“A photograph, which used to be a pattern of pigment on a sheet of chemically coated paper, is not a string of numbers, each one representing the brightness and color of a pixel. An image captured on a 4-megapixel camera is a list of 4 million numbers-no small commitment of memory for the device shooting the picture. But these numbers are highly correlated with each other. If one pixel is bright green, the next one over likely to be as well. The actual information contained in the image is much less than 4 million numbers' worth-and it's precisely this fact that makes it possible to have compression, the critical mathematical technology that allows images, videos, music, and text to be stored in much smaller spaces than you'd think. The presence of correlation makes compression possible; actually doing it involves much more modern ideas, like the theory of wavelets developed in the 1970s and 80s by Jean Morlet, Stephane Mallat, Yves Meyer, Ingrid Daubechies, and others; and the rapidly developing area of compressed sensing, which started with a 2005 paper by Emmanuel Candes, Justin Romberg, and Terry Tao, and has quickly become its own active subfield of applied math.”