Here is one person’s top ten list of ways to fail to obtain a PhD.
Ph.D. school seems to be a magnet for every kind of procrastinator.
Advisors expect near-terminal Ph.D. students to be proto-professors with intimate knowledge of the challenges in their field. They should be capable of selecting and attacking research problems of appropriate size and scope.
A Ph.D. is a small but significant contribution to human knowledge. Impact is something students should aim for over a lifetime of research. Making a big impact with a Ph.D. is about as likely as hitting a bullseye the very first time you’ve fired a gun. Once you know how to shoot, you can keep shooting until you hit it. Plus, with a Ph.D., you get a lifetime supply of ammo.
It does not matter at all what you get your Ph.D. in. All that matters is that you get one. It’s the training that counts–not the topic.