4.1 From solitaire to the ENIAC

In 1946 Ulam was ill. He had been appointed at the University of Southern California, fell ill with encephalitis and had emergency brain surgery, and then returned to Los Alamos [1, 2, 3]. Later he described what came next in his own words: "The first thoughts and attempts I made to practice [the Monte Carlo method] were suggested by a question which occurred to me in 1946 as I was convalescing from an illness and playing solitaires" [1, 4].

The question was: what are the chances that a Canfield solitaire laid out with 52 cards will come out successfully? Later in 1946 Ulam described the idea to von Neumann [4]. In March 1947 von Neumann wrote to Robert Richtmyer outlining a neutron-diffusion calculation for the ENIAC. The Los Alamos laboratory calls it "the first formulation of a Monte Carlo computation for an electronic computer" [3, 4]. The first Monte Carlo calculations ran on the ENIAC in April and May 1948 [3].

The name. Nicholas Metropolis suggested it, "a suggestion not unrelated to the fact that Stan had an uncle who would borrow money from relatives because he 'just had to go to Monte Carlo.'" [2, 3]

Fermi's trolley. Enrico Fermi had used statistical sampling in Rome in the early 1930s without publishing it. At Los Alamos he had an analogue "Monte Carlo trolley" built, later called the FERMIAC [2, 3].

The FERMIAC, Bradbury Science Museum. Photo: Mark Pellegrini, CC BY-SA 1.0, via Wikimedia Commons.

The method was published by Metropolis and Ulam: "The Monte Carlo Method", Journal of the American Statistical Association 44 (247), 1949, pages 335 to 341 [5].

Sources

1. MacTutor, "Stanisław Marcin Ulam", https://mathshistory.st-andrews.ac.uk/Biographies/Ulam/
2. N. Metropolis, "The Beginning of the Monte Carlo Method", Los Alamos Science 15 (1987) 125–130, https://mcnpx.lanl.gov/pdf_files/Article_1987_LAS_Metropolis_125--130.pdf
3. O. Summerscales (ed.), "Hitting the Jackpot: The Birth of the Monte Carlo Method", Actinide Research Quarterly, LANL, 1 Nov 2023, https://www.lanl.gov/media/publications/actinide-research-quarterly/1123-hitting-the-jackpot-the-birth-of-the-monte-carlo-method
4. R. Eckhardt, "Stan Ulam, John von Neumann, and the Monte Carlo Method", Los Alamos Science 15 (1987) 131–141, https://mcnp-green.lanl.gov/pdf_files/Article_1987_LAS_Eckhardt_131--141.pdf
5. N. Metropolis and S. Ulam, "The Monte Carlo Method", JASA 44(247) (1949) 335–341, doi:10.1080/01621459.1949.10483310, https://doi.org/10.1080/01621459.1949.10483310