Mathematicians have a long history of being concerned about computational efficiency. Two examples that come to mind are FFT and Euclidean algorithm. I'm certain there are many others.
Before electronic computing machines pretty much took over, "computer" was a job title/description. The exciting part of Turing's On computable numbers, with an application to the Entscheidungsproblem was his abstraction of what computers actually do to a simple machine. Large chunks of what's currently being explored is in relation to problems that we may or may not be able to solve using machines we're not even sure can, in principle, be built, and on that level "computer science" assumes spherical cows in a frictionless vacuum. It's nice that we have relatively compact, fast and nearly ubiquitous machines with which to apply some of what's been discovered along the way, but fundamentally "computer science" is the mathematics of process.