@article {9999, title = {Surreal numbers, derivations and transseries}, journal = {Journal of the European Mathematical Society}, year = {In Press}, month = {2015/03}, pages = {46}, type = {preprint}, abstract = {Several authors have conjectured that Conway{\textquoteright}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.}, url = {http://arxiv.org/abs/1503.00315}, author = {Berarducci, Alessandro and Mantova, Vincenzo} }