Evaluating red flags in potential advisors' scientific production and impact, past students, research interests and personality In the next few weeks I'll need to pick an advisor for my master's thesis (in a certain subfield of mathematics). I've narrowed down the choice to two (full) professors.


Prof. H I've known Prof H  for two years, took two courses with him, and got the top grade in both of them. He is a very good, peaceful, and punctual person; and he is clear and precise in explanations. He has much academic experience (being over 60 years old) and has supervised many students (at undergraduate, masters, and doctoral level). However, I've noticed that his former PhD students (10, currently still assistant professors) are not  much productive (and mostly publish with him, working on his research program). I've a marked interest in a certain sub-subfield, but he works in a different (smaller and, in my opinion, less interesting) sub-subfield; he is quite productive and in the last 30 years he has covered an impressive (and well-organized) research program (in which I could easily find a thesis topic) and he has grown to be a household name in his area of specialization; but his research, although very solid and original, has not been exactly groundbreaking and his latest works (which are all of high quality and quite innovative) have not been very impactful (in terms of  citations yet).
Prof. K  Regardless of the choice of the advisor, I will take one course taught by Prof K. However, I don't known him personally yet and therefore I'm not familiar with his “style” (although I've been told that he is generally a good person). He also has many years of experience (being slightly under 60 years old) but has supervised fewer undergraduate and master's students (some of whom changed areas of research for their higher studies), no PhD students, and several Post-docs. He works exactly in the sub-subfield I'm most interested in and has produced many solid papers over the last 30 years; comparatively, I'd say that his work is less innovative and much less systematic than Prof H's but maybe broader; in fact, while Prof. H has expanded, organized, and generalized in an original way a couple of (small) research areas (also highlighting connections with other areas), Prof. K has mostly applied a vast sophisticate toolbox to solve several interesting problems and created only few novel "tools" slightly adapting the existing ones (although I must note that Prof. K's area is essentially much more “scattered”). Prof. K does not seem to be quite an household name, but has given substantial contributions, is quite active in the community (and his former advisor was the expert of the area).


Working with either of them has some pro's; however, there are some alarming red flags about both of them. I have a hunch that working with Prof. H may be smoother and simpler; however, Prof K research interests are much more appealing to me (and aligned to what I'd like to do during my PhD – for which I'll apply to another institution anyway).


  Assuming that both of them would accept me as a student, to which red
  flags should I pay most attention? What  factors (also other than the ones I've talked about) should I take into
  account the most when making the decision?
Well, first of all, this is a master's thesis. I would argue that it doesn't really matter that much, because you will at most be working with this person for a year or so and then leaving to go somewhere else.

Given what you've written here, I wonder why this is even a question for you. You know Prof H and have taken courses with him and done well. You know that he gives good mentorship and feedback. You know that his former students end up very successful. You know he's productive and well-known, which could be helpful for getting into a PhD program. The only question here is does he have enough subfield knowledge in your area to advise your thesis?

Also, if he has 30 years of research and is a household name, how is his work not impactful in terms of citations? You don't become a household name as a scientist unless you've written some papers with impact.

Prof K might not be a bad choice either. The fact that he has had no doctoral students is irrelevant because you're writing a master's thesis. But why go for an unknown if you already know Prof H and know that he's a great advisor?