Undecidable problems have arisen in nearly every major branch of mathematics. This lecture will present a sampling of these and will discuss a few problems whose undecidability status is not yet known, including one about chess.
Also, more details on these topics are contained in the following survey articles written by Bjorn Poonen:
http://math.mit.edu/~poonen/papers/h10_notices.pdf
http://math.mit.edu/~poonen/papers/sampler.pdf