Mark Chu-Carroll, on how to tell if someone defining division-by-zero is a competent mathematician,
One good way of recognizing a crank is by looking at what they do with their new division-by-zero defining system. A serious mathematician starts working out what affect their definition has on the basic axioms, and what still works. A crank defines division by zero, and then proceeds to continue working as if they haven’t broken anything.
There are parallels in most every profession.