Part 8/16:
This insight was soon exploited in a groundbreaking algorithm: the Monte Carlo method. During the Manhattan Project in World War II, scientists needed to simulate neutron behavior inside nuclear bombs. Direct calculation was impossible due to the enormous complexity and countless interactions of neutrons.
Enrico Ulam and John von Neumann realized that by generating many random outcomes, they could estimate the probability of chain reactions and critical mass—akin to playing countless simulated games of Solitaire to estimate the chance of winning. They used the idea of a Markov chain to model neutron interactions, randomly sampling transitions, and statistically estimating whether a chain reaction would sustain itself.