There is this feeling I get from attending both my French 2 class, and my Riemannian Geometry class. It’s odd that it’s the same feeling from these two different classes. It’s the feeling of surprise that I understand the words being spoken by the teacher. In one case it might be something like
Qu’est-ce que vous buvez chaque jour?, and in the other case it may be something like
A Riemannian metric on a smooth manifold M is a 2-tensor field g∈T2(M) that is symmetric and positive definite.