[tom_mellior]

> Turing machines are arbitrary and rather unmathematical.

Thus proving the point that a field that studies them cannot be considered a branch of mathematics.

[antonvs]

That might be true if there were no more natural mathematical representations of computation. But as I've pointed out in another comment (https://news.ycombinator.com/item?id=27334163), there is such a representation - the lambda calculus.