Everyone assumes aliens will know higher math. So much so that some people think encoding the orders of the first 26 sporadic groups would be obvious. (IDK why this is better than a list of primes)
But would it, though?
We name the groups by their orders, and think it's neat that exactly 26 are special in this way, like the 5 platonic solids.
But couldn't you do a lot with math and never really focus on these facts? It's not free from culture. math has a culture.
I'm just gonna come out and say it: people think that using math to talk to aliens makes sense because they find math alien.
It's science sauce all over again. There is some universality. But it goes back to this idealization of mathematics-- this notion that it could only possibly be one way-- which is only true within contexts, and there are vast regions of math that we ignore because they are hard, or boring.
I would be exciting to encounter minds with other preferences and ares of focus.
Or maybe because math is universal, where dang few other things are.
