I am currently studying information systems engineering (BA) and I'm thinking of getting a master degree in Artificial Intelligence. What are the main important skills do I need to succeed in this field, and what kind of math does it require?
The most important skill you need is self-discipline.
Regarding the mathematical prerequisites, you will need to study statistics, probability theory, calculus, and linear algebra, given that e.g. most machine learning algorithms are highly based on concepts from these areas.
Regarding the programming prerequisites, Python and R are usually a good choice, given the relevant libraries that are available.
You might also need to learn frameworks like Hadoop, in case you want to work with big data.
"artificial intelligence" is now a mature field and there are many subfields in it. there are entire theories erected around each subfield of artificial intelligence. a simple analogy would like "what are the skills needed for succeeding in mathematics/physics?". the answer really depends on what branch you want to delve into.
if you are planning to go into more application specific side of artificial intelligence (machine learning/ deep learning) then you must be thorough with linear algebra . since most of machine learning algorithms can be boiled down to simple tricks in linear algebra. learning about optimization will help a lot because you will encounter many algorithms involving convex/nonconvex optimization methods.
Also statistics and probability are must for any field in artificial algorithms.
That said, at core artificial intelligence deals with machines that think. So it would be better if you are through with formal logic , automata and complexity theory .