In 1966, Almgren showed that any immersed minimal surface in $S^3$ of genus 0 is totally geodesic, hence congruent to the equator. In 1970, Blaine Lawson constructed many examples of minimal surfaces in $S^3$ of higher genus; he also constructed numerous examples of immersed minimal tori. Motivated by these results, Lawson conjectured that any embedded minimal surface in $S^3$ of genus 1 must be congruent to the Clifford torus. In this lecture, I will describe a proof of Lawson's conjecture. The proof involves an application of the maximum principle to a function that depends on a pair of points on the surface.