Famous Professor vs. Research in Relevant Area

[fluffpark]

For some context, I am a third-year who will apply to grad school in the next upcoming application cycle (i.e. entering grad school fall 2025). In the past I have mostly done computer science research (though it was relatively mathematically heavy), and at this point I plan on applying to grad school in either theoretical/mathematical cs or applied math (possibly applying to both departments at some schools). I have done a lot of graduate coursework in pure math as well though.

I have the option of working with 1 of 2 different professors to do my math thesis, and I am having trouble on deciding who to work with.

One of the professors is quite famous in their field, has publications in very prestigious venues, and also has famous collaborators at some very competitive grad schools. However, their research isn't necessarily related to the previous research I have done nor the exact type of research I would necessarily want to do in grad school. Moreover, I don't expect to produce any original results working with them, and certainly not a publication (their research is in pure math and I expect that I will need to spend a lot of time just reading and working through papers to even get started here). But having looked at their work, I would most certainly be interested in working with them as I find their research very fascinating, this is just to say that I'm not as well acquainted with their work at this point.

On the other hand, the other professor I could work with does work that is somewhat more relevant/related to the work I have done in the past and would potentially be doing in grad school, but they are not as famous as the other professor, and don't have collaborators at many other schools. But, I may have the chance to produce some original results working with them, and *maybe* even publish something (this is both due to the fact that their work isn't as abstract as the other professor's and also I just happen to have more exposure to their field).

How should I decide who to work with? When grad schools are evaluating my application, would they be more impressed by a recommendation letter from a famous professor whose name they might recognize (thought I'm also not sure if *everyone* would recognize their name, especially in cs departments), or (assuming that the recommendation from either professor would end up being of the same quality) would they be more impressed with me doing research that somewhat complements my cs research? Is it possible that even if I was applying to do something cs/applied math related, grad schools would just generally be impressed with experience doing pure math work (beyond my pure math coursework)?

This is also assuming that I don't fall in love with the work I would do with the first professor and completely pivot my interests, but that's a whole different rabbit hole that I don't want to go into right now.

TLDR: Should I do research with a famous and well-established professor who has connections at other schools, but doesn't necessarily do the exact type of work I want to do in grad school, or should I work with a less famous professor who does research that I complements my previous work better and is possibly more similar to the work I would want to do in grad school? I guess I'm asking both about the importance of my recommender's being well-known, as well as having very complementary research experiences vs. more diverse research experiences.

Sorry in advance for such a long post, I'm highkey stressing right now

[frame]

The best people to ask about this would be professors who have previously served on an admissions committee. Naturally, you don't want to ask either professor you're considering working with (certainly not the "less famous" one). Is there a third professor you could ask about this, who you'd trust to keep your concerns private?

Edit: The math or academia Stack Exchange forums are probably reasonable venues for this question. You could also try certain subreddits. I would say these places are more likely to have professors on them than this forum.

[eamath]

Having a defined outcome from your research experience would be very important for grad school apps. This would be some type of journal or conference paper, or an oral or poster presentation at a conference or even a seminar at your school. Relevant area research that may also lead to some original work is likely the best way to go. I would also focus on topics that are at least somewhat closely related to your intended grad school areas of interest. It shows a pattern of interest in research that aligns with the grad school departments and professors you are applying to. Good luck!