What should I do with a year left in PhD?

Question

I'm a phd student in mathematics in US. Basically, I worked hard throughout the first two years because of the qualifying exam. After that, I kind of lost steam when I was supposed to start doing actual research and slacked off for my 3rd year (I was also dealing with anxiety and depression issues at the time). I finally managed to pull myself together after my 4th year and the first semester mostly goes to learning just the introductory literature---I'm in algebraic geometry so the learning curve is deep. I had almost nothing going on in terms of original research. At this point, I have technically a year left before I need to submit my thesis for graduation. My program does not allow extension beyond the 5th year and due to my visa status it is not possible for me to pause my study.

My advisor has always been hands-off to the point where we rarely talks. Last week, when I finally saw him, he told me he has no suitable problem for me at this point given my level of study. Instead, he referred me to a couple papers to read first. I can't even understand the main problem those papers are studying and I feel it may take me years to read them. So I brought up the time constraint to my advisor. His answer is basically that he's not sure what I should do and said it is up to me if I want to try to finish. So it comes down to finishing my phd in a year, or drop out outright. Do you have experience with similar situation? What should I do.

Answer 1

I don't think there is an easy answer to this. I thought US PhDs could drag on forever. I know professors who took 8 years to finish the PhD - one of them is a Nobel Prize winner.

First, you need to check with someone like the graduate adviser or whoever is in charge of the PhD math program, if you could extend you PhD duration. This has to be done first.

If not, you should start thinking of other options. You could cut your losses and get a masters degree. That can be finished in one year. Most universities would allow if you don't already have one from them.

You could also try to transfer your credits to another or to another program at the same university. Having already passed the qualifier will come in handy. I'm not going to say this is a good advise, because you sign up for another 5 years of the same thing, only with a wiser you.

Whatever you do, try not to think of it as a do or die situation. Your mental health will take a big hit if you do and you'll go back to anxiety and depression. Think of it as a setback. Also, I don't know where you're from, if getting back home is trivial, or not. In my case, it was the last thing I wanted, but, in the end, I had to live with it, since my folks never wanted to move to US.

If you end up deciding to quit without a degree don't do it immediately. Better focus your efforts in preparing your next step: getting back to the job market or moving to a different school.

Answer 2

I would say that it is important to have lots of conversations at this point, not just the one with your advisor. I am not in math, so perhaps this idea doesn’t hold in the same way as in my discipline (economics) but consider that you are trolling for ideas here, so put as many lines in as possible (to use a fishing metaphor).

Talk to every faculty member whose work is tangential to yours. Talk to any PhD students who went to industry… what would they have worked on next from their PhD if they didn’t go that route? Talk to visiting faculty (even if they are visiting via zoom) about where the interesting problems are. Heck, talk to your advisor again in a week when they have a chance to come at the question “fresh” or perhaps with a different prompt by you based on something from one of those papers. (Even if you don’t follow everything, can you see something interesting there?)

Answer 3

Not really an answer, but this was getting too long for a comment.

In addition to what @Magicsowon's just posted answer suggested, you might also try find a topic that requires relatively little background study and has a strong potential for a lot of low-hanging fruit, without worrying about how significant or respected the topic is, as long as it's sufficient to get you your degree in the time you have. Unfortunately algebraic geometry is probably one of the least likely subjects (at the current time) to find such a topic.

Examples of what I'm talking about are topic 1 (although it's been getting "milked dry" quickly in recent years) and topic 2 (in the 1970s) and topic 3 (in the late 1960s to early 1970s) and topic 4 (especially 1990s, but still might work today). However, none of these are remotely connected to algebraic geometry, and I only used them as examples because I know next to nothing about algebraic geometry other than what I said above about not having much low-hanging fruit. Well, there might be some pathological behavior in algebraic geometry that you could use the "topic 1" hammer on, I don't know.

Answer 4

My advice would be to find a new advisor as quickly as possible. It doesn't sound like you have much actual time invested in algebraic geometry, so feel free to switch fields.

To find a new advisor I recommend attending lots of talks by professors. Attend seminars. Somewhere in one of these talks there will be a problem which is intelligible to you, interesting, and has the ability for you to start computing examples immediately. Approach the professor about writing your thesis on this problem. Your thesis will consist of whatever progress you can make on the problem (perhaps solving it in a special case).

Answer 5

The correct and long answers are "ask your supervisor", "do what needs to be done", and so on.

But there is a short and almost ubiquitous, generic answer. It is especially suitable for the last PhD year. Maybe not in your case, but in may others. What should you do in your last PhD year?

Write.