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Ramanujan's growing influence

By Krishnaswami Alladi

Srinivasa Ramanujan's influence seems only to increase and not diminish with time. In the early part of the twentieth century, Ramanujan was perceived as a mathematical phenomenon emerging from the East by the great stalwarts like G.H. Hardy and others at Cambridge University. Although they admired Ramanujan for his genius, Hardy and his contemporaries could not measure the full significance of Ramanujan's discoveries and the eventual impact this would have. Over the years, the magnitude and importance of Ramanujan's mathematics has been realised, and its impact in various branches of mathematics such as Number Theory, Combinatorics, Analysis, Modular Forms, Basic Hypergeometric Series, and Special Functions, is deep and everlasting. Indeed, Ramanujan's identities have made their presence in other subjects like physics and computer science.

Hardy nurtured Ramanujan, and lectured often on Ramanujan's work. Hardy's Twelve Lectures on Ramanujan's is a model of the mathematical exposition. These lectures, along with Ramanujan's Collected Papers, served as the principal source of inspiration and reference for many years for those who desired to understand the remarkable work of the Indian genius. In the last few decades, there have been several significant publications expanding on Ramanujan's work, and therefore have impacted a much wider community of research mathematicians. We owe a special debt of gratitude to the great Trinity of the World of Ramanujan — (i) to George Andrews for explaining the significance of many of Ramanujan's identities, especially in the context of partitions, and for discovering Ramanujan's "Lost Notebook" and helping us understand hundred's of deep identities contained therein including those on mock theta functions, (ii) to Bruce Berndt for editing Ramanujan's Notebooks in Five Volumes, and (iii) to Richard Askey for providing the broad picture of how Ramanujan's work is in the world of Special Functions. Thus the present-day researcher can easily enter the mansion of Ramanujan's theorems and make connections with current research.

The Ramanujan Centennial, celebrated in 1987, was an occasion when mathematicians around the world gathered to pay homage to the Indian genius. The centennial celebrations showed clearly how alive Ramanujan is in current mathematical research, and how much an inspiration he was to celebrated mathematicians like Atle Selberg. While attending the centennial, I was inspired to create something which would simultaneously be a tribute to Ramanujan and would connect Ramanujan to current research developments continuously. Thus I got the idea to launch The Ramanujan Journal — an international journal dedicated to all areas of mathematics influenced by Ramanujan. This desire of mine became a reality in 1997 after this idea received support from the international community of experts, some of whom serve on the Editorial Board with me.

In the last decade, Ramanujan has made an impact beyond mathematics, on society in general. Of course, throughout India, Ramanujan's remarkable story is well-known, and Ramanujan, a hero to every eager Indian student of mathematics. But with the publication of Robert Kanigel's book, The man who knew infinity, Ramanujan's story reached out to society around the world, and the importance of this impact cannot be underestimated. Subsequently, Bruce Berndt and Robert Rankin have published two wonderful books. The first one called Ramanujan — Letters and Commentary collects various letters written to, from, and about Ramanujan, and makes detailed commentaries on the letters. For instance, if a letter contains a mathematical statement, there is an explanation of the mathematics with appropriate references. If there is a statement about Ramanujan being elected Fellow of the Royal Society (FRS), then there is a discussion about the procedures and practices for such an election. The second book called Ramanujan - Essays and Surveys is a collection of excellent articles by various experts on Ramanujan's life and work. The book also contains articles about certain individuals who played a major role in Ramanujan's life. Thus both books will appeal not only to mathematicians, but to students and lay persons as well.

In what other ways will we see Ramanujan influence us in the future? Courses on Ramanujan's work are regularly ordered at various universities where there are groups of experts working on Ramanujan's manuscripts. In writing the Editorial for the rest issue of The Ramanujan Journal, I said, "The very mention of Ramanujan's name reminds us of the thrill of mathematical discovery."

Now with the appearance of these books that are now having an impact on society in general, it may not be an exaggeration to predict, that in the future, Ramanujan will be a topic or subject that undergraduate mathematics students worldwide may be studying regularly.

The latest big event in the world of Ramanujan is the recent acquisition of Ramanujan's home in Kumbakonam by SASTRA University. This private university that was founded recently, has grown by leaps and bounds. We owe special thanks to Prof. R. Sethuraman, Vice-Chancellor of SASTRA University, and his family, for taking steps to ensure that Ramanujan's home will be properly maintained. Since a university has purchased Ramanujan's home, we now have the active involvement by administrators, academicians, and students, in the preservation of Ramanujan's legacy for posterity.

(The author is with the Department of Mathematics, University of Florida, Gainesville)

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