Currently I am Bachelor student in Psychology. My plan is to do a Master in Artificial-intelligence. And then I wish to do research on the interface in Computer Science/Artificial-intelligence and Mathematics. Is is possible to do a Phd in the Computer Science/Artificial-intelligence - Mathematics interface?
You can certainly do a PhD in mathematics and apply it to AI. You should also look at CS PhDs in addition to mathematics ones, as the boundary between the fields is pretty nebulous and which department will have the faculty you wish to work with will vary by the university. You should in particular look for university with a strong program in Combinatorics, Algorithms, and Topology (especially if you want to go into object recognition/computer vision).