Context: I am currently a 4th-year PhD student in Computer Science (Theory), expected to graduate next year (gosh, this went by quickly). Since I end up finding more questions I'd be interested in solving that time or brainpower to actually solve them all, I am maintaining and keeping for myself a list of cute, elegant, or interesting (IMO) research problems I'd like to solve at some point, or see solved. (Preferably, the former.)
I have mentioned a few of these questions to friends or during open problem sessions in workshops, and currently a (subsampled version) of this list is hidden somewhere on my academic website for ease of access.
Question: what are the pros and cons of making this list actually public? I am specifically thinking along the following axes:
Research: while I suppose advertising problems I deem interesting can only be good for the field I am in (i.e., the more solved, the better!), is there any downside?
Short-term interests: to be blunt, I like these problems, and I do believe at least some of them are good ones. I'd be rather sad if some other people methodically solved all of them without me, although it's a bit selfish of me. (Especially if I do spend some time on some of them before my graduation -- I only have that much time left to get new results and consolidate job applications for postdocs...)
Long-term interests: well, sooner or later I'd like to have a position in academia, and who knows even advise students. As far as I can tell, being able to suggest research ideas (from small problems to bigger questions) taylored to a student's interest is a big part of the job: should I try and keep as many as these questions as possible in case I may need them sometime for this purpose?
(I may have forgotten things to consider, or be overthinking that a lot... basically, the point is that my inclination is to put this list online ("of course, why not?"), but would like to be sure there is not actually a good reason not to do so.)
Edit: something I had forgotten to mention.
Some of these problems, I really would like to see them solved, and I fear that I may not have the right set of tools (yet?) or (let's be honest) sufficient insight/intellect to achieve it by myself. Ideally, I'd love to see someone get interested in them, and possibly start a collaboration (best case scenario) leading to a solution. But I'd hate to see these questions get buried and forgotten, fading into oblivion without ever being addressed — just because I kept them to myself.
Point to keep in mind:
Asking questions is easy. Asking questions other people think is interesting is less easy (see some questions on this site). Asking questions that lead to important results is hard.
Fundamental ideas come up over and over again, so even if they don't take off at first, they'll spread eventually.
If some of the questions are indeed interesting, you could help people find good problems. If you're lucky, you may get asked to collaborate, but I wouldn't count on it.
Such a list, may help get your name out there. Maybe the questions are great and people think you're brilliant.
The most obvious and serious con for you is that someone else solves what you're working on before you do, and a lot of your work becomes unpublishable, and you don't get a job you want.
Some of your questions are trivial/well known and people think you're stupid/ignorant.
Worst case scenario (exaggerated): everybody in the field finds your questions super-interesting and all work on the same question but nobody solves it for the rest of their life and the field dies.
Think very carefully about which of your ideas you want to share, with whom, and with what purpose. I'm not going to advertise to the world what new idea I'm working on, or even a good one I have on the back burner, until I make serious progress or have compelling evidence. Because (1) I don't like to compete with people, and (2) if nothing works out (most common) then it's likely either not a good idea or not the right time for this idea. This doesn't mean I won't tell people, or ask other people related questions, I just don't post a pdf on the internet. I tell some people I trust, and sometimes this leads to collaborations. Occasional "further problems" to projects I've done, I mention in papers, but this is when either I don't want to do it myself or I deem it unlikely anyone else would solve it before me.
Also, at least for me, often it's years between first asking a question and answering it, but if I had advertised it, maybe someone else would've done it in the meantime robbing me of the satisfaction of answering it myself.
If you decide you are willing to share some of your ideas on the internet, and you think they may be of wide interest, rather than just posting a list, consider making a blog of some of your thoughts. If you get readers, this could provide generate interest in things you like, which might make your work more popular. At the same time, you can pose your questions in a very informal way, so they're not presented as if they're supposed to be a grand list of the most fundamental problems in the field.
Not everyone has the same philosophy as me, but I would consider being too open about your ideas somewhat risky at your stage.
Oh, and maybe ask your advisor first.