How to use Stack Exchange for research-level questions

Question

I'm a first-year PhD student in Quantum Cryptography. As such, I frequently have to deal with mathematical problems that are quite difficult for me. That's perfectly OK: research's precisely about this in my opinion.

But it may happen that I get stuck on some problems. After some days of trying to solve it, I used to ask the question on a Stack Exchange site and more often than not get an answer there. However, now that I'm doing a PhD, I feel that the situation's a bit different.

I struggle to draw the line between "don't ask anything that would undermine your work as a researcher" and "ask anything you want as long as you cite the relevant author afterwards". Of course, the whole point of a PhD is to show that one is able to conduct meaningful research, to perform an efficient review of the current state-of-the-art and to show that one is able to come up with original and interesting ideas. As such, I feel like asking for help on problems related to my thesis would undermine the final work, and I don't know to which extend this feeling is exact.

Even worse, I sometimes think that some particular sub-problem I try to deal with is actually already known elsewhere. For instance, suppose that in order to make a security proof for a cryptographic scheme, I have to prove that the sum of natural numbers up to n is n(n+1)/2. I may think that this problem is already solved in the litterature but suppose that I didn't find any reference to it (in my case, the problems I'm interested about are a bit niche). I would like to ask on Stack Exchange "Is this problem already known?" just to be sure that I'm at least not wasting my time not reinventing the wheel, but that would be taking the risk that the problem wasn't actually solved, but is subsequently solved in an answer. In this case, I would have lost an opportunity to perform original research: maybe I should have had spent one or two more day on this problem.

Essentially, my question is the following: of what use can Stack Exchange be when it comes to research? Are the cons presented here of asking a research-level question on it justified?

Answer 1

There are a few issues to unpack in this kind of circumstance, so let's go through them.

First let's look at the problem setting aside the issue of a PhD program. In this case, there is nothing wrong with conducting joint research where another person does some of the work and you acknowledge them in your paper. If necessary, you can get an answer on SE and give an appropriate acknowledgement to the person who wrote it, or you could even invite them to write a joint paper with you. (I presently have a joint paper under construction with another researcher based on a good answer he gave on SE in relation to an aspect of a problem I was examining; this led me to invite him to write a joint paper with me, and we are presently in the process of doing that.) It is rare for answers on SE to contribute to research-level problems, mostly because those problems are usually too large and complex for this forum. However, it is not unheard of and I have seen some SE answers that are extremely insightful and could easily form the basis for published scholarly work.

Now let's look at the additional complications that arise when your research is being done as part of a PhD candidature. In this case there are two complications: (1) you are there to gain skills that will allow you to do research yourself; and (2) the program requires you to produce novel research where you are the primary driver of that research.

With regard to the first point, it is important that you practice through difficult problems even if these are things that could be done easily by another researcher. As EarlGrey points out in the comments, it is useful for you to "reinvent the wheel" with respect to a whole bunch of problems and results; this will help you acquire the analytical skills you would be expected to acquire during a PhD candidature and it will help you work independently in your subsequent career. Nevertheless, there is a limit to this, and some trade-off may be considered if a problem is too difficult. Try working on difficult problems for a substantial amount of time and seek help and advice from your supervisor if you are blocked. If it gets to a point where you are wasting more than a few months, ask your supervisor if it is worth getting someone else to solve the problem and then give an appropriate acknowledgement/citation, so that you can move your efforts to a new problem. There are sometimes cases in PhD work where the student hits such a blocker that they do joint work with another researcher for part of their research; sometimes this means adding an acknowledgement to another researcher or even joint authorship of work.

With regard to the second point, you need to make sure that you have made an overall research contribution that is sufficient for award of the PhD. This does not necessitate you being the progenitor of every new idea/result/proof in your research, but it does mean that once you take out the work done by others there must be enough of your own novel contribution left to justify the award. Typically, if a PhD candidate has done research where there has been a contribution of work from another researcher, their submission for their PhD will have some statement of contributions or something else that makes it obvious to the referee who did what. Each part that is done by another person reduces your own contribution, but it may be a worthwhile trade-off in some cases. Again, your best option is to seek guidance from your supervisor on whether your own contribution is likely to be sufficient to warrant the award, and under what circumstances it makes sense to have someone else solve a problem that is impeding you.