Because pure math is the purest form of logic, there is little to argue about other than perhaps axioms. And everything from those axioms that follows is true. Therefore, it lends itself to discussion much more easily than physics.
If I were to ask: >find the oscillatory motion of a set of magnetic spheres suspended on a string with a sinusoidal magnetic field.
This question is not just hard, but it is extremely badly posed. Can we take approximations? What model do we use? Does relativity come into play? Does QM come into play? Can we assume point particles? Friction? Is the string taut? Is the string perfect?
You would most likely have to approximate a solution to get anything, and it will be an imperfect answer.
While if I asked:>show that there exists an element of prime order p if p divides the order of the group
I immediately understand the assumptions and the conclusion, even if they're vague. No approximations will come here, and the answer will be perfect.