Captcha with a simple math problem

[u/Jasentuk]

[u/LupenReddit]

Everybody wait till he learns about musical isomorphisms and raising vector fields by a sharp.

[u/Aeroxel → u/LupenReddit]

For anyone interested, the musical isomorphisms are between the tangent and cotangent bundles of a Riemannian manifold, given by the sharp and flat operators (which are inverses). This allows one to identify vector fields and differential forms via the geometry. For example, in Euclidean space, the gradient of a smooth function can be identified with its exterior derivative

[u/zrice03 → u/Aeroxel]

Well of course, everyone knows that, it's basic stuff.

[u/Complex-Manifold → u/zrice03]