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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.

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I was also enrolled in a Math PhD (Numerical Optimization), with difficulties due to lack of time (I was working as a Math teacher simultaneously); when I finished my PhD courses my advisor proposed a research topic... One year at a half later, I also was at a dead end, unable to find any good result and doubting myself.

When I told my advisor at last that I'd decided to move to another program in another university, he propose another topic, assuring me success. He was sure I would get it (as we know, advisors spend time with their doctoral students, and a student failure is also a fiasco for them) because he knew the subject well (the first topic was more unknown to him, and therefore more challenging, but it was also possible that there was no solution!).

He was right: In the new topic, I quickly got results, tutored for my advisor, I was able to present partial results in congresses, got some articles accepted in journals, and at last, two years later, I finally got my PhD. I lost almost two years, but seen from afar (ten years have passed since then) everything is OK.

By the way, recently I saw (in www.researchgate.net) that somebody has the answer to the first problem that I wasn't able to solve ... so it was solvable, and my advisor was right in proposing it to me!

Well, that was my experience, I think similar to yours. Hope this is helpful.

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