I attend a competitive mathematics department that is very active in research. The downside of this is that it is hard to get any professor to agree to work on a Master's thesis with.
I have tried asking about 5 professors - all say the same thing, "thank you for your interest in wanting to work with me. I'm afraid I have to say no, because I am very busy."
To be honest, though, I did ask the top researchers in our dept. Partly because I should take that risk for my own career benefits, and partly because I just do not know much about the younger, less established professors / post-docs, people whom I am guessing I would have a better chance to work with.
What are some general recommendations from this community? Keep trying to work with a tenured, well-known professor, or better to hedge my bets and just find someone who will say "yes, you can work on a project with me."?