"Alexander Polyakov, a now at Princeton University, caught a glimpse of the future of in 1981. A range of mysteries, from the wiggling of strings to the binding of s into s, demanded a new mathematical tool whose silhouette he could just make out. ... In his paper he sketched out a formula that roughly described how to calculate averages of a wildly chaotic type of surface, the “.” His work brought physicists into a new mathematical arena, one essential for unlocking the behavior of theoretical objects called strings and building a simplified model of quantum gravity. Years of toil would lead Polyakov to breakthrough solutions for other theories in physics, but he never fully understood the mathematics behind the Liouville field. Over the last seven years, however, a group of mathematicians has done what many researchers thought impossible. In a trilogy of landmark publications, they have recast Polyakov’s formula using fully rigorous mathematical language and proved that the Liouville field flawlessly models the phenomena Polyakov thought it would."