Writing this from a temporary account. I am enrolled in a PhD program in math, and more and more often I am doubting my abilities in doing the program.
I work, so it happens, de facto under two scientific advisors. I continue my work which was quite successful at undergrad level, but feel stuck into a dead end. Furthermore, all I obtain after hard work seems to be easily generalised by other people who spend much less time thinking on my problems, rendering my effort obsolete. This PhD is very important for me, allowing me to get satisfaction from teaching younger students, talking to scientists, earn money and receive grants, but I find myself undeserving of all that and actually suspect myself to be an impostor masterfully imitating mathematical research. It is exacerbated by the fact that these unsurety problems seem to disappear when I move, as an amateur, to a completely unrelated discipline; I’ve already published articles and suspect that, were I able to supplement vigour with formal training, I could have been a monograph-level of researcher right now. However, as I mentioned, changing PhD to such an unrelated field is not even an option.
It is vital for me to complete my PhD. So I’m looking for some advice from this remarkable community how to drag myself out of this learned helplessness; some possible options would include:
Change topic and do some unconnected math research? I feel that would put itself as a silent rebellion against my scientific advisor, as well as contravening my PhD, to say nothing of the fact I’m unsure in the very ability to produce a fast result from any branch already;
Slightly alter the direction? Similar;
Force myself and push until I produce something meaningful for my topic? As one can see, I’m hesitant about it.
In fact, I’m currently abandoning my “world level, Fields medalist” hopes and would be satisfied with getting any king of PhD to be allowed to teach undergrads in peace. No other career but academic is imaginable; and yet I find myself with inability to progress in mine.
Another option everyone will introduce at once is “why don’t I talk with advisor frankly”. I’ve tried that but found myself too timid to be completely frank, and I am wary about latter due to PhD importance. It is necessary to maintain some cordiality with advisor. Hopefully there is some way out of this self-made problem. Especially invited are opinions of those people who had rocky PhDs back then and persevered.