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
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)
was on my wish list for a long time because it seemed like a perfect blend of the academic and applied branches of mathematics, as the irrational number φ appears in numerous places in nature and (I thought) art. Unfortunately, Livio’s book spends more time talking about where φ is not than about where it is, making this more of a book of mythbusting than of math.
, the book that first established him as one of the best writers on food and cooking today. 
is the one non-fiction book in this bunch, a history-of-math tome that incorporates a fair amount of philosophy, physics, and religion all in a book that’s under 200 pages and incredibly readable for anyone who’s at least taken high school math. The subject is the number zero, long scorned by philosophers, theologians, and even some mathematicians who resisted the idea of nothing or the void, yet which turned out to be critical in a long list of major scientific advances, including calculus and quantum mechanics. I generally prefer narrative non-fiction, but Zero moves as easily as a math-oriented book can get without that central thread. 
is one of three major Hammett short-story collections in print (along with The Continental Op and the uneven The Big Knockover), and my favorite for its range of subjects and characters without feeling as pulpy as some of his most commercial stories. The twenty stories are all detective stories of one sort or another starring several different Hammett detectives, including early iterations of Sam Spade and the character who eventually became the Thin Man, as well as a western crime story that might be my favorite short piece by Hammett, “The Man Who Killed Dan Odams.”
for several years, usually any time I mention reading another book that deals with the Vietnam War and/or its aftermath. The book, a set of interconnected stories that feels like an novel despite the lack of a central plot, is based heavily on O’Brien’s own experiences in that conflict, especially around death – of platoon mates, of Viet Cong soldiers, of Vietnamese civilians, and of a childhood crush of O’Brien’s who died at age 9 of a brain tumor. The writing is remarkable, more than the stories themselves, which seemed to cover familiar ground in the genre, as well as O’Brien’s ability to weave all of these disconnected stories into one tapestry around that central theme of death and the pointlessness of war. The final story, where he ties much of it together by revisiting one of the first deaths he discussed in the book, is incredibly affecting on two levels as a result of everything that’s come before.
, a top-ten novel for me that hit on every level. Dance is just too introspective, without enough of Murakami’s sort of magical realism (and little foundation for what magical realism it does contain) and no connection between the reader and the main character.
(filmed as The American) and listening to Jonah Lehrer’s 
. The Booth book is on sale through that link for $5.60.
trilogy on sale for $49.99 (almost 60% off). Not sure how long that sale will last.
(known as Alex’s Adventures in Numberland in the U.K.) is a little lighter than the last math book I read, focusing instead of numerical oddities and paradoxes as well as the history of basic math. He keeps the tone light by revolving each chapter around one or more interesting personalities, such as the English dentist who used ϕ (the golden ratio) to design more attractive dentures or the various people involved in the invention and rise of sudoku.
, written by the very funny folks behind the 
(still on sale for $6.38 as a bargain book on amazon), Donal O’Shea, Dean of Faculty at Mt. Holyoke College and a professor of mathematics, gives a brisk history of the Conjecture with a quick mention of its solution. The first half of the book, from Euclid and Pythagoras up to Henri Poincaré and the early 20th century, was relatively fast-moving (for a math book) and easy to follow, but when O’Shea got deeper into topological discussions of the Conjecture, his explanations became shorter and I found myself getting lost.
, also rather tricky to follow because of its heavy use of topology but with a bit more drama to help the reader plow through the less scrutable parts.
as much as I did. It’s a book about an obscure question in the field of number theory, one that remains unsolved after 150 years and probably has little to no practical application, but John Derbyshire manages to give the subject some real personality while doing his best to make it accessible to readers who haven’t taken a lot of advanced math classes or who, like me, are a good 13 years removed from their last one.
. Erd?s was a Hungarian-born savant who lived most of his life out of a suitcase, traveling the world, arriving at the doors of mathematicians he knew and announcing that “my brain is open,” after which he’d settle in for a few days or weeks and embark with his host on a streak of problem-solving and paper-writing. He had his own peculiar vocabulary, consumed large quantities of caffeine and later amphetamines, and combined brilliance and prolificacy (that’s peak and longevity for you Hall of Fame watchers) to the point where other mathematicians are referred to by their “Erd?s number,” where a person who co-authored a paper with Erd?s has an Erd?s number of one, while others are marked by how many papers you must go through to create the shortest possible chain back to Erd?s.