What theorems are more “inevitable”
Meaning that an intelligent species in the Andromeda galaxy that maybe has 17 tentacles and reduce reproduces by emitting spores or whatever would nevertheless almost certainly stumble across?
For example if a species starts thinking about numbers at all it seems almost impossible to not figure out what a prime number is and develop something like the fundamental theorem of arithmetic. And if they keep thinking about it seems really likely they’d discover something like Fermat’s little theorem, for example.
Another example are the limits that Church and Turing discovered about computation. If an intelligent species finds ways to automate algorithms, it’s hard not to run into the fact that they can’t make a general purpose algorithm to tell if another algorithm will halt, though they might state it in a way that would be unrecognizable to us.
Whereas, it don’t seem at all inevitable to me that an intelligent species would develop anything like what we call set theory. It seems like they might answer the sorts of questions set theory answers in a way we wouldn’t think of. But maybe I’m wrong.
What do you think?