Mathematics
Randomized Algorithm and Monte Carlo Methods
Quick fact
Monte Carlo methods, like estimating π by randomly scattering points in a square, can achieve accuracy that improves with the square root of the number of samples, meaning you need only a few million samples to get a few decimal places.
Why this is interesting
Imagine trying to find the area of a weird shape by throwing darts at it—randomness might seem like a terrible idea, but it can give you a great answer. How can flipping a coin possibly lead to a reliable result?