He was a programmer on John von Neumann's computer at the Institute for Advanced Study, Princeton, NJ, from 1953 to 1956, where he notably programmed the Blackman–Tukey transformation.
His most significant contribution to the world of mathematics and digital signal processing is re-discovering the fast Fourier transform,[3] which he co-developed with John Tukey (see Cooley–Tukey FFT algorithm) while working for the research division of IBM in 1965.
The motivation for it was provided by Dr. Richard L. Garwin at IBM Watson Research who was concerned about verifying a nuclear arms treaty with the Soviet Union for the SALT talks.
Garwin thought that if he had a very much faster Fourier Transform he could plant sensors in the ground in countries surrounding the Soviet Union.
They did the work, the sensors were planted, and he was able to locate nuclear explosions to within 15 kilometers of where they were occurring.