I hope you are having a wonderful day. My main question is how/what are the best ways for a high school student to go about working on, or at least attempting to do mathematical research.
I am currently a senior in high school, and have a working understanding of integral and differential calculus (Im in AP calc BC right now if that helps) and all preceding subjects. I have already been dabbling in self-study of vector/multivariate calc, basic differential equations, and basic linear algebra, but I would not yet trust myself to work with these concepts yet. I can look at work and understand it, but am not sufficiently skilled yet to tackle these problems myself. I could study these more thoroughly if it is essential, and I am honestly very interested in all of these subjects.. but I digress
I am really just asking all of you (much more advanced mathematicians than I will probably ever be) what your experience researching math tells you would be the most effective way for me to start. My career plan is to major in physics, get a PhD, and work in some form of theoretical or research physics.
Thank you for any time or thoughts you can share with me. It really means a lot, and I apologize for any inconvenience.