/sci/ - Science & Math

>>6979347
You see surfaces and curves ? it's their study and their equivalent in higher dimension vector space (the relation to linear algebra) called Manifolds. The study is based essentially on the overview of tangent spaces (tangent for curves, tangent planes for surfaces) and resulted fibrations (here is the source of "differential" because of the relation with infinitesimal open limits).

This is the source of it, but you can do better with general topological manifolds where the structures are all replaced by general topological space and where a manifolds is defined by "set of points so that for all points it is homeomorph to a unique smooth topological space (ex : R^n) "
then the study revolves around doing geometry with those weird but pretty spaces.

TL;DR : differential geometry is study of higher dimensional curves and is way more technical than classical linear algebra