Mathematicians (and computer scientists) view functions as maps, taking a given input to a prescribed output. The symbols are just placeholders, with no significance. This leads to notation such as T=f(x,y) to describe the temperature as a function of the rectangular coordinates x and y.
Physicists and other scientists view functions as physical quantities. T is the temperature here; it's a function of location, not of any arbitrary labels used to describe the location. This is the differential geometer's notion of a scalar field on a manifold (surface). Writing something like T=T(x,y) is merely a statement that, for the moment, one wishes to regard the temperature as depending on x and y, rather than a statement that T is some particular function.