I am just curious about this. Please don't include anything about programming.
Artificial intelligence requires extensive use of decision logic. The gateway to this type of logic is Turing machine analysis and recursive/primitive recursive functions. In other words, it really involves the mathematics of the relationship between computability and logic. Additionally, AI requires statistics (used for decision-making and testing probabilities associated with decision-making, i.e., hypothesis testing) and the mathematics required for engineering.
We have quite a lot of A.I. on university -- probably because I picked specialization called Artificial Intelligence and Software Engineering. Most of methods that were presented used a lot of optimization e.g. for learning neutral networks. Analysis and linear algebra also played crucial roles. We didn't use much beside that but professionals claim that language of A.I. is statistics but we haven't use it extensively.