This is the Fourier Transform. You can thank it for providing the music you stream every day, squeezing down the images you see on the Internet into tiny little JPG files, and even powering your noise-canceling headphones. Here’s how it works.

The equation owes its power to the way that it lets mathematicians quickly understand the frequency content of any kind of signal. It’s quite a feat. But don’t just take my word for it—in 1867, the physicist Lord Kelvin expressed his undying love for this fine piece of mathematics, too. He wrote, “Fourier’s theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.” And so it remains.

Math Will Tear Us Apart