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TL;DR: I'm applying for a PhD program in mathematics, but my academic performance was bad for a long while and I already have a PhD attempt that I ended early. (However, I now have good enough results to apply again.) Given this background, should I spend any time in my SoP addressing the reasons for these poor outcomes? If so, is it a good idea to only mention them as indicators of how serious I am about getting a PhD? Or, should I leave it out altogether?


More detail: I'm filling out applications for math PhDs (to start fall of 2024), but I'm a fairly non-traditional student in a lot of ways and could use some pointers on how to address that in my personal statement, if at all.

For a little background, I grew up extremely poor and was functionally a high school dropout by the time I got out of public school. I took an extra year to graduate, was placed in "at risk" courses, had a 1.2 GPA; just all around bad. I started community college a couple years after high school, starting out in basically 7th grade math and it took eight years to finish my undergrad. Maybe unsurprisingly, much of my undergrad was pretty rocky; most of my math classes were C's, with a couple of B's and a couple of D's and a few withdrawals. I had a handful of life circumstances that got in the way, like having to work full time to support my mom, a family death and a fiancé that ended up having an affair (I know for sure not to mention that last one in my statement), but more fundamentally it took a long time to master the essential soft skills like how to study. In my last three semesters of undergrad my math performance improved substantially and I started getting mostly A's in my upper division courses, with two B's. I did well enough to get into a masters degree in statistics, which was fairly theory focused and in which I continued to do well (final GPA was a 3.8 in the masters). I also had some extra room for elective course work, so I used it to take some courses like topology and abstract algebra, which I also got A's in.

After the master's, I applied to Math PhD's and managed to get into a couple of programs. But, covid hit six months later and I did not deal well with the isolation at all. My mental health completely tanked, and I couldn't work on anything for more than 5 minutes at a time. I left that program at the end of my second year and started working in industry, but I wanted to go back to a PhD eventually. This fall, I enrolled in a graduate analysis class at my alma mater (as a non-degree seeker) so I could get back into the swing of things, and I'm continuing to do very well. The professor has only posted a handful of the distributions on a couple of assignments and one midterm, but based on that and how discussions in class go I estimate that I might be one of the top three students in the class; my professor volunteered to be a letter writer for me when he asked about my long term plans and my background.

I have a few ideas about possible areas of research I want to go into; something that broadly fits somewhere in the umbrella of analysis, like probability or dynamical systems. Or possibly PDEs, but I don't have a very strong familiarity with that area yet, so I can't say that too confidently. Post-PhD the dream would be to work in academia, but given the need to post-doc and how tight the academic job market is that might be unrealistic for me, so working in a national lab might be up my alley. I don't think I can say anything more concrete than that until I'm a couple years into a program and I have a clearer view of what kinds of opportunities would be available to me given wherever I happen to be.

I know it's kind of a mess, but I am extremely determined to get a PhD in math. If I don't get in now, I'm just going to keep trying to improve my application until I do get in. Math has been life changing for me. I want to continue working with it in substantial and meaningful ways as an essential part of my career and continue to stay engaged with the math community in general. Any thoughts, suggestions or advice on what to say about this would be greatly appreciated.

Thanks.

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    Could you highlight exactly what is the question that you’re asking?
    – user126108
    Nov 26, 2023 at 21:43
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    Yeah, that wasn't very clear was it. I included an edit, but I'll post it here: To be more concrete with my question. Given that my performance was not good for a while, and given that I already took a swing at a PhD and needed to leave, should I spend any time in my SoP addressing the reasons for these? If so, is it a good idea to only mention them as indicators of how serious I am about getting a PhD? Or, should I leave it out altogether?
    – bears
    Nov 26, 2023 at 21:53
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    If you're looking at PDE's, make sure to include "applied math" departments in your search. Often enough "PDE's" is precisely what people mean by "applied math".
    – user176372
    Nov 26, 2023 at 22:24
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    Possible duplicate of: How are Ph.D. applications evaluated in the US...? In particular, recommend reading at least the SOP section in that lengthy canonical answer.
    – cag51
    Nov 27, 2023 at 0:25
  • TL;DR: OP had bright results in mathematics during their masters, then they began a PhD in mathematics but when covid lockdown happened, they stopped and went to work in industry. Now they're wondering if they can apply to another PhD in mathematics and what to write in their statement of purpose.
    – Stef
    Nov 27, 2023 at 11:01

2 Answers 2

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Little of what you say here is relevant in any way to a SoP. It is all backward focused and gives excuses. None of that is positive, nor appropriate in a SoP. I doubt that anyone is admitted to a graduate program because the committee feels sorry for them. Very few, anyway.

