Ramanujan was one of the most remarkable and prolific mathematicians who ever lived, a self-taught prodigy who grew up in modest circumstances in south India during the time of the British Raj, rediscovering the previous 150 years’ worth of number theory while also uncovering over 3000 theorems and identities of his own. “Discovered,” in a sense, by the far more famous English mathematician G.H. Hardy, Ramanujan moved to England for about five years, where his work finally received a wider audience, but where he also contracted an unknown illness that eventually killed him at age 38.
Robert Kanigel’s biography The Man Who Knew Infinity: A Life of the Genius Ramanujan tells two main stories – that of Ramanujan himself, and a partial biography of Hardy, whose professional life was thoroughly altered by his time working with Ramanujan and to whom we owe most of the credit for what we know of Ramanujan’s life and work today. It’s a very strong, even-handed biography of Ramanujan, sympathetic without becoming patronizing, but was extremely light on its discussion of the math itself, with just a few cursory discussions of some of his findings that still bear his name today.
Born in southern India in what is now the state of Tamil Nadu, near the city of Madras (now known as Chennai), Ramanujan was a member of the Brahmin caste, the highest social stratum in the caste system, but was born into a poor family and received only a basic education. His mother was domineering and remained deeply involved in his life even into his adulthood and arranged (by her) marriage, only, according to Kanigel, supporting her son’s obsession with mathematics when it appeared it would at least bring him fame – and bring her fortune. Ramanujan failed out of university twice because he couldn’t be bothered with any coursework other than mathematics, but in that subject he was light-years ahead of his professors, filling notebooks with conjectures and equations, most of which he knew intuitively to be true, but couldn’t have published – even if he’d had access to such outlets – because he didn’t need to or understand how to develop the proofs.
In 1912 and 1913, Ramanujan, at the encouragement of some of the few Indian nationals in a position to advise him, sent letters with copies of some of his work to three English mathematicians, only one of whom responded: G.H. Hardy, at the time a professor of maths at Trinity University at Cambridge. Hardy was a purist, a mathematician who studied number theory (the study of the behavior and properties of the integers, with a special emphasis on prime numbers) for its own sake and overtly disdained any branch of “applied” mathematics – that is, math that had a practical purpose, such as the math required in physics or engineering. Hardy was open-minded enough upon seeing Ramanujan’s letter that he overcame his skepticism about an uneducated Indian clerk coming up with mathematical insights that took Western experts over a century to develop and wrote back, asking to see more of Ramanujan’s work. (There’s some irony in Hardy’s hesitation and the other mathematicians’ rejections of Ramanujan, as number theory has its own tradition in India dating back over 1500 years.) The subsequent correspondence led to an invitation for Ramanujan to come spend two years with Hardy at Cambridge, two years that turned into five before ill health sent Ramanujan back home to south India, where he died shortly thereafter.
Kanigel’s presentation of the life of Ramanujan leans toward the personal rather than the professional side, focusing extensively on his upbringing, cultural opposition to much of what he did and wanted to do with his life, and on the non-professional side of his life in England. The emotional cost to Ramanujan of traveling to a foreign country where he’d face outright prejudice but also would struggle with differences in language, weather, and, most importantly for Ramanujan, food. The devoutly spiritual and nominally Hindu mathematician was a strict vegetarian, but had great difficulty adapting his diet to the abysmal food of World War I-era England, where to cook something implied cooking it to death, where all flavor and texture was safely removed from the item to be consumed. Hardy was Ramanujan’s mentor in maths, but not in life, as Hardy does not (in Kanigel’s telling) have any close emotional ties to anyone but his sister once their parents had passed away, and with Ramanujan’s wife in India for the entire time he was in England, Ramanujan lacked for friends and for anyone who could help him look after himself. Kanigel reports on the speculation that malnutrition contributed to Ramanujan’s illness and decline, but his book was published before the 1994 report that he died of an amoebic infection in his liver common in India at the time he lived there.
I also found Kanigel’s mini-biography of Hardy, essential to the story of Ramanujan, fascinating. Hardy’s a great figure for biographers, appearing in one of my favorite books about math, Prime Obsession, for his role in attacking the unsolved Riemann Hypothesis. (Ramanujan’s pre-Hardy work was remarkable, but he did make some mistakes, one of which involved Riemann’s zeta function; Ramanujan assumed the function had only real zeroes, not complex ones, but its complex zeroes lie at the heart of the Hypothesis.) He’s also ripe for caricature, something Kanigel avoids entirely. A lifelong bachelor, Hardy was obsessed by numbers, but also had an equal passion for cricket (and, after a stint at Princeton, baseball). He was a strict atheist who once set out a goal for himself to craft a disproof of the existence of God convincing enough to convert most of the general public, and a pacifist who fought persecution of Trinity colleagues who spoke out against British involvement in World War I. Hardy viewed Ramanujan with great pride, almost as a father would view a son, someone with limitless natural talent whom Hardy could mold into one of the greatest mathematicians the world has ever known, and he was diligent about assigning credit to his protégé whenever possible. He brought Ramanujan to the world, yet it also seems that Ramanujan brought much more out of Hardy than we’d otherwise have had.
My lone criticism of The Man Who Knew Infinity is its scant treatment of the math in question. The reader of a book like this probably has an appetite for math, and the author has merely to explain the theorems or identities under discussion, not to teach them or prove them. Kanigel does very little of any of this, only dipping occasionally into discussions of continued fractions and some of Ramanujan’s explorations of the nature and frequency of prime numbers. Kanigel appears to have skipped the mathier material in favor of asking open-ended questions about the source of Ramanujan’s inspiration and culpability for his illness and death.
Kanigel’s epilogue discusses the final years of Hardy’s life, but it is his discussions with Ramanujan’s widow, Janakiammal, that punctuate the book’s last handful of pages. Still alive at the time of the book’s publication in 1991, Janakiammal spent a long part of her life as a widow in obscurity and poverty before she was rediscovered several decades after her husband’s passing, eventually reaping rewards, both honorary and monetary, before her death in 1994 at age 95. Her few comments evoke a great bitterness at how her husband’s legacy was underappreciated and how her own life was adversely affected by that and by quarrels with Ramanujan’s family.
Next up: The Supper of the Lamb: A Culinary Reflection (Modern Library Paperbacks) by Robert Farrar Capon, a chef and Episcopalian priest. The 1967 book is a classic of the food-writing genre and was reissued in 2002 as part of the Modern Library Food series, edited by Ruth Reichl.