Considering this line:

" In 1973, Jacques Morgenstern proved that you couldn’t get a Fourier transform faster than ½ n log n if you required that complex coefficients used in the computation had bounded magnitude"

I highly doubt this is going to somehow inspire people to make faster algorithms than the mathematical bound...

I have no problem with pure mathematics, my training was in it; but it seems very possible to me that most people funding theoretical computer science (as opposed to pure maths) probably assume the work has a more realistic computational model backing it up.

Does the apply to representation of complex numbers, which is not uncountably infinite and represented by floats?