Srinivasa Ramanujan: His Life, Legacy, and Mathematical Influence

This authoritative volume covers aspects of the life and enduring mathematical research of Srinivasa Ramanujan. Born in the late 19th century, Ramanujan had little formal training in pure mathematics. This iconic figure made extraordinary contributions to many facets of mathematical analysis and number theory. During his short life, Ramanujan published 37 papers and curated in notebooks more than 3900 identities which he recorded without proof. Nearly all of his claims that were new have now been proven correct. He stated numerous results that were both original and highly unconventional. Many of these identities have led to major achievements in a wide range of areas of mathematics and theoretical physics. The eight editors of this Handbook have assembled articles on many aspects of Ramanujan’s life and mathematical legacy with a focus on the evolution of his discoveries into many important sub-disciplines of current mathematical research. Included are 234 articles supplied by 88 authors. The book will be of interest to students, teachers, researchers and anyone who is intrigued by the legacy of one of the most striking figures in the history of mathematics.

KRISHNASWAMI ALLADI is professor of mathematics at the University of Florida where he was department chairman during 1998–2008. He received his PhD from the University of California, Los Angeles, in 1978. His research covers many areas of number theory such as analytic number theory, diophantine approximations, sieve methods, probabilistic number theory, and the theory of partitions and q-hypergeometric series. He is the Founder and Editor-in-Chief of The Ramanujan Journal (Springer), Founder and Editor of the book series Developments in Mathematics (Springer) and Chair of the SASTRA Ramanujan Prize Committee. He was an Associate Editor of the Notices of the American Mathematical Society. In 2012 he was inducted as an Inaugural Fellow of the American Mathematical Society for his distinguished contributions. In recognition of his research accomplishments and service to the profession, he was awarded an Honorary Doctorate (Honoris Causa) by SASTRA University in September 2022.GEORGE ANDREWS received his PhD from the University of Pennsylvania in 1964. He was Hans Rademacher’s last student. He is the Atherton Professor of Mathematics at the Pennsylvania State University. He is a member of the National Academy of Sciences (USA), a fellow of the American Academy of Arts and Sciences, a fellow of the American Mathematical Society and a fellow of the Society of Industrial and Applied Mathematics. He holds honorary doctorates from the University of Parma (Italy), the University of Florida, the University of Waterloo (Canada), SASTRA University (India), and the University of Illinois. He was awarded an honorary professorship at Nankai University (China). He was a Guggenheim Fellow in 1983. In 2022, the Institute of Combinatorics and its Applications presented him with the Euler Medal. He was President of the American Mathematical Society from 2009–2011. In 1976, while visiting the Wren Library of Trinity College, Cambridge, he had the good fortune to find the manuscript now called Ramanujan’s Lost Notebook. He and Bruce Berndt collaborated on a five volume explication of the unproven identities in this masterpiece.BRUCE BERNDT received an A.B. degree in 1961 from Albion College, and a PhD in 1966 at the University of Wisconsin, where his primary mentors were Rod Smart (thesis advisor), Marvin Knopp, and Richard Askey. He held a one-year postdoctoral position at the University of Glasgow, where his mentor was Robert Rankin. In 1967, Berndt joined the faculty at the University of Illinois, where he taught for 52 years before retiring in 2019. While at Illinois, he served as the thesis advisor for 37 students; he also mentored about ten postdocs. Since 1974, Berndt has devoted the bulk of his research to explicating and proving claims from Ramanujan’s notebooks and his lost notebook. He published five books on Ramanujan’s Notebooks (Springer), for which he received the Steele Prize for Mathematical Exposition from the American Mathematical Society. Furthermo