[staunton]

When you've read that passage in the math book twenty times, you eventually come to the conclusion that you understood it (even if in some rare cases you still didn't).

When "struggling through" a philosophy book, that doesn't happen in my experience. In fact, if you look up what others thought that passage means, you'll find no agreement among a bunch of people who "specialize" in authors who themselves "specialized" in the author you're reading. So reading that stuff I feel I have to accept that I will never understand what's written there and the whole exercise is just about "thinking about it for the sake of thinking". This might be "good for me" but it's really hard to keep up the motivation. Much harder than a math book.

[voidhorse]

I agree with the phenomenon you are talking about, but for mathematics, beyond calculation, the situation isn't really different (and no wonder since you'll quickly end up in the philosophy of mathematics).

You can take an entire mathematical theory on faith and learn to perform rote calculations in accordance with the structure of that theory. This might be of some comfort, since, accepting this, you can perform a procedure and see whether or not you got the correct result (but even this is a generous assumption in some sense). When you actually try to understand a theory and go beyond that to foundations, things become less certain. At some point you will accept things, but, unless you have enough time to work out every proof and then prove to yourself that the very idea of a proof calculus is sound, you will be taking something on faith.

I think if people struggle with doing the same thing with literature/philosophy, it's probably just because of a discomfort with ambiguity. In those realms, there is no operational calculus you can turn to to verify that, at least if you accept certain things on faith, other things must work out...expect there is! Logic lords over both domains. I think we just do a horrible job at teaching people how to approach literature logically. Yes, the subtle art of interpretation is always at play, but that's true of mathematics too and it is true of every representational/semiotic effort undertaken by human beings.

As for use, social wit and the ability to see things in new lights (devise new explanatory hypotheses) are both immediate applications of philosophy and literature, just like mathematics has its immediate operational applications in physics et al.