The statement of purpose should be forward looking. It should say what you want to study and what your goals are, both for graduate school and thereafter. What is your purpose, not what is your history.

In the US, at least, which I'm assuming, doctoral applications are broad based. There may be opportunities for saying some of what you list here in other places, but much of it is irrelevant. You need a good or better GPA. You need to have done well in important courses in your field, especially upper level courses. The time it took and the difficulties you faced are of little importance if you are a good candidate for success in the program and thereafter.

Letters of recommendation are also relatively important. A letter writer can say things that you cannot. "The candidate overcome many obstacles to get to the good place they currently occupy and have developed both skills and attitudes that will carry them..." That sort of thing. If you say how hard you had it, it is just an excuse. If others say you've overcome, it will be believed.

So, focus your SoP on the field and sub-field. If you have general ideas for the research path you'd like to follow, write about that. A few short phrases indicating you have the background for that path can help. A few words about your after graduation goals is good - your planned career path.

Your CV/resume gives the history. Your SoP is the future. Your letters connect them as needed.

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  • I guess that's the balance I'm finding difficult to strike. I think I have understandable reasons for such a poor performance for the first chunk of undergrad, and I feel like the poor performance needs to be addressed in some way, but I want to avoid telling some sob story and trying to get in on pity. Further muddying the issue is that I already attempted a PhD and ended up leaving. I guess I worry that there's a lot to address but I'm not supposed to say much about it. It sounds like just keeping it predominately forward focused and letting my letter writers say good things is the way to go
    – bears
    Nov 26, 2023 at 21:08
  • You can specifically and politely ask letter writers if they would address A B C and point out D. You say “letting “ them say good things, which is probably too passive.
    – Dawn
    Nov 27, 2023 at 1:25
  • [Caveat: UK-based comment] While I agree that most of the background is irrelevant, I would absolutely expect the previous PhD attempt to be addressed in a SoP, along with an argument for why "this time will be different".
    – Aant
    Nov 27, 2023 at 13:30
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First, yes, your statement of purpose should primarily be forward-looking. On the other hand, yes, it is very good to recount difficulties you've overcome... sure, don't go on tooooo long... poverty, lack of role models, etc. create a much different context than middle-class, college-educated family...

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  • That makes sense. Thanks for the suggestion. I'm sure there aren't hard and fast rules, but is a paragraph an acceptable amount? The only real reason I care to bring up past difficulties in the first place is to highlight a capacity for growth in the subject and to emphasize my seriousness about doing this. Outside of that I'll mostly be focusing on potential areas of research, why I'm interested in a given school and what I'd like to do after school.
    – bears
    Nov 26, 2023 at 22:49
  • Yes, I'd think a small paragraph explaining your context in not-too-dramatic terms would suffice, and not be seen as excess. :) Nov 26, 2023 at 22:51
  • Okay. That's very helpful. Thank you again for sharing your thoughts.
    – bears
    Nov 26, 2023 at 23:07
  • Reframe your view on this from "making excuses for poor past performance" to "pushing yourself to be the best you can be" may be a good way to approach this aspect of your history. You need to address 1) your poor high school and undergrad performance, and 2) you started a PhD before and dropped out. You can say you've worked (and plan to continue to work) to improve your academic skills which you demonstrate with the masters. You also dropped out to preserve your mental health, demonstrating you've learnt to manage yourself so you don't burnout. Then your references can support these claims. Nov 27, 2023 at 13:25
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    I have not run the rounds of graduate admissions, but I can comment on the rhetoric, and this answer is imo a good one. The rhetorical value of hardship (a phrase that is a bit horrifying to say) is often in the demonstration of commitment to the cause, and to convince a reader that one is truly serious about their goals. My advice builds on this answer: Linger no longer on the past than is required to develop this thesis; use it as a tool to an end. Several components of your above story, @bears, can easily aid this focus - but need to be honed to a fine point to make them easy to understand.
    – Slate
    Nov 27, 2023 at 19:57

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