[bobthechef]

> the Turing machine model is designed to be a mechanistic model of what a mathematician does (in rote day-to-day tasks at least)

Or more accurately, what human computers did in those days (i.e. the rooms full of people algorithmically working out numerical calculations for e.g. physicists or whatever without understanding what they were doing beyond the mechanical steps they were taking). In other words a formalization of so-called effective methods.