As another physicist who used mathematica what you mean is that you were too lazy to think about what assumptions were made implicitly in the calculations you were performing and liked mathematica because it did them automagically for you.

This is shown no where better in the paper than when they try to calculate Integrate[Exp[-pt](Sinh[t])ˆ3, {t, 0, Infinity}]. In a good cas, such as maxima, you will get no result and a ton of errors. Which is what you should get without specifying what sort of variable p is, is it a matrix, polynomial, group of some sort? That it's implicitly assumed to be a real number that might turn out to be complex under some circumstances isn't a feature, it's a bug.