@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. – Mehrdad – 2016-04-13T23:26:26.253

5The 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. – paul garrett – 2016-04-14T23:09:49.543

5I 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? – O.M.Y. – 2016-04-17T11:24:22.307

6I 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.. – Wetlab Walter – 2016-04-17T14:50:42.510

3It'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. – Noah Snyder – 2016-04-18T14:56:00.167

3@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. – quid – 2016-04-19T20:09:19.240

14

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.

user1259098

Posted 2016-04-12T23:42:58.247

Reputation: 173

Totally agree ! – optimal control – 2016-04-14T10:17:07.237

1BAD 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. – O.M.Y. – 2016-04-17T11:07:55.547

9I 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 Church – 2016-04-17T12:38:22.867

6Tom'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. – Noah Snyder – 2016-04-18T15:54:04.903

11

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.

Physical scientist

Posted 2016-04-12T23:42:58.247

Reputation: 139

"undergrad to continue on to do graduate work" this is about undergraduate research. – Anonymous Physicist – 2016-04-13T04:29:57.807

6I 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. – Jessica B – 2016-04-13T06:10:57.003

1who 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 :)) – WoJ – 2016-04-14T14:04:16.477

10

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.

Noah Snyder

Posted 2016-04-12T23:42:58.247

Reputation: 12 794

+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." – Yemon Choi – 2016-04-19T17:27:39.120

4

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.

Prof. Santa Claus

Posted 2016-04-12T23:42:58.247

Reputation: 413

4

(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 ;-)

dtldarek

Posted 2016-04-12T23:42:58.247

Reputation: 708

1

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!

megachuck

Posted 2016-04-12T23:42:58.247

Reputation: 401

3I do not consider beer to be a professional solution, but it depends on the local culture. The rest is good. – Anonymous Physicist – 2016-04-13T01:03:13.770

22I agree with @AnonymousPhysicist. Awkward professional situations like this require whisky. – JeffE – 2016-04-13T03:34:18.793

19a wealthy round of thanks for the "great" work that he has already done - Dishonest flattery is not becoming. – Kimball – 2016-04-13T05:24:09.933

2Okay, 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. – megachuck – 2016-04-13T17:25:19.257

-3

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.

O.M.Y.

Posted 2016-04-12T23:42:58.247

Reputation: 828

1I 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. – Armfoot – 2016-04-16T23:15:06.047

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. – O.M.Y. – 2016-04-17T10:57:32.923

4

@Armfoot and O.M.Y. You should probably read this. (Let me also add that as far as I know, it is not possible to copyright a mathematical idea.)

– Najib Idrissi – 2016-04-18T14:20:17.040

9Apart 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] – paul garrett – 2016-04-19T00:14:09.267

4... [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. – paul garrett – 2016-04-19T00:16:50.013

@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. – O.M.Y. – 2016-04-22T22:31:37.917

@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. – O.M.Y. – 2016-04-22T23:02:50.537

I don't think that you read the post I linked. Let me quote it: "You cannot establish priority without circulating your paper widely. Or, more precisely, you can prove that you had the idea first, but that won't help you much. Academic credit is awarded for contributing to the research community. If you have an idea and don't publicize it (so few people find out or learn from it), and someone else rediscovers the idea and tells everyone, then they will get most or all of the credit; because the community will have learned far more from them than from you." Anyway, I'm done. – Najib Idrissi – 2016-04-23T07:34:40.103

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.

– O.M.Y. – 2016-04-24T03:41:36.743

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. – Pete L. Clark – 2016-10-28T13:57:34.240

-4

All of this assumes your idea is indeed great.

  1. 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.

  2. Forget these fools if they act like they don't know you. Nourish relationships with those that matter; move on to somewhere else.

  3. Catering to people's weaknesses is the real faux pas.

user296844

Posted 2016-04-12T23:42:58.247

Reputation: 369

4"All of this assumes your idea indeed kicks fucking ass." Why are you assuming that? The OP describes doing as an undergraduate what a below-average math PhD student at a small university could not do. That is more in the realm of "excellent work for an undergraduate, that the OP should be able to leverage into a publication and (more importantly) admission into a strong graduate program." Much of the rest of what you say is similarly off-center. – Pete L. Clark – 2016-04-19T17:45:13.657