I don't think I am confusing anything, you are reacting exactly as I would expect from someone who does not get the point I'm making: we don't have to necessarily program with steps of instructions. If we have a good solver for our language, we can very efficiently execute definitions like my example. I agree that this presents the challenge of efficiently executing such high-level definitions, but this is irrelevant to my point.
> Mathematics sits at a level of abstraction unsuited to physical hardware.
Precisely what I am talking about. Mathematics sits at a level of abstraction convenient for humans not machines.
Have you ever programmed in Prolog? I strongly suggest you try it to get a feeling of why programs are not inherently lists of instructions and how computation can be viewed as deduction.