Mathematics
Fast Fourier Transform (FFT)
Quick fact
The FFT algorithm reduced the number of operations needed for frequency analysis from roughly a million (for 1,000 samples) to just 10,000—a 100x speedup that made real-time audio processing possible.
Why this is interesting
When you listen to music, your brain effortlessly separates instruments—but how does a computer do it in milliseconds? The answer is a clever mathematical shortcut called the Fast Fourier Transform.