Mathematical Brownian motion was orginally devised as a model for the random bouncing of pollen grains in a liquid. But these days it's used to model everything from stock prices to atmospheric noise to drunken mathematicians. In my talk, I'll show you how Brownian motion arises and talk about some of its many weird properties, as well as some applications. I'll discuss how they can help solve PDEs without hard analysis. I'll throw around funny-sounding names like Donsker, Wiener, and Doob. Time permitting, I'll also say a little about stochastic calculus, the art of differentiating the non-differentiable and making sense out of noise. This talk should be accessible to all and no prior experience with probability is required.