If there's a mathematical idea that applies itself to almost everything in everyday life but is almost unknown outside the scientific world, the Fourier transform has to be the most unsung contender.

Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform? [Shalma] begins by telling you a little about Joseph Fourier, the French mathematician with an interest in heat propagation ...

As we listen to a piece of music, our ears perform a calculation. The high-pitched flutter of the flute, the middle tones of the violin, and the low hum of the double bass fill the air with pressure ...