  Several authors have conjectured that Conway's field of surreal numbers,
equipped with the exponential function of Kruskal and Gonshor, can be described
as a field of transseries and admits a compatible differential structure of
Hardy-type. In this paper we give a complete positive solution to both
problems. We also show that with this new differential structure, the surreal
numbers are Liouville closed, namely the derivation is surjective.
