In March 1947, John von Neumann developed a “tentative computing sheet” for the application of the Monte Carlo method to a problem of neutron diffusion, describing the plan as “well suited to serve as a basis” for either a manual calculation or one performed on the ENIAC. Within a year, however, the ENIAC had been converted from its original programming regime to run in “stored program mode” and von Neumann's initial plan had evolved into a complex program of around 800 instructions which first ran in April 1948.

A rich collection of archival material, including a number of flow diagrams and the source code for the second version of the program which ran in the autumn of 1948, allows us to trace this development in great detail. This material provides a unique insight into the transformations in computational practice that accompanied the introduction of the automatic digital computer and the effects of these transformations on the conceptualization of mechanical calculation. This presentation will give an overview of the evolution of the Monte Carlo programs, highlighting a number of aspects including:

• the practicality of the Monte Carlo method itself;

• the increasing scope of automation, encompassing organizational as well as mathematical aspects of the problem;

• the growing complexity of algorithmic thinking and the increasingly idiomatic use of patterns such as loops and subroutines;

• negotiation between table look-up and the ad hoc calculation of numerical data;

• the generation and use of pseudo-random numbers;

• the use of the Goldstine/von Neumann flow diagram method in practice.

Historical discussion of the stored program computer has tended to emphasize technology and computer architecture. Consideration of these software artefacts allows us to develop a more rounded picture of the computer in use, however, and suggests that the significance of the machines of the late 1940s to mathematics has as much to do with the coding style exemplified by the ENIAC Monte Carlo programs as with innovations in hardware.