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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.

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    This is an interesting question as I had the same exact story, what I really liked is your persistence! First of all, to reenter, you dont have to mention this professor for any future applications, he didnot believe in you that you can make it, but you can. According to references, try to find a supervisor from undergrads or any other one who believe in you and can write a good reference letter – Monika Feb 19 at 18:31
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    You can mention if you have been asked that you left for compelling personal reasons, dont mention what your supervisor did to you, try to be positive and I think you will find the real professor who support you and understand your passion and persistence. – Monika Feb 19 at 18:32
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    What sort of objective assessment of your mathematical skills do you have? Do you have an undergraduate degree in it? GRE? Did you take qualifying exams for your grad program? The two primary questions you should be focusing on are: was your supervisor's assessment accurate, and has your ability changed? – Acccumulation Feb 19 at 23:06
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    @Acccumulation - I'd say that the biggest question is whether the depression is being adequately treated or not, and if the treatment will withstand the rigorous demands of a math PhD program. – Jon Custer Feb 19 at 23:27
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    @Acccumulation yes I did a four year undergraduate and finished with first class honours. We don't have the GRE system here. I would say there was improvement, although my supervisor would say that my ability to reason mathematically has not improved. I think that is largely down to my illness, and communication. – Joe Feb 19 at 23:53
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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.

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    Not “possibly”. Definitely seek out a new supervisor. – JeffE Feb 21 at 7:54
  • Don't choose the project! Choose a good natured supervisor. Your project changes evermore. Yesterday I was doing optical physics. Today my supervisor walks in smiling saying, "Figure out how to grow this algae. It's our new model system for your project." Now you might think that doing plant biology in a biophysics lab is absurd. But it's a highly logical solution to my project. – xyz123 Feb 24 at 5:11
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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...)

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  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.

  • I would have preferred to finish, but my mental health had deteriorated to the point that it wasn't practical. I would prefer a good PhD than a mediocre one that I finished because I had started. My goal is an academic career. I have put some thought into this and I am convinced that maths research is the right path for me. Obviously a PhD is the basic qualification for this. Even outside of career research, I am set on mathematics research. At this stage, earnings are not a concern for me. I am happy to sacrifice that for maths. That was a decision I made when I decided on research. – Joe Feb 20 at 14:03
  • Joe, could you please how you deal with what happened to you as I am exactly had the same story like yours, and when I am looking to peers get their PhD, I feel failure. I am the same wanted an academic career as that was my passion, however, I worked with a well established professor and forced me to leave saying that I am not for research. – Monika Feb 22 at 15:21

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