When I was learning it, I always felt like calculus (and honestly algebra and trigonometry too) struggled to “justify” itself: whenever they presented real-worl

When I was learning it, I always felt like calculus (and honestly algebra and trigonometry too) struggled to “justify” itself: whenever they presented real-world applications, they always seemed so artificial that I ended up feeling even more confident that higher math was just complex for the sake of being complex. Although I understand that there are professions that “directly” apply calculus (i.e. solving integrals or derivatives) I went into computer programming where direct applications of calculus are few and far between, and ever the places where it’s applied like gradient descent and elliptic curve cryptography can be used without any understanding or appreciation of the base theory anyway. Still, I’ve come to appreciate that the real-world applications were deliberately simplified because the real real-world applications are mind-meltingly complex and that the presentation of calculus teaches you more to solve problems methodically than to apply specific processes and procedures.