The Math Trick Behind MP3s, JPEGs, and Homer Simpson’s Face

Nine years ago, I was sitting in a college math physics course and my professor spelt out an idea that kind of blew my mind. I think it isn’t a stretch to say that this is one of the most widely applicable mathematical discoveries, with applications ranging from optics to quantum physics, radio astronomy, MP3 and JPEG compression, X-ray crystallography, voice recognition, and PET or MRI scans. This mathematical tool—named the Fourier transform, after 18th-century French physicist and mathematician Joseph Fourier—was even used by James Watson and Francis Crick to decode the double helix structure of DNA from the X-ray patterns produced by Rosalind Franklin. (Crick was an expert in Fourier transforms, and joked about writing a paper called, “Fourier Transforms for birdwatchers,” to explain the math to Watson, an avid birder.)

You probably use a descendant of Fourier’s idea every day, whether you’re playing an MP3, viewing an image on the web, asking Siri a question, or tuning in to a [pdf].)