Mathematics
Cohomology Theory and de Rham Cohomology
Quick fact
De Rham cohomology was introduced by Georges de Rham in 1931 and later proved to be a topological invariant: spaces that are homeomorphic have isomorphic de Rham cohomology, meaning the calculus-based construction detects the same holes as other cohomology theories.
Why this is interesting
Imagine you could count the holes in a shape using calculus. That's exactly what de Rham cohomology does—it turns the smooth functions on a space into a way to measure its global structure.