PhD Suggestion in 3 rd year without any progress

Question

I am a Mathematics PhD student currently in 3 rd year. I have a funding of 5 years. But being in 3 rd year also I haven't started working on a problem yet. Whenever I ask my supervisor he always says there is still a lot of time or sometimes ask about 6 th year or something. I had very little interaction with my supervisor as he is very busy and we only meet mostly twice in a month for maximum 1 hour or less. I can see now all my peers have some preprint whereas I haven't started anything yet. Sometimes I get demotivated and cry for the whole day knowing that is not a solution. Do anyone have any suggestion regarding how to progress? I am now trying to find some small problems but that also is taking a lot of time.

Answer 1

My experience is that it is possible to do a dissertation in a year once you have a suitable problem. Everyone's experience is different, of course. But suitable problems in math are hard to come up with. Especially for novice researchers, but even for experienced people.

My experience, also, is that you might spend a lot of time on problems that aren't suitable or even feasible. It is a three bears problem. I had one problem that was "too easy" and I could generate a theorem just about daily. It wasn't sufficiently deep for a dissertation. The next problem was "too hard" and I couldn't crack it at all after a month of trying. The third problem was just right and led to a fairly significant thesis.

It isn't "time" that your advisor needs to give you, at this stage. It is ideas for things to try. If you aren't getting that, then he isn't doing his job properly. Coming up with the insight to know what might be true is a very difficult thing to do in math. It comes with experience that you don't yet have, I suspect. The same is true of many (most?) doctoral students in math. I know I didn't at that time.

If he is giving you papers to read in your (and his) field then he is on the right path. Look for holes. Look for extensions. Look for parallel development possibilities. He should be passing you unfinished and unfocused ideas that are, to him, "worth looking in to". If that is happening then you are probably ok, as long as you follow up. But if he is without ideas to share then it is very difficult, maybe impossible. Maybe you can even ask other professors in the field for ideas.

Some places have seminars for professors and doctoral students in some subfield. They meet regularly and toss ideas around. Some, not all, of those ideas are worth a good look.

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One idea for examining existing papers. Take a paper that you understand and that has some significance. Compare the results (and methods) in that paper with the results and methods of those papers that it cites. What is the nature/essence of the extension in the new paper. There was something "missing" from the earlier papers. What is it, exactly. What insight did the author gain from the older papers that led to the problem solved in the new one.

Answer 2

Just for some context, my PhD dissertation result was mostly discovered and written in about 6-8 months towards the end (the memories are now a little fuzzy). I don't know how typical that is though. The problem naturally grew out of a class assignment. I came up with the specific question myself though simply because I wanted to know the answer. I wouldn't call it a great result, but it was sufficient.

I find coming up with questions easy and natural, but it's determining which can be suitable for reasonable progress that is difficult. I tend to work on things that are too hard for me, and I advise being very wary of falling into that trap. That's where input from an advisor would hopefully serve as guidance.

My gut reaction is that having 2 years of funding left without even an idea of a project is cutting it close. Do you have an area or general subfield to work in?

I'd have an honest and direct conversation with your advisor about this. You may need more careful guidance on how to find a suitable problem where progress can be made.

With the right project you do have plenty of time left. But having a doable project is a key and uncertain part.

If you are doing well and making progress during the 5th year, making a case to stay for another year may be possible. In my experience, getting a teaching assignment for a year is fairly easy unless they think you have no chance of finishing. But that will vary according to time and place. Don't quote me on that as you'll want insight from those with current experience in US math grad programs. Ask your advisor explicitly and directly about what it generally takes to get an additional year.

Answer 3

Your situation sucks, I know. My PhD supervisor was a big shot that just didn't talk to me. In fact, he derailed me more than helped, all in all. Here are some points you should consider.

1. Talk to the guy. I mean, really sit down and confront him. Tell him the situation is untenable and that you are really lost. I never did this with my supervisor, and I wish I had done it. At the very least he has to know what is going on.

2. Find other people to work with. It can be tricky to approach other professors because of politics, but postdocs should be easier to approach.

3. I had an area (like number theory, functional analysis, etc.) but not a specific topic/subject. It seems you have one, so at least you are more focused than I was. You may end up just having to come up with your problem yourself, like I did, and do all the work. As someone else said, once this happens, it goes really fast. My PhD only progressed once I realized my supervisor didn't care and wouldn't help, and decided to stop talking to him altogether and just do everything myself.

4. The world has changed a lot in the past 10 years. Now I'm a professor and I would be reprimanded if I treated a student like I was treated. You are in the US, so it should be easier for you to change supervisors; consider doing it, as soon as possible. Give it a deadline. Find out who you can talk to about what is going on. What is not okay is for you to be crying alone because of the situation.

5. Think, really think whether you want to have a PhD in math. Is it really worth it? I didn't even consider quitting at the time, but I should have. It is actually nothing special. If it makes you miserable, you can quit. There is nothing wrong with it, no shame. Heck, you may end up better off!

How my story ended: at some point, I was desperate since I was not doing anything (like you). I chose a problem left over from my master's and figured out some stuff for it. It was decent, but nothing groundbreaking. I was fun to work on it and write it down. I showed it to my supervisor, and he basically told me to not bother him with trivial stuff like that anymore.

Then I spiraled into depression. I disappeared for 2 weeks (great decision) and just stopped thinking about math. I decided to stop talking to my supervisor. Next thing I know, during a seminar from one of the postdocs, I had an idea of applying some method that was discussed to an old problem I knew, and it worked. In a matter of 2 months I had collaborated with this postdoc and had all the main results of my thesis. It was really fast. But, I can't help but feel I was also very lucky.