In 1811, Joseph Fourier, the 43-year-old prefect of the French
district of Isere, entered a competition in heat research
sponsored by the French Academy of Sciences. The paper he
submitted described a novel analytical technique that we today
call the Fourier transform, and it won the competition; but the
prize jury declined to publish it, criticizing the sloppiness of
Fourier's reasoning. According to Jean-Pierre Kahane, a French
mathematician and current member of the academy, as late as the
early 1970s, Fourier's name still didn't turn up in the major
French encyclopedia the Encyclopdia Universalis. Now, however,
his name is everywhere. The Fourier transform is a way to
decompose a signal into its constituent frequencies, and
versions of it are used to generate and filter cell-phone and
Wi-Fi transmissions, to compress audio, image, and video files
so that they take up less bandwidth, and to solve differential
equations, among other things. It's so ubiquitous that "you
don't really study the Fourier transfo