This is insightful and rings true for me as well. A good blend of theory and practical knowledge is important to get the most out of any education. Do you have any recommendations for learning math this way?
This person describes an experience similar to the one which inspired my mindset.
One other thing to note is that the order you might learn math, even the 'bundles' of math confined to the standard classes, is somewhat arbitrary. If you take on the freedom, you are responsible for the direction. That being said the linear path from arithmetic to Calculus or Linear Algebra, or Vector Calculus (to combine the two) will give you very strong fundamentals and chops that will apply broadly. It feels like once you get some understanding of Vector Calculus you can branch off wherever you want, though many advanced topics past that don't strictly require it, learning to derive concepts in that subject is excellent preparation.
All that said, there are plenty of interesting topics not involving Calculus or Linear Algebra. I really recommend what As_You_Wish has said as being honest with your own understanding and developing deep rigor, even across just one chapter or one sentence, will be your guide. Once you get deeply acquainted with one area, even if just a tiny area like "I finally understand trig functions," you understand better where you can jump off to next.
