Is transferring to another university an option for an unhappy PhD student?

Mathematics

Let me specify that by transferring, I mean moving to another university in the middle of a graduate program. Switching universities between undergrad and grad or between a master's degree and a Ph.D. is very different. Basically, those are the only mainstream opportunities to move, and anything else will require an exception.

Transferring is certainly not unheard of, but there are some serious caveats:

1. It's difficult to transfer to a substantially more prestigious department. It can happen, but the admissions committee will be very skeptical, and it's just not going to work out unless the application is outstanding. In particular, many committee members specifically do not want to reward rolling the dice again and seeing what happens, so for transfers the question is not "Does this application look better than our weaker students?" but rather "Is this application so obviously wonderful that we would be shooting ourselves in the foot if we accepted someone else instead?"

2. Expressing any unhappiness will make it much harder to transfer. You may think you'll be happy at the new school, but they will worry about ending up with an unhappy, unproductive grad student on their hands. And they are right to worry about that: the best predictor of future happiness is past happiness, and many unhappy people have unrealistic beliefs about what would make them happy.

3. It's hard to transfer once you start seriously working on a thesis. If your work isn't going well, then that's a reason not to accept you. If your work is going well, then that's a reason you should continue working with your current advisor. Unless your advisor has died or left, it will be tough to convince anyone you are a good candidate for transferring.

4. No matter why you say you want to transfer, there will be some suspicion that your goal is to end up in a stronger department or a more desirable location. If you have another reason, you'll have to make a powerful argument for it.

I've heard of people transferring between graduate schools because of their advisor moving to another school and taking their students with them.

Sometimes they transfer officially, and sometimes they still get degrees from the previous school but complete their theses while in residence at the new school. The latter is generally easy to arrange when an advisor moves.

Computer Science

Yes, PhD students transfer for many reasons besides moving advisors. Sometimes the reasons are purely professional; for instance, I've seen several students successfully transfer because they discovered a passion for a subfield that didn't match the interests/experience of the local faculty. Sometimes they're more personal things like two-body problems (especially when they become three-body problems). Sometimes advisors die or leave academia. Sometimes it's because of an irreconcilable disagreement between student and advisor/committee. Sometimes the student just thinks they can do better than their current department (and has the publications to prove it).

Probably the most painless time to transfer is immediately after completing a master's degree. (I did this.) That's a natural time to switch research directions, and many PhD programs allow their students to pick up a Master's degree along the way, even if they don't have a separate Master's program. (Mine didn't.)

Still, applications from MS students in PhD departments will face skepticism, especially if the applicant already has a good track record with their former advisor.* (Why do they want to leave their current advisor? Shouldn't we offer this slot to someone who doesn't have one?) So it's important for the applicant's research statement to explain why the new department would a better match, without disparaging the old department. It's also important to have a strong and supportive recommendation letter from the former advisor, to address possible concerns about technical weaknesses or personality conflicts.

(*And if a PhD applicant doesn't have a good track record with their MS advisor, they're not likely to be admitted anyway.)

Field: Mathematics.

Transferring is possible although you might have to 'start over' at your new university. For example, perhaps you have completed the first year sequence of courses in University A and passed some prelims before transferring to University B. At University B you might either be required to go through their first year sequence, or take (and pass) the relevant prelims to have the courses waived. This can be difficult since first year courses and topic and prelims tend to vary across departments. In addition, depending on how much prior experience you have before coming to University B, they might require you to finish your degree in less than usual time (say, 3-4 years instead of 5). In particular, folks with Masters degrees applying to PhD programs are often required to get a second Masters in their second university.

Source: A friend of mine transferred from Rice Mathematics to UW Madison Mathematics; additionally this was a topic of conversation at a Nebraska Conference for Undergraduate Women in Mathematics where a breakout session leader had transferred universities mid-PhD.