Mathematics
Fast Fourier Transform (FFT)
Quick fact
The FFT algorithm reduces the number of operations from roughly N² (for a DFT) to N log₂ N. For a signal with 1,024 samples, that means about 10,000 operations instead of 1,000,000—a 100x speedup.
Why this is interesting
You use the Fast Fourier Transform every time you listen to music, speak on a phone, or look at a JPEG image—yet this mathematical trick is so efficient it was once considered a national secret.