In the footsteps of Euler and MacMahon: combinatorics, the mathematics that counts

Abstract

This article is based on my presidential address, given at the BSHM Christmas meeting on 7 December 2013. It features the history of combinatorics, a much neglected area, with particular reference to the work of two mathematicians who have always interested me—Leonhard Euler and Major Percy MacMahon—and with further contributions by Arthur Cayley (on trees) and G H Hardy and S Ramanujan (on partitions).