Mathematics is founded in logic. You cannot use logic to prove logic. Instead, we start with some axioms and build from there using rules that we think we reaso

Mathematics is founded in logic. You cannot use logic to prove logic. Instead, we start with some axioms and build from there using rules that we think we reasonable and intuitive. I vaguely recall learning about a position in philosophy that holds that these axioms and rules come from the way the human mind is structured. If this is true then there is no reason to think that an alien mind would use the same axioms. For example, something that seems entirely fundamental to us might require a very complicated proof in the alien system. If the two systems are pragmatic and useful then they can produce conclusions that correspond to the physical world, and from there we can relate the two. However, a major plot point in the movie is that time does not exist and that there is no such thing as causality. In the world of Arrival, there is not a lot of reason to believe that mathematics, logic, and science are capable of bringing us to a true understanding of the universe. It wouldn't work to teach human mathematics to the aliens because human mathematics is weird and wrong.