Mathematics
The Rank-Nullity Theorem and Its Geometric Implication
Quick fact
The rank-nullity theorem was implicitly used by Carl Friedrich Gauss in his work on linear equations, but it was formally stated in terms of these dimensions much later by Paul du Bois-Reymond and then popularized by Soviet mathematicians in the 20th century.
Why this is interesting
You've seen a 3D object flattened onto a table—its shadow loses dimension, yet the object itself hasn't disappeared. What if the same principle governed all linear equations?