All of your descriptions are quite reductivist. Claiming that a computer doesn't do math has a lot in common with the claim that a hammer doesn't drive a nail.

All of your descriptions are quite reductivist. Claiming that a computer doesn't do math has a lot in common with the claim that a hammer doesn't drive a nail. While it is true that a standard hammer requires the aid of a human to apply swing force, aim the head, etc it is equally true that a bare-handed human also does not drive a nail. Plus, it's relatively straightforward and inexpensive using contemporary tech to build a roomba-like machine that wanders about on any flat surface cuing up and driving nails of its own accord with no human intervention. If computers do not add numbers, then neither do people. It's not like you can do an addition-style turing test with a human in one room and a computer in another with a judge partitioned off of both of them, feed them each an addition problem and leave the judge in any position where they can determine which result is "really a sum" and which one is only pretending to be. Yet if you reduce far enough to claim that humans aren't "really" adding numbers either, then you are left to justify what it would even mean for numbers to "really" get added together.