Abstract: Two of Wolfgang Haken's important achievements in mathematics were (1) the construction of an algorithm to decide whether a tangled loop is truly knotted or not, and (2) his landmark proof with Kenneth Appel that four colors suffice to color the regions of any map. Today, there are many new ways to settle the first of these questions, but the Appel-Haken proof remains the only successful approach to the second problem. This talk will examine a way in which both of these problems can be brought together, still involving "colorings", but also some elementary group theory and the Yang-Mills equations from mathematical physics.