I am violating my own rule concerning giving advice to any prospective applicant:
So please take my advice for a huge grain of salt.
- Spend some time understanding the intellectual approach of the University of Chicago, especially the math department. Research on CC and Reddit/UChicago about the math classes. There is a wealth of information in those threads.
- Ignore ranking, name recognition and your friend/relatives opinion of the school (unless they recently enrolled there). Learn about the university and its math department and decide whether that fits your personality and work ethics.
- If after all the research you feel U of Chicago is the right fit for you, then pour your heart in writing essays telling the admission office why they should pick you over many other Asians who excels in math.
Oh, one more thing. Check with your high school college admission counselor on how you would be able to afford a U of Chicago education. There will be nothing more disappointing to a college applicant that he/she is admitted but money problem prevents him/her from enrolling. Check your finance first.