> I'm unable to think algebraically very effectively but can 
> think visually (for example I didn't understand the fourier transform 
> algebraically (the double integral formulation), but understand it 
> perfectly well as an infinite set of infinite integrals of the products 
> of a sine wave with an arbitrary waveform (itself composed of sine 
> waves)).

As a visual person myself, Fourier transform did only really click with 
me intuitively when I saw it related to epicycles. See Mathologer's 
video here:

https://www.youtube.com/watch?v=qS4H6PEcCCA


Stef