How to assess whether it is imposter syndrome or actual low quality work during Ph.D.?

Question

I am a Ph.D. student and my field is pure maths (analysis). It has been 33 months since I enrolled in Ph.D. I have produced a few papers as well. However, serious doubts have been rising in my mind regarding the quality of work that I have produced, ever since I collaborated with an established researcher, Dr. X of another country. Before this collaboration, I had four papers published in journals indexed in SCOPUS and ESCI (I made sure they are not predatory and have no APC). Additionally, I have one paper accepted for publication in SCI journal and three more papers are under review; one in SCI journal and two in SCOPUS+ESCI journal (again, no APC).

After I finished my collaboratory paper with Dr. X, I checked his complete publication list and noticed that all his work has been published in top-tier SCI journals. I know that he is much senior to me and is well established in our field, yet I feel embarrassed as most of my work is published in non SCI journals.

I talked about this with my Ph.D. advisor and he said that I am just being too hard on myself and he is actually quite happy with my work. However, I still feel disappointed with myself.

So, I would like to ask how to handle my dissatisfaction with my own work and assuming that many senior professors, who are advisors as well, are reading this, what would be your honest assessment of my work.

Answer 1

Generally, the best source of validation of you work and, hence, your ability, is others with experience in your field; especially senior researchers . By this standard you have tons of validation, including your advisor, your collaborator(s), and the reviewers of your papers.

Imposters are usually "outed" fairly early. You seem to be quite a bit beyond that especially with less than three years at "the game". Relax. Have a culturally appropriate beverage.

In the US, most doctoral students in math are still taking courses after three years, but that is starting without a masters. I assume you are somewhere else with more of a background before starting, but to an old math PhD from the US, your record seems pretty impressive.

Thinking that "I can do better" can be a good thing as long as it doesn't lead to depression. In the latter case, professional help is needed.

Answer 2

There are several reasonable ways to assess the quality of your research work relative to expectations at your career stage. Here are some of them:

• Get feedback from senior academics in your field: It appears you have already done this, and the feedback indicates that you are performing at or above level for your career stage. Senior academics in your field are likely to have a reasonable understanding of the range of outcomes for researchers at your career stage and so they can probably reasonably calibrate where you stand relative to expectations.

• Successful publication of peer-reviewed work: You have already published four papers while you are still a PhD student. That is substantially above average for a PhD student in mathematics. While the "level" of the journal is one possible measure of esteem, time will tell if your papers yield interest and citations, and whether or not they are well regarded. In any case, on this measure you appear to be performing above career level.

• Comparison of publication record to others at the same career level: A reasonable further comparison you could make is to look at your own publication record relative to other PhD students in your program and other similar programs (ideally comparing students at the same stage of their PhD as you, if you have a large enough sample size). It is likely that such a comparison would confirm that your publication record is substantially above average for a PhD student in mathematics.

• Fish for reassurance on Academia.SE: Done --- consider yourself reassured. ;)