Mathematics
The Monte Carlo Method for Numerical Integration
Quick fact
The Monte Carlo method for integration has an error that decreases as 1/√N (where N is the number of samples), regardless of the number of dimensions—unlike traditional grid methods whose error degrades rapidly with increasing dimension.
Why this is interesting
Suppose you want to find the area under a curve, but the curve is so complicated that a ruler seems useless—what if you could just throw darts at it and count how many land underneath?