Was forced out of PhD for academic/health reasons, need advice on what to do next

Question

I was accepted into a PhD in maths at a fairly highly ranked school in 2017. My supervisor was known for being quite demanding, but I wanted this because I wanted to push myself, and he is quite well known in the field I was interested in, which is algebraic geometry.

During the first year I was doing background work and developed my maths up to the point where I could start actually doing research. This involved going through textbooks and exercises and generally learning maths at a high level. Each week he was unhappy with my work, and would find holes in the proofs and logic, and holes in my understanding. After this happened over months, he began to suggest that maybe maths wasn't for me. Eventually he basically explicitly said this, and said that I wasn't understanding the material and wasn't able to think mathematically. He suggested that I drop out and "do something else with my life".

The other issue here is that I was suffering from depression, and was fairly burned out from my undergrad, and I blame that in large part for not being able to study efficiently and think clearly. I did end up leaving the program late 2018, and I got a medical certificate to document the depression.

The thing is, I am determined to succeed. I know for a fact that a PhD in maths is what I want to do, and I am not willing to give up on that. I am certain I have the ability, and am putting my failure down to the above mentioned issues. I am still doing maths every day to keep my skill level up and increase my understanding. At some point I want to reenter a PhD program. That is where my question comes in.

What is the best way to get back into a PhD? How much will my past dismissal (technically I left voluntarily) affect my chances? Given that my supervisor has said flat out that he doesn't think I am cut out for maths research, how would I go about getting an academic reference for any future application? Any other advice is appreciated.

Answer 1

If you want to continue at the same school I'd start by going to talk to the administrators in your department, hopefully as a PhD student they will be familiar with you and your situation. Ask about your options to continue your studies, and possibly seek out a new supervisor.

I'd also make a list of other schools you'd be interested in attending, and find faculty there with similar research interests, ideally you could try setting up a meeting to discuss your shared interests and ask them if they might be willing to supervise you or if they have any projects that might be a good fit for you as a PhD student.

Answer 2

Given that my supervisor has said flat out that he doesn't think I am cut out for maths research, how would I go about getting an academic reference for any future application?

Who gave you a reference in the first place? I'd suggest going back to them. You don't have to tell them the full details of what happened; you dropped out for health reasons, you're moving to a different supervisor because you didn't work well together, and your supervisor isn't in a position to give you a reference for that reason. It's not unusual for people to be asked for references even a few years after they last saw you.

A word of support, too. Stories of students not getting along with their supervisors certainly aren't unusual. When you say that your supervisor was known for being "demanding", well... sometimes "demanding" is a euphemism. I also suffer from long-term ongoing mental health issues, and they are enough of a barrier in their own right, but during the periods in my university career when it was made clear to me on a regular basis that I was a disappointment, the quality of my academic work plummeted and I completely lost my passion for the subject. In that respect, a patient, understanding supervisor can make all the difference, and I think most academics know that. (Maybe don't rant about this at interview with your new prospective supervisor, though...)

Answer 3

1. I am generally in favor of finishing the Ph.D., once started, even for weaker students. At least it is a decent resume bullet, even if you are not top of the heap. If you're halfway through, you might as well get it done and cross it off.

2. But getting back into another program after not hacking it in a first one? Seems low reward/risk. Even in general, starting a Ph.D. should be looked at very skeptically (there is a lot of push to get students, but it is not always the right thing when you look at foregone earnings and issues with jobs after getting out). But once you have not made it in a first one? Sure there is the possibility that you hack a second one ore that it is a good use of your time. But I think you need to adjust your Bayesian prior even lower (after all you have data, the first attempt).

3. If you really want to just get the Ph.D., the best thing would be to talk to the department where you were. They may feel some responsibility for you and give you an easier, more agreeable, etc. advisor.

4. I'm not sure why you have to go for this Ph.D. You state it like it just makes sense to want one, but you don't clarify why or what will change after you get that particular certification. Do you think you are a research grade mathematician? A professor? I just would seriously consider other areas. There may well be something else satisfying and that you are good at (even have a differential advantage) versus top tier algebraic geometry. Note, even if this isn't for sure the answer (do something else), you should at least examine the possibility. Not just stay wedded to this initial dream. Just seriously investigate this.