As a fresh pure math phd student, I aim to become a mathematical physicist, and currently I try to schedule out what I should do step by step in this four years on phd program. But in my university, there is no professor in this field could help me as my advisor. So I wish to get some advice here. I wonder how could I get into research of quantum theory, quantum gravity, surviving in this research circle, that means, after my graduation, finding some university which is good at quantum science accepting me as its postdoc or faculty. I suppose I should start with learning all the advanced stuff on modern math and theoretical physics. And seek some mathematical problems that need to be solved for quantum theory and solve it, making it as my desertation. But the problem is, to seek this kind of mathematical problem could cost me long time after long term of learning has already been payed on these tough stuff. So it could be a really long term helping me unable to graduate and getting me into embarrass. Thus, I wonder if there is any mathematical problem that has already existed in quantum theory and quantum gravity constructing, and remains unsolved yet today, which I think I could pick up to consider and aim at right now.