Informing advisors on a tangential sole-authored paper

Question

Over the last year, I conducted research under two professors A and B on two topics A and B. In the last few months, I have come up with an idea that uses concepts from topic A to present a solution to a problem in B, i.e. the idea could be called "Solution to B using A". As far as I can tell, the idea is new, and (if I may say so myself) quite elegant. I intend to write this up and submit to a decent, normal-ish conference. Note that neither of my advisors are aware that I have been working on this, and hence I intend to put my name as the sole author. I have, however, drawn from research I conducted under them.

Question: Am I under any obligation to show the two advisors my work, and inform them that I plan to submit to a certain conference?

I am a little afraid of negative feedback if I show my work, feedback I would rather get anonymously from reviewers rather than from advisors under whom I continue to conduct research. (This is possibly irrational, and I need to deal with it, but for the moment, it is what it is.)

Neither advisor is familiar with the other topic, and hence neither will be able to judge the paper as a whole. I am also a little worried that by the time I obtain feedback from either (or both) of them, the deadline for my preferred conference would've passed. While I do realize that consulting with them will likely improve the quality of the paper, I will mention that:

• I am confident that the mathematical details are correct.
• Both advisors have been very complimentary of my writing style in previous paper(s) I have published with them. The final, published manuscripts do not differ from the drafts I wrote by more than 5%.
• I don't believe that asking both of them to work together on looking over my paper is a viable option, as it's unlikely they could spare the time. Also, they don't really get along with each other.

If I don't consult with them, I am worried that either (or both) of them would be a little offended, since I have drawn from work I conducted under them. I don't wish for them to think that I have an over-confident or arrogant streak in me, and hence did not consult them. Is that logical?

EDIT: I am not a Ph.D. student. I have just completed my undergraduate degree, and will be joining a master's degree in Fall-2021. The research I conducted under both advisors was not to obtain a degree, it was voluntary. Advisor A is at my undergraduate institution, advisor B was at that institution until last year. There were no institutional rules I was bound by while conducting research.

Answer 1

There is a delicate balance here that only you can resolve. It is good to keep advisors advised, so to speak, about your activities. Most will support you provided that the tangential stuff doesn't detract from your main work.

OTOH, you need to consider personalities. There are certainly those who would object, but you can probably judge that from past interactions.

Ultimately the purpose of doctoral education is to have the student eventually surpass their advisors. Only then does science make breakthroughs. But not everyone can deal with that idea.

It might be that one or the other would react badly to any action you take. It shouldn't happen that way, but think about your relationship to these people.

One thing you might consider, but need to judge for yourself, is to tell them that you've been working on a side project that has come to fruition, but is different from your main-line studies. You'd be happy to share it if asked, though it is outside their main interest.

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Edited to add in response to the edited question. I think that the balance shifts strongly toward informing them. I'd guess my suggested format is even more appropriate in your case. And you are lucky to have people supporting you at an early stage of your career.

I'll leave the answer in place as a general one that applies to the more common situation where advisors are also "supervisors" in some sense.

Answer 2

A few things to consider:

1. Consult the rules for PhD students at your university (I assume you are one). The university where I did my PhD had rules stating that a student needed permission by their supervisor to submit stuff for publication. My understanding is that such rules are rare however.

2. If I put myself into the shoes of your supervisor, I would consider it rude if I only learn about this paper in hindsight. I would not necessarily expect to be ask for permission, but I would like to be informed (and the chance to provide feedback). It's perfectly fine to say "I will submit this paper to conference X on the YYth. I know you're busy, but if you have any feedback for me please let me know".

3. It is also rude to the referees. Since referees perform a voluntary and mostly thankless duty, there is a responsibility on authors to submit stuff which is as good as possible. Its your supervisors job to read potentially horrible drafts and tell you how to fix them, not necessarily the referees.

Neither my point 2 nor my point 3 have the conclusion that you absolutely must not go ahead with your plan, but that it would be better to overcome your reservations.

Answer 3

I've been in a very similar situation about two years ago. Now I'm a PhD student.

While you are not under any obligation to tell them, I would strongly advise that you do. There are multiple reasons why:

1. It will most likely improve your paper.

Talking to people about your research tends to improve your research. Especially if the people are more experienced than you. For example, maybe B can tell you that your result has other cool consequences in their reseach area, or A sees a way to generalize some part of your proof, or....

In my case, input from one of my advisors helped generalize my theorem, greatly improving the quality of my paper, and I got my paper into a much better journal than my original version would have been accepted in.

2. It can help improve your chances of a career in academia.

Math that connects two areas of research is very interesting. You finding these connections yourself is impressive and will make you a very good candidate to offer a PhD position to when the time comes. At the very least, the more promising you show to be, the more likely they are to show attention to you, involve you in future projects, give extensive feedback on other projects, etc. So, showing them your research is good.

In my case, I got two very good PhD offers out of it, and I could choose my advisor.

3. It will show that you are a good person to work with.

A couple of comments on quotes from your question:

As far as I can tell, the idea is new, and (if I may say so myself) quite elegant.

As an undergrad (and even as a grad student), you are probably not a good judge on this. This is why we have advisors, because they have a much better overview of the field, and can tell whether something has been done before.

I intend to write this up and submit to a decent, normal-ish conference.

Again, you probably can't judge whether that's the appropriate format. Maybe the result is so cool that it should be submitted to somewhere better. Maybe it doesn't stand a chance for acceptance at even a decent conference because the result is so niche. Another reason why talking to someone more experienced could be helpful.

I intend to put my name as the sole author.

You can do that even if they read through it and provide feedback.

I am a little afraid of negative feedback if I show my work, feedback I would rather get anonymously from reviewers rather than from advisors under whom I continue to conduct research. (This is possibly irrational, and I need to deal with it, but for the moment, it is what it is.)

Me too. But I can tell you that your mentors will most likely not judge you, even if you give them complete nonsense, or a very niche result. I can't tell you how many times I showed mine math that was just plain wrong, or that they found uninteresting. I can assure you, the fact that you are an undergrad trying to produce (from what it sounds like) sensible independent research will be far more important than any mistake they could find in your draft. (And most mistakes are fixable.)

Neither advisor is familiar with the other topic, and hence neither will be able to judge the paper as a whole.

I wouldn't be too sure about that. Most professors know a huge amount of math, and even if they might not be experts on that topic, they could very well be fluent enough to provide meaningful opinions.

I am also a little worried that by the time I obtain feedback from either (or both) of them, the deadline for my preferred conference would've passed.

Why are you rushing to get it submitted? Why do you want it submitted at that exact conference? I can't answer that for you, you might very well have good reasons. But you should probably ask yourself whether an increase in quality would remedy a later submission.

Answer 4

Since you're an undergrad, I suggest that you're not the most experienced with the dynamics of presenting at a conference, the subtleties about which conference is the best for your type of work, and a whole bunch of other things.

Also, since you're an undergrad, you don't have any real allegiance to any PI. Your time is largely your own (assuming you haven't used any resources you're not really entitled to use).

If somebody experience is willing to review your work before submission, this would be a favor, and worth pursuing.