You can't always learn with the expectation that everything has a perfectly applicable use case (i.e the point about learning Geometry to build a renderer). This may be fine if all you want to do is (re-)implement things that have been done before but if you want to develop new things and solve new problems, you won't know beforehand what tools and what theory will lend to the solution. I'm doing a PhD now and I will take classes and read papers outside of my focus to see if anything will lend itself to my research. Much of this doesn't go anywhere until one day I go, "this problems kinds of sounds like what they did in [that other field]".
Also, many complex topics build upon many, many smaller results. I've found this true for large portions of math. Many readily applicable theorems, for example with applications in signal processing and control systems, require many years of math background and maturity. It's very difficult on the onset to connect the basics to the complex theories. (On a personal note, I've found that I had a relatively extensive math background as an undergrad. You could argue that the extra math I did was not worthwhile as it isn't all applicable. However, in some of the classes I've taken in grad school, I've noticed the gap in math background and familiarity as other students try to catch up.)
That said, I do admire the OP for taking hold of his education. I did not find my high school education, targeted at the average or at most students, to be well-suited for myself. I would just say that there's a reason the topics and material chosen are what they are. Extending what's done in school is a great idea, but if you are going to deviate, make sure you have a very good idea of what you are deviating from (and why).
You can't always learn with the expectation that everything has a perfectly applicable use case (i.e the point about learning Geometry to build a renderer). This may be fine if all you want to do is (re-)implement things that have been done before but if you want to develop new things and solve new problems, you won't know beforehand what tools and what theory will lend to the solution. I'm doing a PhD now and I will take classes and read papers outside of my focus to see if anything will lend itself to my research. Much of this doesn't go anywhere until one day I go, "this problems kinds of sounds like what they did in [that other field]".
Also, many complex topics build upon many, many smaller results. I've found this true for large portions of math. Many readily applicable theorems, for example with applications in signal processing and control systems, require many years of math background and maturity. It's very difficult on the onset to connect the basics to the complex theories. (On a personal note, I've found that I had a relatively extensive math background as an undergrad. You could argue that the extra math I did was not worthwhile as it isn't all applicable. However, in some of the classes I've taken in grad school, I've noticed the gap in math background and familiarity as other students try to catch up.)
That said, I do admire the OP for taking hold of his education. I did not find my high school education, targeted at the average or at most students, to be well-suited for myself. I would just say that there's a reason the topics and material chosen are what they are. Extending what's done in school is a great idea, but if you are going to deviate, make sure you have a very good idea of what you are deviating from (and why).