One thing we'd share with any alien species is our perception of the universe, and stars and galaxies are eminently countable, so the development of numbers seems inevitable.

There is the example of the sheepherder who cannot count but ensures all sheep are accounted for by with the bag of pebbles: as the sheep leave the enclosure in the morning, a pebble is placed in the (initially empty) bag; as the sheep return, a pebble is removed for each sheep, and if none are missing, the bag ends up empty. This quickly fails for many issues, such as two sheepherders wishing to discuss the relative size of their flocks, however.

Regardless, an alien species might have started from entirely different premises then numbers. A lot of the images in this article are graphs, node-and-edge constructions, but it's a bit odd that graphical algorithms are a relatively new feature of human mathematics - Dijkstra's algorithm was only described in 1956.

https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm

What if the ancient Greeks had instead started there, what would mathematics look like today? An alien species might have done so, leading to system in which number theory would be of much less importance than graph theory.