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?