Bigelow obtained a master's degree at the Massachusetts Institute of Technology, studying electrical engineering and mathematics. During World War II, he assisted Norbert Wiener's research on automated fire control for anti-aircraft guns.
When John von Neumann sought to build one of the very first digital computers at the Institute for Advanced Study in Princeton, he hired Bigelow in 1946 as his "engineer," on Wiener's recommendation. Dyson (1997) argues that the computer Bigelow built following von Neumann's design, called the "IAS," and not the ENIAC at the University of Pennsylvania or the Colossus designed as part of the code-cracking project at Bletchley Park in England, was the first true stored-program digital computer. Because von Neumann did not patent the IAS and wrote about it freely, 15 clones of the IAS were soon built. Nearly all computers subsequently built are recognizable descendants of the IAS.
Before working on the IAS, Bigelow coauthored with Norbert Wiener and Arturo Rosenblueth one of the founding papers on cybernetics and modern teleology, titled "Behavior, Purpose and Teleology." This paper mulled over the way mechanical, biological, and electronic systems could communicate and interact. This paper instigated the formation of the Teleological Society and later the Macy conferences. Bigelow was an active member of both organizations.