Wave Theory and Compressed Sensing: Applied Mathematics to Watch Netflix.

In 1619, mathematician Henry Savile, a patron of Oxford University, interviewed fellow scholar Edmund Gunter as a candidate for the new chair of geometry. Gunter arrived with his astronomical quadrant and compass in hand and began showing Savile how he could calculate the position of the stars or the distance between churches. Savile dismissed him with a stinging rebuke, asserting that this was not geometry but a “mere showing of tricks.” It was once common for mathematicians themselves to disregard the practical applications of their subject. But although mathematics has always found uses, nowadays it is the cornerstone of our digital age; even something as everyday as, for example, watching a streamed movie from our armchair can be derived from abstruse mathematical theories.

In Spain, the Princess of Asturias Foundation has awarded its Scientific and Technical Research Prize in 2020 to four mathematicians: Yves Meyer, Ingrid Daubechies, Terence Tao and Emmanuel Candès, for their “immeasurable and ground-breaking contributions to modern theories and techniques of mathematical data and signal processing.” According to the jury’s decision, the contributions of the award-winners have been key in the development of various digital technologies, especially from two related fields: the theory of wavelets and the techniques of compressed sensing and matrix completion.

Wavelets were developed as a mathematical instrument in the 1970s by Jean Morlet and Alex Grossmann. Any signal, like an image, can be represented by a complex curve with sharp rises and falls. That signal can be broken down into a set of simpler, brief oscillations, which are born and die at specific frequencies. Thus, these wavelets allow a representation of the signal that permits the original information to be recovered more accurately than another classical mathematical instrument called a Fourier transform. From the 1980s onwards, the work of Belgian physicist and mathematician Daubechies —whose doctoral thesis was co-directed by Grossmann— and Meyer, from France, pioneered the development of wavelets of various shapes and sizes.