I'm now a programmer in a Shanghai based IT company. I have been graduated from college for 4 years and my major in college is not math or physics related. But I kept thinking my "philosophical stuff" along and recently found there's answers for me in both pure mathematics and theoretical physics(M-theory/LQG, etc). so I decided to apply for a pure Math PHD study to make a sound base to do researching job. it's some difficult for me because: My undergraduate transcript just show very poor performance, also in those math classes as calculus, linear algebra and probability theory. and recently I got my first and terrible GRE score and a TOEFL 537. Someone told me I'll be competitive if I had journal papers. I think this is interesting on this condition that my goal is just present my thoughts in academic paper after learn mathematics systematically in graduate school. for now, if I have ability to send serious paper I would most probably not that urge to apply for a graduate study. now I'm learning Garrity's book, All the Mathematics You Missed... I'm looking for your suggestion, thank you!