Mathematics
Markov Chains and Their Steady-State Distributions
Quick fact
Google's original PageRank algorithm treats web surfing as a Markov chain, where the steady-state probability of being on a page determines that page's importance ranking.
Why this is interesting
Have you ever wondered how a random process like the weather or a stock price can settle into a predictable pattern over time? Markov chains explain how systems with no memory still reach a stable long-run behavior.