Mathematics
Curvature and the Theorema Egregium for Surfaces
Quick fact
The Theorema Egregium, proved by Carl Friedrich Gauss in 1827, states that the Gaussian curvature of a surface is invariant under isometries—meaning it can be measured without ever leaving the surface itself. This is why a flat piece of paper cannot be bent into a sphere without stretching, but can be rolled into a cylinder without altering its intrinsic geometry.
Why this is interesting
Imagine a world where the shape of an ant's universe is determined entirely by the ant, not by the space around it. What if bending a surface without stretching could change its curvature?