Crows are fascinating because they are collectively very active and vocal. It is often unclear what they are doing but there seems to be a lot of communication involved. In particular, they have many different calls.
An important feature of their calls is that they often involve a specific number of unit calls, which I call caws. For example there is a three caw call that may be repeated a number of times. There is also a four caw call that includes a slight pause between the second and third caws, sort of caw-caw caw-caw.
In order to make these calls the crows have to count the caws. This is not counting in the sense of naming the numbers. It is not like saying or thinking one-two-three, etc. Rather it is counting in the sense of knowing how many caws have been made. The hearers must also count the caws if communication is to occur.
This is really a case of the distinction between verbal thinking and non-verbal thinking, which I discuss early on in this blog. Because so much human thinking is verbal, it can be hard to see what non-verbal thinking looks like. But I can see that there are, say, three horses in view without going through the numbers one, two, three mentally.
As with other cases we have discussed, it is useful to think about building robots that do what the animals do. In order for robotic crows to make or respond to these various calls, there would have to be some sort of counting mechanism. In short, crows can count.