Not to detract from Gauss' remarkable discovery but there is no relation between Gauss' FFT algorithm and the continuous Fourier transform that Fourier discovered. It is also worth mentioning that credit for the discrete Fourier transform goes to Vandermode and pre-dates Gauss' FFT algorithm by about 30 years.
I didn't know about Vandermonde, its always nice to learn something.
I'm no mathematician, and my understanding of the subject is limited. How is the discrete Fourier transform unrelated to its continuous counterpart? Their definitions are extremely similar...
From a semantic point of view, it is nice that all these transform bear the same name, but historically, it is a bit unfair to attribute Fourier analysis to Fourier, who didn't discover it (even though he greatly developed the subject).
I know there's an eponymous law that describes this phenomenon, and it is of course not named after its inventor, but I can't remember its name.
The discrete and continuous transforms are closely related. DFTs and their properties were known before Gauss and his 1805 paper is about computing them quickly. I wanted to emphasize the difference between the problem of finding ways to quickly compute DFTs and Fourier's discovery of the continuous transform.
