What kind of PhD proposals should I read?
Ask them the purpose of not providing a mathematics proposal. A hard science looking at a similar science might get tunnel vision, but I doubt a mathematics PhD would face the same problem seeing as they're less experimental method than other fields.

PhD proposals, unlike theses, also seem to be much more readily accessible online. A quick search for theoretical physics phd proposal on Google, even without Scholar, yields a decent amount of samples that provide a significant amount of differing examples in sufficiently different subjects from math that the content can be differentiated from the style.