so-called "free thinkers" when they're left adjoint to a forgetful thinker (me)

I'm so confused about my academic future

ive been varying degrees of familiar with differential forms for like 6 years now and i still dont understand why anybody cares about them. like. sure. if youre a physicist or whatever, you wanna use stokes's theorem. but you dont really need differential forms to USE it. just move the d's around

Do you have another way of expressing integration on abstract manifolds that you prefer? Like I think it's quite natural that you'd need some sort of gadget to express the fact that, say, the function that's constantly 1 gives different integrals on spheres of different radii, even though they are diffeomorphic.

For me the answer is stratification of M_{g,n} by strata of abelian differentials, and also de Rham cohomology, but mainly the former for my current area of research.

Just steeped my tea for like 30 minutes idgaf im crazy

Spend more time thinking about math than actually doing math.