This doesn’t feel true about mathematics. Much of the math I teach I would enjoy going down a similar rabbit hole with students, though it hopefully wouldn’t take as long.
But this comic also made me think about calculus. There are plenty of gaps in my calculus understanding — I’m not sure I could prove the product rule without some significant help, for instance. I’ve worked through proofs of Lagrange error before but I’m a long way from really understanding how that whole thing works. Not to mention the Fundamental Theorem of Calculus, which I can use pretty fluently yet don’t particularly understand why it’s true.
Maybe this is a reminder to deepen my own content knowledge. At the same time, my instinct is that there are times when it’s appropriate for a tool to remain an abstraction. I would like to verify that abstractions work — for instance, use Desmos to verify that a few product rule applications do, in fact, produce appropriate derivatives. I wonder if I could come up with criteria for when an abstraction is far more useful than understanding why that abstraction is mathematically correct.