Cooley-Tukey and Other Algorithms for Fast Fourier Transform
Mathematics Accomplishment | 1965
Where the work was done: IBM T.J. Watson Research Center
What we accomplished: James Cooley (pictured) co-invented with John Tukey (and possibly repeating Gauss in the 1800s) the Fast Fourier Transform (FFT) to convert time-domain signals to frequency domain. Another fast alternative was invented by Shmuel Winograd.
Related links: Wikipedia entry on Cooley-Tukey FFT Algorithm
Image credit: Engineering and Technology History Wiki