Mathematics
The Fast Fourier Transform (FFT)
Quick fact
The FFT algorithm is so important that a 1965 paper by Cooley and Tukey is among the most cited scientific papers of all time, and it helped ignite the digital signal processing revolution.
Why this is interesting
Every time you make a phone call, listen to a digital song, or take a medical scan, a hidden mathematical shortcut is working behind the scenes. How can millions of data points be broken apart into individual frequencies in just a fraction of a second?