Enrico Fermi in the 1930's used Monte Carlo in the calculation of neutron diffusion, and later designed the Fermiac, a Monte Carlo mechanical device used in the calculation of criticality in nuclear reactors. In the 1940's, a formal foundation for the Monte Carlo method was developed by von Neumann, who established the mathematical basis for probability density functions (PDFs), inverse cumulative distribution functions (CDFs), and pseudorandom number generators. The work was done in collaboration with Stanislaw Ulam, who realized the importance of the digital computer in the implementation of the approach. The collaboration resulted from work on the Manhattan project, where the ENIAC was employed in the calculation of yield [60,59,17,43].

Individuals in the IBM corporation were pioneers in the field of random number
generation, perhaps because they were first engaged in it due to their
participation in the Manhattan project, where Richard Feynman then directed
their computing operations (a fascinating exposition of their approach to
performing large-scale computing involving a parallel approach exists in
Richard
Feynman's * Surely You're Joking, Mr. Feynman*). It is interesting to note
the extremely primitive computing environments in existence at that time, and
the challenges this presented to researchers
(see [27]).