I have kind of an interesting scenario that I would like to get advice on. I apologize if this is a bit lengthy, but I want to get all the facts out there.
A bit about me first: I have just finished my first year of grad school in an applied math program at a top 40 program in the US. I have undergraduate degrees in both pure and applied math, so I really have a love for both topics, although I lean more towards applied.
I have spent about 9 months doing some investigatory research with a distinguished professor at my school. Let's call him Dr. G. I have really enjoyed this research and I feel like it is a no-brainer to pick Dr. G as an adviser. He is very active in research, he has plenty of grant money, etc. He is also one of the top people in the world on the work that he does. On top of that, he is very supportive, great to work with, and willing to be my adviser.
So I thought I had definitely found my advisor.
Here is where my doubt comes in. There is another professor, Dr. T, who recently spent 3 hours helping me with preparing for my qualifying exams (this was way above and beyond what I thought he would do). I had so much fun talking about the math with Dr. T. He was so patient and helpful. We talked briefly about my research with Dr. G as well. He told me that sometimes people struggle with working with Dr. G because Dr. G is so busy traveling and such. This kind of made me doubt my decision a little. Dr. G is very busy, but we meet almost weekly, although not for very long. Dr. G has also told me that he is a very hands off adviser.... and I think a more hands on adviser might be better for me.
With all this said, I was considering doing a reading course with Dr. T IF he was interested in having me as a student. I don't currently know if he is accepting students or not. My thought was that if Dr. T was willing to spend 3 hours with me working out problems together, that he might be much more involved in helping me when I am working on a thesis than Dr. G could be.
I don't know if I have a misconception on this or not, but those 3 hours that I spent with Dr. T talking about the math problems was what I really pictured an advisor doing for me. Maybe not 3 hours worth, but enough time to really talk and ponder the problem at hand. Maybe someone could comment on the truth of this idea for me... Is it true that some advisers actively work on the problem with you, or do they just check in with you on the work that you have done?
A couple further notes: Dr. G has had about 5 students graduate and Dr. T has had 2 (only 1 recently). I also don't know about the level of research that Dr. T is doing; however, the quantity is definitely much less than Dr. G.
I would really welcome any advice or comments you may have. *My big question is if I should even ask Dr. T if he is interested in having students or not (I don't think he has any right now). I just feel like that although Dr. T might not be as flashy as an advisor as Dr. G, Dr. T may be way more involved and helpful. So I am trying to figure out if working with Dr. T is worth looking into, or if I would be unwise to not work with Dr. G.
Thanks for your time.