I actually like the machines/mathematics dichotomy in CS, though it often seems to come up as a one-versus-the-other holy war. I guess I'm actually okay with both of these statements, and am glad people are pushing both:

1. Computation is fundamentally a machine doing things; although of course these machines' operation is also analyzable via mathematics; and

2. Computation is fundamentally a mathematical phenomenon; although of course it is also implementable on machines.

I guess there's a philosophical debate about which is more fundamental (does mathematics 'exist' ontologically?), but pragmatically I'm okay with considering them both fundamental approaches to CS.