[mafribe]

You can find descriptions of the FFT algorithm's history in [1, 2]. Both are available for free only for subscribers, sorry.

[1] http://www.springerlink.com/content/j30x8k122v828w87

[2] http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1162...

[te_platt]

Or here for no fee.

http://www.cis.rit.edu/class/simg716/Gauss_History_FFT.pdf

As a Gauss fanboy let me just say wow. Especially note that from 1828 to 1965 there a various versions of the FFT presented for special cases but Gauss had the complete version in 1805.