In fact, I'd say that the FFT has done more to change society then any other general-purpose computer-based algorythim. FFT made the digital transfer and storage of near-photo-quality images practical, through it's use with JPEG, thus brining porn to the internet, creating huge social issues (see, for example, today's (well, now yesterday's, technicaly) US supreme court rulling), as well, in no small part, fulling the growth of the internet. Also, mp3s, with their own social problems and growth, MPEG and other compressed video, and in general most lossy compression algorithms.

FFT has made taking real-life media into the digital world possible, and it's real-life media that creates much of the contriversy of the digital world, and contraversy moves both worlds forward.