On the other extreme, what distinguishes CS from math?
Doesn't that support the argument even more? CS and math share a lot more then CS and AI, yet CS and math are different disciplines.
Neural nets came from biology and rely on math.
The art of application
Of course, computing is closer to pure math than applied maths. Computing is applied pure maths, perhaps.
The majority of what computer science practitioners do is general purpose coding, which doesn't have nearly as much to do with the underlying math.
Or, in other words, how proficient would an applied math person be at building a front end? And how many of their skills would they be able to leverage?
That's the overlap, or lack thereof.