In 2013, Martin Hairer made a breakthrough in solving the KPZ equation by an extension of the Cole–Hopf transformation and constructing approximations using Feynman diagrams. In 2014, he was awarded the Fields Medal for this work on the KPZ equation, along with rough paths theory and regularity structures. There were 6 different analytic self-similar solutions found for the (1+1) KPZ equation with different analytic noise terms.