So I have only started gaining an interest in seriously pursuing a math/physics career in the past year. Before, I have only been "good" at these two subjects and understood them relatively easily. I just thought about doing engineering and never actually had a serious interest in doing them. With regards to physics, I'm mostly ahead of others now since I have been self studying more advanced topics in the past year such as advanced EM and general relativity and the like. However, with math, even though I am mostly at the top of my math classes and took multivar calc/diff eqn in the past year, I don't think I'm good at math at all. I never did any competition-based math and only did it a little in freshman year of high school. Now, I only recently gained an interest in math and started doing math team again this year in senior year. Having done no practice at all, I only did slightly above average at competitions like NYSML and ARML. However, I'm mostly behind others who have much more experience and practice regularly. Even though I think I can pick up stuff easily and have a talent in these two fields, I'm slightly behind with regards to math. I will be attending college next year. 1) Having only recently gained an interest in these two subjects, how would I catch up with others with regards to math and competition-based math since I intend on taking the putnam? 2) Also, I did not attend a lot of math camps either, am I missing out on a lot? How would I catch up with those that have been doing this kind of problem solving math stuff 6 years more than me that usually come at the top of those regional math competitions? thanks.