Hello, I am going into my final semester of undergrad and will be applying to PhD programs this fall. I have a unique mathematical background. I am curious how this will weigh against other aspects of my application. Here goes:
I shirked college and moved to a big city to try to be an artist after high school, but a year later I enrolled in city college to study english. After a year I ran out of money and moved home and finished another year of community college as an english major (I earned an AA). I transferred to a big prestigious university and decided in the second semester of my first (and junior) year to try taking upper division linear algebra. I had hated math in high school (and in fact failed algebra 2 and barely scraped by in summer school) but was compelled for some reason to take this class. It was quite hard (I literally didn't know FOIL at the beginning lol) but I ended up learning a lot and got a C+ after recovering from a terrible midterm grade. I became very obsessed with mathematics and have progressed very quickly. I have taken and received very high grades in numerous graduate level courses and will graduate having completed all requirements for both a BA and an MA in math (although my university doesn't offer the latter to undergrads unfortunately) after only four semesters. I skipped calculus 1 and 2, lower div linear algebra, and tested out of discrete math. I received a poor grade on one occasion due to circumstances beyond my control, and mediocre grades due to poor exam performances (so it goes), and have a 3.23 major GPA. I've written and posted to arXiv a couple of survey papers in higher algebraic geometry and representation theory, and am doing independent research remotely with a professor outside of the US. My letter-of-rec situation is grim because I have only had three semesters to build any significant relationships with professors, and for approximately two of these semesters I was a bit useless, being incredibly new to mathematics and not even knowing that I was going to be interested in grad school. I have not really been open whatsoever about my past experience with math, aside for with one professor, who verbally berated me on multiple occasions and has assured me that I will not succeed as a mathematician (an analysis based on zero qualitative understanding of my character or intellect). Since this, I have been quite hesitant to speak to professors, and especially to tell them of my experience. In essence, I am not sure if it will help or harm me from their perspective. I have the same question regarding graduate school. Will my experience hurt me in applications? Or will it help me? I am also unsure where I should direct my attention w/r/t these applications. Should I even bother with reach schools? Or should I focus on reaching out to professors who might accept me or relate to my situation (do such professors exist)? In a sense I am still unexperienced, I am far from perfect, and I have not demonstrated my potential at full. But I progress very rapidly in mathematics and am quite confident in my creativity and unique ability to solve problems. So I am nervously optimistic. Nonetheless, I would greatly appreciate any sort of advice that might help quell this persistence of uncertainty. Thanks very much
