  A knot is said to be slice if it bounds a smooth disk in the 4-ball. For 50
years, it was unknown whether a certain 11 crossing knot, called the Conway
knot, was slice or not, and until recently, this was the only one of the
thousands of knots with fewer than 13 crossings whose slice-status remained a
mystery. We will describe Lisa Piccirillo's proof that the Conway knot is not
slice. The main idea of her proof is given in the title of this article.
