I'm a 20-year-old Singaporean who got rejected by the local university as my high school grades were terrible. However, I have self-studied a good amount of math in my free time, including the standard undergraduate fare and some graduate-level topics (e.g., measure theory and graduate real analysis from Tao, computational complexity from Arora–Barak, etc. — as evidence, I have written detailed solutions on my website [0]). As additional proof of my geekiness, I also have 0x$5d.60 in Don Knuth's Bank of San Serriffe [1] for finding bugs in his books, making me the 14th richest person there.
But I have little to show for all of this — no fancy grades or awards, and no publications either. I'm not sure what to do at this point, since it'll be another year before I can apply to any universities.
I'm quite lost. Should I just find a job? Should I push myself towards publishing something? Should I sharpen my programming skills and try to get hired? I'd love to just be alone and study my own math, but it seems that it is finally time for me to face the real world.
What should I do? Thank you. (I will do my best to answer any questions you may have!)
[0]: https://boonsuan.github.io/misc/ [1]: https://www-cs-faculty.stanford.edu/~knuth/boss.html