Problem of the Week
Hilton Memorial Lecture
Louis Kauffman showed that the four-color theorem is equivalent to the existence of solutions of certain equations. These equations involve the cross products of the standard three unit vectors in Euclidean 3-space. We will outline Kauffman's argument and discuss how the equations are ``parametrized'' by elements of one of Thompson's finitely presented groups. An invitation will then be given to the audience to find a simple proof of the four-color theorem.