Interesting point. Before the theory of gravity was formulated, planets were still behaving the same way. Then when Newton said F = Gm1m2/r^2, and we came up with equations to define exactly how they move, does that mean planets started doing arithmetic? Did they start solving differential equations that describe their motion?
I think ultimately it means that "doing arithmetic / doing math" are defined by the observer rather than the doer. True for any abstraction - the brain does exactly what it does, then to ask if its doing "abstracted task X" is not really meaningful from the perspective of brain, the abstraction in the first place is a mental construct we create.
The computer doesn't do arithmetics either. Signals just pass through wires and gates according to their nature (or as we might say: while obeying the laws of physics).
I think ultimately it means that "doing arithmetic / doing math" are defined by the observer rather than the doer. True for any abstraction - the brain does exactly what it does, then to ask if its doing "abstracted task X" is not really meaningful from the perspective of brain, the abstraction in the first place is a mental construct we create.