I am in my last year of high school. I do not know if I will become a mathematician or physicist. Right now, I enjoy physics more but I will double major in math and physics anyway. I know that research experience is important in undergraduate physics. However, how important is undergraduate research in math? I have a slight idea of what undergraduate physics research is like but I do not know anything about undergraduate research in math. I don't even know if it is needed for graduate school. So is there anything other than taking math classes that I need to do to be competitive for math graduate school? I am asking this because I might switch to considering math more seriously in college. I have not taken a pure math class (one involving proofs) yet. I am trying to teach myself to write proofs but I have not found a way to easily teach myself. It is hard and I don't know if my proofs are formal or if they're even correct. Would I be okay if I only do what is required of me in my math classes?