An Argument for the Uncomputability of Infinitary Mathematical Expertise

To a majority of the people involved in the study of expertise from a computational perspective, `expertise' tends to refer to domains such as medical diagnosis, aircraft piloting, auditing, etc. The reasoning in domains like these appears to be ready-made for computational packaging. But what if we try to cast a broader, braver net in an attempt to catch varieties of expertise out there in the real world which don't, at least at rst glance, look like they can be rendered in computational terms? In particular, what about mathematical expertise? In this chapter I focus on elementary \in nitary" expertise in the domain of mathematical logic. I argue that at least some of this expertise is indeed uncomputable. I end by brie y discussing the implications of this argument for the practice of AI and expert systems.