How do I deal with diverse interests when applying for a PhD program?

(My experience with non-American PhD programs is limited, so some of what I say here may not be relevant or possible.)

First, I think you may have painted yourself into a corner. More important than being specific, PhD applications should be honest. Hopefully your applications described the breadth of your interests, perhaps with some extra emphasis and detail in one area, rather than implying falsely that you are only interested in one topic. It's better to be rejected than to be accepted into a PhD program where you won't thrive.

I think you need to look for overlaps and connections between your various fields of interest. Decision theory and machine learning are not that far apart. Quantum computing and philosophy of computing are not that far apart. Parallel computing and logic are not that far apart. Decision theory and logic are not that far apart. Machine learning and computer music are not that far apart. Finding something at the intersection of five or six different areas is almost certainly impossible, but lots of interesting stuff happens at the interface between field X and field Y.

On the other hand, all the areas you describe are incredibly diverse within their own boundaries. You may find enough different topics within (say) machine learning to keep your fickle heart satisfied.

One thing you should ask about (quickly!) is the possibility of having multiple (ie, two) advisors in different areas. Some departments encourage inter-disciplinary co-advising; some don't. Some advisors encourage collaboration with other faculty; others flatly forbid it. (In many European PhD programs, students are attached to specific projects of specific faculty from day one, and moving between projects or fields is almost impossible.)

What worries me more than the diversity of your interests is this sentence: "Whenever I've tried to restrict myself to one topic of study - even for a month - that feeling is lost, and I am quickly bored". You have to get over that. Research requires long-term focused attention. Early in your PhD program, you may be able to juggle a couple of different research projects at once, but eventually, you have to focus on a coherent thesis topic. It can be an interdisciplinary topic, sure, but it has be coherent. You will have to work on that one topic for years. If that sounds awful to you, then maybe you don't want to be a PhD student after all.

My department head has changed fields several times in his career, so I think his advice on this topic is worth repeating. Assuming good health and good luck, you have a 50-year research career ahead of you. So if you're deeply interested in half a dozen different areas, you can afford to spend seven or eight years on each one.

I'd start with a fundamental question: why do you want to get a Ph.D.? It's a major commitment of time and effort, so it's only worthwhile if you need a Ph.D. to accomplish your long-term goals. Getting a Ph.D. really isn't worth doing for its own sake, or out of a feeling that it's something you ought to do (because you like computer science, or enjoy education, or feel you should have the highest degree you can get). Really, it's just preparation for what you'll do after you graduate.

So from this perspective, the question becomes what you hope to be doing in ten or fifteen years. Not specific topics, but rather what sort of career. When you look around at faculty or industrial researchers, do you see people who make you say "Yes, that's exactly the sort of work and the range of topics I'd love"? If you do, then you should look into these cases specifically. You can study websites and CVs, and maybe even e-mail a few questions (although keep in mind that people will be busy, so don't be pushy and don't waste time with questions you can answer in other ways). How did they end up in these positions that appeal to you?

If you can find many people doing what you'd like to do, then that's an excellent sign, and you just have to learn how they did it. If you can find only a few, or even none, then you should worry that maybe a Ph.D. isn't the right path for you. In that case, if you enter a Ph.D. program you've got to hope for one of two things. Either academia will change you, or you will change academia. Either is possible, but neither is likely.

I don't mean for this to be discouraging, but I strongly recommend thinking this through carefully before getting too far into a Ph.D. program (if you haven't already). Once you start, quitting is difficult psychologically even when it's clearly the right decision. It's easy to spend years in denial, knowing things aren't really working out the way you had anticipated but hoping they'll somehow get better. This isn't healthy, so the more thinking you do in advance, the better.

Good luck! I hope you either find role models in this career path or find another that suits you better.

I found your question today. I also have "diverse interests". Worse, my interests are more diverse than yours. I am interested in quantum physics, in biology, in history, in computer, in mathematics, in electronics, in music, etc.

Your problem is just in what JeffE had found: "Whenever I've tried to restrict myself to one topic of study - even for a month - that feeling is lost, and I am quickly bored". I get bored after a month of intense reading, or after half a year of leisure reading. It might be with the "instant gratification" vs "delayed gratification" kind of thing. Picking low hanging fruits in a new field is exciting. Having to do hard work for difficult fruits is boring. You might even have procrastination if my theory is right.

I worry that you might not be able to finish your Ph.D, like me. I chose one of the above as my Ph.D direction and I lost interest in reading boring (difficult?) papers and spent easy time in other fields. My GPA was good, I had no problem to pass exams. I just did not want to read those boring papers (the truth was that they were more "difficult papers" than "boring papers") in the field. I finally dropped out after years of struggling and got a job with my master's degree. Today, a day I find out that I am reading in parallel many materials on diverse topics at the same time, I decided to google and found your question.

If you can't focus, it might be better for you to get a job with your master's degree in CS and live an everyday Joe's life, like what I am doing now. On the other hand, if you can untwist your mind so that you realize that life is difficult, research is difficult, and doing difficult work is unavoidable, you might be able to escape being bored ( Now you know it is not about being bored, it is about being unable to face difficult problems for delayed gratification), you may be able to survive your Ph.D life.

[Update after 3 years] Today I found this answer made by me three years ago. I can tell you what I have done to overcome the problem. I am proud of myself as an amateur scientist that I have focused on one narrow field unrelated to all my previous interests for three whole years and got deep understanding of it. I almost dropped all my other hobbies and interests. How?

The first reason why I can make this change to my style was three years ago I suddenly realized that the old saying that we used only 5% (or 10%) of our brain capacity thus we had enormous capacity for learning was a lie. This is easily seen if you believe in evolution (why keep an energy hungry giant brain if there is no need). The truth is we have limited memory capacity. Don't jam garbage information in it! The second reason is somehow related ---- Those highly respected big figures in the past had limited brain capacity too! I believe if a person with good IQ and required education spends 10 years (sometimes 3 years) focusing on on topic, he can surpass almost all past and existing experts in the field, except for maybe one or two greatest.

With this second reason in mind (Most great figures are average Joe's themselves) I think I have made a discovery in a field I once was interested in. I have to pick it up and set aside my current main focus for a while (maybe as long as a year). Hope the above two reasons can help some people here.