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This is a history question, so you need to know something about math history to answer it. There's a rumour that says that Carl Friedrich Gauss knew the FFT in 1805, but he thought it was useless, because the speedup wasn't very big for small numbers of N. And at that time there were no supercomputers, so you couldn't calculate large N's anyway.

But what's is the best evidence you can find that support this rumour?

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There is some information here: cis.rit.edu/class/simg716/Gauss_History_FFT.pdf –  Integral Apr 23 '13 at 20:39
    
Can you quote the part in which Gauss stated that FFT was useless, please? Thank you! –  user1095332 Apr 23 '13 at 20:47
    
Nice question. I did my senior project on the DFT and FFT to approximate the path of the asteroid Pallas as he once did. This discussion actually came up in my presentation, but no one knew if it was true or not. –  Suugaku Apr 23 '13 at 21:19
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This is a history question, so you need to know something about math history to answer it.

Oh yeah? The first Google hit I get for "Gauss fast Fourier transform" is this paper, which says that Gauss wrote down something that looks like the FFT in an unpublished paper that appears in his collected works.

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Can you quote the part in which Gauss stated that FFT was useless, please? Thank you! –  user1095332 Apr 23 '13 at 20:45
    
Nice find! I really love that table in the back with the different implementations of the equivalent to some FFT. My take is that the first practical FFT built for the computer was the Danielson-Lanczos implementation. –  Ron Gordon Apr 23 '13 at 20:45
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@user: I do not think Gauss said this. In fact he seems to say that it is quite useful. See the quote at the bottom of page 270. –  Qiaochu Yuan Apr 23 '13 at 20:50
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