Introduction

The quoted passages of Vivekananda, Klein, and St. Paul each point to a certain facet of Ramanujan’s work. First, on June 1–5, 1987, the centenary of Ramanujan’s birth was celebrated at the University of Illinois with a series of 28 expository lectures and several contributed papers that traced Ramanujan’s influence to many areas of current research; see the conference Proceedings edited by Andrews et al. [1]. Thus, Ramanujan’s mathematics continues to generate a vast amount of research in a variety of areas. Second, in the sequel, we shall see many instances where Ramanujan made profound contributions but for which he probably did not have rigorous proofs; for example, see Entry 10 of Chapter 13. Third, although St. Paul’s passage is eschatological in nature, it points to the great need to learn how Ramanujan reasoned and made his discoveries. Perhaps we can prove Ramanujan’s claims, but we may not know the well from which they sprung. These three aspects of Ramanujan’s work will frequently be made manifest in the pages that follow.