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Background: I am a senior at a (fairly prestigious) university in the United States, and I am applying to PhD programs in the country for pure math, aiming as high as I can. I am majoring in mathematical physics, and by the time I graduate, I will have taken over 10 graduate courses (mostly in pure math, some in theoretical physics); for some topics, I have taken every graduate course offered at my university on them. I mostly have As on my transcript with some Bs (including two on math grad courses) with a near perfect concentration GPA (only a few math courses I took count toward my concentration courses, however). I have more Bs overall in math than in physics. I have done some research/advanced reading courses in topics beyond what is covered in any graduate courses at my university with professors in both the math and physics departments (with whom I took upper-level/graduate courses), and I'm on very good relations with these professors. I will be asking them for recommendation letters. I do not have any publications or REU experience.

I have a long-running issue: I am terrible at in-class written exams. In every course I have taken so far, my homework average has been near perfect, and the same is true for take-home exams. I want to stress that this is true across the board for all of my courses, a huge portion of which includes custom problems assigned by the instructor, in case someone is worried that these results have been achieved through Internet searches. So in all the courses I didn't get an A in, I did terribly on at least one of the in-class exams with a performance in sharp contrast to other portions of coursework which brought my grade down.

I don't know for sure why this is the case. I suspect I am a slow worker and compensate by drawing as much time as necessary to solve untimed problems, and this seems to explain poor in-class exam performance. I also verge on a nervous breakdown/panic attack before exams, but I have never mentioned this to anyone at my university to get accommodated, as I believed it would be asking for special treatment and be merely an excuse for poor performance as I convince myself there is nothing wrong with me.

I recently took the math subject GRE, and my performance was abysmal (40th percentile). My mind went blank during the test and I had very bad pacing. I think the result is very incongruent to the rest of my application, and I am at a complete loss at what to do. I will be retaking the test in a couple of weeks, but I am not sure if I can turn things around. (I am good at proofs but not so good at computation.) Worse yet, the extra pressure that "this is my last chance or I submit my 40 percentile score" might make me much more prone to having a breakdown.

I initially considered taking a year off before applying after looking at my test result, but I run the risk of diluting my recommendation letters and being subject to a much more intense scrutiny of my new score and of what I did besides studying during that entire year off. I am terribly afraid my score puts me into an instant reject pile at top institutions. I might add that personally, taking a year off due to a low GRE score would be very torturous for me, as I would agonize everyday over studying things I frankly do not care so much about (as opposed to tackling proofs and potential research work, which draws me to a PhD program in the first place) and constantly be haunted by what looms ahead, but I would also try very hard to get a publication in that time to make it worth it if I did take one off.

Questions: Should I take a take a gap year before applying? If not, is it worth applying to a good number of top schools with this kind of score (say half of all programs I apply to, with the other half reach/safety)? Should I get a psychological evaluation for my test performance and mention my test panic/anxiety issues on the the applications? Should I talk about this with a professor I am asking a recommendation letter from?

The whole experience with the Subject GRE has been quite dejecting, to be honest, and now I am doubting my capability. Is there some other way I can (personally) determine if I am cut out for math grad school in my case? I really enjoy thinking about math problems and trying my hand at them, but I don't know if it is worth it if I can't go to a good school at the end of the day.

P.S. I understand that graduate schools need a form of standardization to compare applicants, and I might be heavily biased here, but I really don't see how the subject test, which (in my opinion) to quite an extent requires employing computation tricks, assesses research ability in math. How strongly is "I cannot solve these integrals at lightning speeds" correlated with "I cannot solve this problem for my dissertation"? I am perfectly happy and capable of doing category theory problems or talking in person in great depth about functional analysis topics I've seen, but I am bumbling about with a convoluted plane geometry question on paper with a 90 second timer ticking. It's confusing because I can't tell if the latter is what a math grad student rather ought to be capable of doing instead of the former if one had to choose between the two. When I talked about the rationale behind timed-exams with a professor who taught me a grad class, he echoed what I've said above: it is just to standardize and to ensure students solved the rest of the coursework themselves instead of relying on some other person/source. Maybe someone has some insight on this?

Sorry for the long post.

EDIT: Just a quick update - I retook, and my score bumped up by 20 points. I think this is still pretty average, but definitely better than a 40. Any thoughts, given this update? (I was waiting for the scores to update my answer.)

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    In brief, as you already have observed, the GRE math subject test is ... silly. But, yes, given the personalities of many math faculty making admissions decisions, the GRE math subject test can be used as a filter... But, other places (e.g., mine) recognize that the GRE subject test, as a test of how well people can answer multiple-choice questions in a timed setting... has very little to do with mathematics. Also, sure, I guess it's better if everyone is taller? better looking? (whatever this means), but what does this have to do with math? (mm...) – paul garrett Oct 11 at 23:42
  • @paulgarrett So you would not consider my score as a disqualifier for applying to good schools? I was told to pretty much give up on the idea of receiving any slack/holistic consideration given how cutthroat admissions have become. (On a related note, I have no clue how much the parts of my application I've described compensate for my score...) – SystematicDisintegration Oct 12 at 1:24
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    You might find it helpful to talk to a psychologist or therapist in any case. Not necessarily to get any accommodations or to explain away a low score, but just because they are likely to be able to actually help you with the anxiety issue itself, and that may help you do better when you retake. Even relatively quick simple things can make a significant difference. – Nate Eldredge Oct 12 at 2:13
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    GRE math subject test don't tell us much. I'd say most math faculty see it that way. It is, however, the easiest way to limit the pool of applications. I had even worse GRE scores, but I was able to get into a good program. You'll need other evidence of your ability in that case. Having a published paper would be very strong evidence. Otherwise recommendation letter will be very important. You may need to apply many places as some schools do use GRE scores as the first filter. That said, your anxiety may be a bigger issue. Once in, there'll be many high stake exams waiting for you. – ssquidd Oct 12 at 4:36
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Have you considered looking at master's and PhD programmes beyond the USA? In the UK, Europe, Australia, etc there are no GREs or equivalent and you will be considered on the strength of your marks, experience, recommendations, and research goals.

I took the GRE only once as a sophomore as they were about to get rid of the "logic" section of it (read: the only bit I knew I would do well on). I got a perfect score on that now-defunct part and did horribly on the rest. I'm sure few US schools would have looked at me, the scores were so bad. I didn't even bother to try again, totally ignored US schools, and ended up with an Oxbridge Master's and PhD, plus a pretty snazzy academic career.

  • Just to clarify, the OP is talking about the GRE Mathematics Subject Test and it sounds like you're talking about the Analytical Section of the GRE General Test, which was introduced in 1977 and removed in 2002. (I took it 3 years after its introduction, and I remember having discussions with my friends planning to attend graduate school about how math/physics graduate admissions committees might interpret the scores, given the newness of the test and the fact that the general quant test was entirely unsuitable.) – Dave L Renfro Oct 14 at 17:44
  • Oh I know. I was just relating my story as parallel but not totally equivalent. My answer is essentially "if you have any sort of negative GRE test score that might prevent you from getting into the type of graduate programme you know that you can succeed in, why not skip the US entirely and go somewhere where admittance isn't based on an unsuitable test" – GrotesqueSI Oct 14 at 17:52
  • That is interesting. I will try to apply to some international PhD programs, just in case. I did hear, though, that unlike the US, international schools don't combine a PhD and master's into one program. I'm not sure I can afford a master's program alone without the stipend, so I'll have to check into the specifics while applying. – SystematicDisintegration Nov 22 at 11:45

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