Hey everyone! Great forum.

I'm looking for a sampling of advice. I think I'm in an interesting position, so any thoughts would be appreciated.

I'm a senior mathematics student, here's my basic info:

Undergrad Institution: Big State School

Major(s): Mathematics

Minor(s): n/a

GPA: 4.0/4.0 (may drop a bit after this semester, I did iffy in a grad-class midterm)

Type of Student: domestic white male

I attended an REU this summer in combinatorics/graph theory at a top-20 school. No publications yet, but I might still submit. I have some academic distinctions: many scholarships, won a math competition at my school. Plus I'm attending the Math in Moscow program next Spring.

Now, the thing is, I've only been in my university for the last two years. For two years in high school I was technically "homeschooled"--really my parents just put me in a community college and I started earning college credit before graduating. So when I went to college, I transferred in with already half the credits required for my degree.

I took the Mathematics GRE this October and bombed, ended up just cancelling my scores. I took it again this November, did better, but might have scored as low as in the ~60'th percentiles. I'm really bad at standardized testing, I'm a nervous wreck. To give you an idea of how poorly represented I am in standardized test scores: four years ago I failed my calc placement test, I had to beg the teacher to let me in, she did and I became the first student to get a perfect 100% grade in the class.

I have some grad courses, some pretty good recommendations, REU experience etc. However I really feel my Math GRE score is going to bring down my application something brutal. I'm so concerned about this, that I'm considering taking another year to take some more courses, maybe finish a minor, and work on getting a better score on the Math GRE. I could also do another REU next summer, and definitely by then publish my work from this summer's REU.

I want to get into a good top-20 school, I know my job prospects for a career in academics largely depend on it and I love math research so that's my goal. Do I have any chance of getting in anywhere really good with such a low GRE score and nothing phenomenal on my CV otherwise?

Also I feel that, having only been at my university for two years, another year wouldn't look so bad on my record. Any thoughts? I think I'm in an interesting position here, so I hope people find this interesting to think about and contribute their ideas.