Co-authors (though attributed solely to him, causing controversy) the 'First Draft of a Report on the EDVAC', which outlines the logical design of a stored-program computer, later known as the von Neumann architecture. This architecture becomes the foundation for most digital computers. It describes how the instructions and data could be held in the same memory space.

Leads the development of the IAS machine at the Institute for Advanced Study. This machine is one of the first electronic computers built according to the von Neumann architecture and serves as a model for many subsequent computer designs. Julian Bigelow served as the chief engineer on the project.

Pioneers the concept of cellular automata, self-replicating machines and artificial life. His work in this area lays the groundwork for later developments in artificial intelligence and complex systems theory. He believed that the complexity of biological life could be constructed using mathematics.

Contributes to the development and application of the Monte Carlo method, a computational technique using random sampling to obtain numerical results. This method proves useful for solving complex problems in physics, engineering, and finance.