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Ramanujan's Place in the World of Mathematics: Essays Providing a Comparative Study
Publisher: Springer (2013)
Details: 177 pages, Hardcover
Topics: History of Mathematics, Number Theory
MAA Review[Reviewed by Michael Berg, on 01/30/2013]
This is a difficult book to review. Not because it’s hard to describe, appraise, and evaluate, but because it’s hard not to get lost in it, meaning that the review would be much delayed, if not indefinitely so. George Andrews, who wrote a Foreword to the book under review, aptly notes that “[t]his is a great book to ‘dip into’”, and indeed, it is in fact a great book to go swimming in. Alladi has put together a sweeping compendium of essays on Ramanujan (or things to do with Ramanujan in some way — consider, e.g., chapter 16, “Ramanujan and π”), some taken from his publications over the years in India’s The Hindu newspaper, others being book reviews, yet others being essays specifically written for the present book, and there are other things besides, but all pertaining to the redoubtable figure of Ramanujan. It is a wonderful book to browse through, and before you know it, you’ll have read it all.
Qua specifics, the book is split into four parts, respectively, “Ramanujan and other mathematical luminaries,” “Some aspects of Ramanujan’s mathematics,” “Book reviews,” and “Preserving Ramanujan’s legacy.” By way of samples, Part I features, besides the players who come to mind first, like Euler, Hardy, Littlewood, Rogers, and MacMahon, such scholars as Erdös and Rankin — and this is of course no surprise upon a moment’s reflection. (By the way, the picture of Rankin on p.95 bespeaks an austerity that might be at odds with his manifest sense of humor: see, for example, the article, “The life and work of R. A. Rankin (1915-2001),” by Berndt, Kohnen, and Ono, found on-line at http://www.math.wisc.edu/~ono/reprints/076.pdf.) These biographical essays contain a good deal of fascinating material about the subjects themselves, even apart from their relation to Ramanujan and his work — and how could it be otherwise, given for instance that we have Hardy and Erdös in the mix?: a bonanza for anecdotes!
To continue with the samples, Part II contains the article I would certainly turn to first, if only because of the well-known story about Ramanujan triumphing over Hardy’s initial skepticism vis à vis their now famous formula: “Ramanujan and partitions” (cf. pp. 112–113: “The Hardy-Ramanujan formula,” followed by “Ramanujan congruences”!).
Part III includes Alladi’s review of Kanigel’s The Man Who Knew Infinity: A Life of the Genius Ramanujan — he not only likes and recommends the book, but adds the following fascinating comment: “Ramanujan, who was a gregarious and orthodox Brahmin, found himself in an awkward position amidst educated Englishmen who were socially so aloof. [Kanigel’s] book is a dual biography — of Ramanujan and Hardy. And the author succeeds wonderfully in showing the gulf that separated the two. What bridged the gap was mathematics, but here too there was a considerable difference in the way they thought. Ramanujan was a genius who conjectured and made giant leaps of imagination … Hardy put emphasis on rigor and proceeded by logical step-by-step reasoning. Kanigel’s description of Hardy’s British upbringing is superb, but he spends too much time on Hardy’s lack of interest in women.” Fair enough. (By the way, Kanigel’s book is an MAA BLL book.)
Finally, Part IV contains an abridged version of a Focus article (May, 2005), “A pilgrimage to Ramanujan’s hometown,” the pilgrims including, besides Alladi himself, George Andrews and Noam Elkies. This article additionally contains a great deal of fascinating material on Hinduism. The last essay in this section, and in the book, is titled “Ramanujan’s growing influence” — hear, hear!
All in all, this book is clearly entirely irresistible. Get a copy for yourself. Get copies as gifts for friends. You can’t miss.
Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.