Mathematics
Topological Invariants: Euler Characteristic and Betti Numbers
Quick fact
The Euler characteristic of a polyhedron is always V - E + F = 2 for convex shapes, no matter how many faces or vertices it has, and this number remains unchanged under any continuous deformation.
Why this is interesting
How can we tell if two shapes are secretly the same? A coffee mug and a donut look nothing alike, yet topologically they are twins—what hidden features let us compare them?