Mathematics
The Rank-Nullity Theorem: Connecting Matrix Dimensions
Quick fact
For any matrix, the rank and nullity add up to the number of columns—a surprising and elegant balance that holds for every matrix, no matter its size or entries.
Why this is interesting
You have a machine that takes in 3 numbers and spits out 2 numbers. It always loses at least one dimension of information. But how much exactly? The rank-nullity theorem tells you precisely how much is lost and how much is kept—without even running the machine.