The Metropolis method
The paper described how to sample from a distribution that cannot be computed directly, by accepting or rejecting a random step on a ratio of probabilities.
Why it matters
Sampling instead of exact computation became the standard move wherever a distribution is known only up to a constant.
The work was written for statistical physics problems on the MANIAC machine at Los Alamos. It matters here as the origin of a technique that Boltzmann machines, Bayesian inference and present-day diffusion models all rest on: draw a sample rather than compute a sum.