A professor once told me, for example, that the act of counting is widely regarded as a first sign of mathematical intelligence. Is it though?, can the act of counting (or performing simple arithmetic operations such as division or multiplication) be thought of as a sign of mathematical intelligence among a group of species?
Can it be? Of course! Counting falls under the sphere of skills and knowledge that we typically call "mathematics". A number of animals have rudimentary skills of this sort (even pigeons; this is at least estimation-of-number if not counting-one-two-three, which if accurate falls under mathematics (cardinality of small sets)). You can even implement it with biochemistry (hence plants); you might not want it call that "intelligence" though just because it's not implemented with neurons but with cellular processes.
Do we want to use the term mathematical intelligence this way? That's a more complex and subjective question. If you're interested in highly reflective and axomatized mathematics (e.g. ZFC), probably not. In that case you probably don't want to call it mathematical intelligence when people count, add, etc., either; abstract axomatic mathematics is rather different, in terms of the type of thinking required, than formulaic skills like counting or long division.
Counting is probably the most basic mathematical operation; and need not involve arithmetic; but probably should involve order.
One should be careful in distinguishing this from recognition of similarity & differance.
After all, a hawk can distinguish a rabbit from a pigeon - they are different, and recognise that one pigeon is not much different from another.
Likewise, it may recognise that two pigeons and similar to another two pigeons, and is different from six pigeons.
But it isn't counting until it can place them in order - and one can presume that is so, if the hawk recognises that six pigeons is more than two pigeons.
I can't resist adding, though it is irrelevant to the intent of the question, that counting doesn't stop there, after the invention of set theory, Cantor showed that you can count infinite sets, and place them too in order. So even a basic idea like counting can be revolutionised after the many millenia since it was first invented.