The Strange Math That Predicts (Almost) Anything

Markov Chains provide a powerful mathematical framework for modeling dependent events by focusing on current states rather than entire histories. This concept emerged from a 1905 intellectual feud between Pavel Nekrasov, who erroneously linked probability to free will, and Andrei Markov, who used Russian poetry to prove that dependent events could still follow the Law of Large Numbers. This breakthrough later enabled Stanislav Ulam and John von Neumann to develop the Monte Carlo method for nuclear bomb simulations. The same principle underpins Google’s PageRank algorithm, which treats web navigation as a series of probabilistic transitions, and informs the predictive capabilities of modern large language models. By simplifying complex systems into memoryless chains, this mathematical tool remains essential for solving diverse problems, from predicting climate feedback loops to determining the number of shuffles required to randomize a deck of cards.