I am a 16 year old high school student with too much free time. For the past two years I have been teaching myself university level maths in my free time. I have studied the basic first year subjects such as multivariable calculus, linear algebra and ordinary differential equations. My question is what should I study next?
I have tried more pure subjects such as real analysis, abstract algebra and number theory and additionally more applied subjects such as nonlinear dynamics, chaos theory and topology, but they either didn't spark my interest or were too difficult. I have even written a few papers that never really worked out.I posted one here I feel as if I need to regain my curiosity for mathematics and look for something beyond what academics present at seminars for children (referring to topology). Therefore, what is a subject that is seldom presented to an undergraduate but still is an valid field in mathematics?