Hi physicsforums, this is my first time posting here, but I've lurked here and there before. While reading over a lot of the threads, I noticed how some people advised to not rush the learning process and to take things as they come, but at the same time I see a lot of other high school students probing deeply into very high level math and physics like PDE's or quantum theory. My question is: if I want to major in physics during college and eventually move onto graduate school to pursue a PhD in physics, where on the spectrum should I be at right now? I wouldn't describe my mathematics background as shallow, because I'm currently excelling in my school's AP Calculus BC course. But at the same time I have to admit that I find mathematics here less than satisfying, because there has been almost no emphasis placed on proofing since geometry back in middle school. Should I be very knowledgeable of how to proof by the time I enter college? If so, where can I find resources to build this skill? I have checked my local library, but none of the mathematics books there help in this specific area. Thank you for your time.