**The Fourier transform lets you have your cake and understand it**

Teasing apart the ingredients of a jumble helps scientists to study complex things that change over time or space

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. It pops up wherever scientists need to study complex things that fluctuate in the real world – sound, heat, light, stock prices – and has been used to separate the signal from the noise in data collected for astronomy, medicine, genetics and chemistry. It is also the main equation used in the compression of digital images and sound on the web.

The noted physicist Lord Kelvin wasn’t exaggerating when he wrote, in 1867: “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.”