Submission date: 11 August 2016

Abstract:

The present article surveys surreal numbers with an informal approach, from their very first definition to their structure of universal real closed analytic and exponential field. Then we proceed to give an overview of the recent achievements on equipping them with a derivation, which is done by proving that surreal numbers can be seen as transseries and by finding the `simplest' structure of H-field, the abstract version of a Hardy field. All the latter notions and their context are also addressed, as well as the universality of the resulting structure for surreal numbers.

Mathematics Subject Classification: 03C64, 03E10, 12J10, 12J15, 12L12, 13J05, 13N15, 26A12

Keywords and phrases:

Full text arXiv 1608.03413: pdf, ps.