I thought a lot about this over night. As a parent, it's a question I constantly grapple with. "What will I tell my child when they want real-world applications

I thought a lot about this over night. As a parent, it's a question I constantly grapple with. "What will I tell my child when they want real-world applications of an abstract, yet extremely important, topic?" The conclusion I've come to is that asking for practical, real-world applications in one's life misses the point. The reason to learn calculus also has nothing to with mental exercise. The reason to learn calculus is that it provides the theoretical foundation upon which modern society is built. Differential equations provide solutions to engineering formulas that allow us to build skyscrapers. We can calculate the trajectory of celestial bodies and use that information to explore our solar system and to peer into the stars. We can train machine learning models that realize our imagination. The list of things calculus enables is near-infinite. Now, do you need to know calculus to survive? No, of course not. You can live your entire life without even needing calculus. But, calculus is one of the wonders of the world. Its beauty is similar to something like the Grand Canyon or Mt. Rainer. Yes, it takes a little work to "see" calculus, similar to how you might need hike quite a distance to reach a beautiful peak, but the view from the top is worth it. There is no need for natural beauty, too. You can easily live your life without experiencing the wonderful things nature has to offer. But to live a life without experiencing nature is dull compared to what is possible. And it's the same with calculus.