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It's easier to appreciate math when you are disinterested in the results or applications, because the nature of academic topics near the core grouping of math/philosophy/empiricism is that they are discovered with a lot of meandering at first, and then sometime down the line they become repurposed into a direct application that can be learned by rote. School tends to instruct in some of the most directly applicable stuff first - the "three R"s" plus some civics and training aligned with national goals. And that means that school predominantly teaches associations between math and rote methods, to the disgruntlement of many mathematicians. The "meandering" part is left to self-selected professionals, so it doesn't get explored to much depth.

So I think a good motive for math study is really in games and puzzles, where the questions posed aren't about win/lose or right/wrong, but about exploring the scenario further and clarifying the constraints or finding an interesting new framing. Martin Gardner wrote a long-running column and a few books in this vein which are still highly regarded decades later.