Incarnations

by Sunil Khilnani

  The harshness of his sentence became a cause célèbre, shaming even some British officials. Funds for his defense were raised all over India, and by Tamils in South Africa, too. Eventually, his sentence was commuted to six years, but this didn’t entirely ease the popular sense that he was the victim of a great injustice. In 1911 one of his young supporters shot dead the district’s senior British official and revenue collector, a man believed to be responsible for Pillai’s arrest. It was the only political assassination in the history of colonial South India—and a hollow coda to both Pillai’s movement and the larger Indian protest. Curzon’s Partition had been rescinded earlier that year. Local strains of radicalism had failed to weave into a genuinely national movement. The surge of national agitation was over, for now.

  * * *

  Tuticorin today is one of those places that reminds you that the “self-made” has its limitations, and that the desire to extract profit at the expense of public good was not exclusive to colonial powers. Despite sea winds, the port city is the most polluted place in Tamil Nadu. The detritus of copper smelting plants and coal-fired thermal power plants mixes with the effluent of chemical factories in a sulphurous, hot, fish-killing sea. Even the salt mined here comes dusted with ash. Ask about Pillai in these parts, and you’re as likely to get directions to the port, named after him, as a discussion of a once-famous leader. The cultural historian A. R. Venkatachalapathy notes that he’s one of the few nationalist or literary figures in the state who is not claimed only by people of his own caste. But if his appeal remains broad, it’s not deep. Periodic calls to build a museum celebrating his Swadeshi work have come to nothing. It’s as if he’s still, all these years later, shy of a mass following.

  In the story of twentieth-century freedom across the world, prison can look something like a school playground, a place where heroes are made. Gandhi, Nehru, Ho Chi Minh, Kenyatta, Martin Luther King Jr., Mandela—in each case, the hardship appears productive in hindsight. It forged them into the leaders they became. More often, though, prison is where individuals are broken, and then forgotten. Pillai, in Cannanore jail in Malabar, was doing hard labor, making jute and pressing oil, and comforting himself by writing poetry. In Venkatachalapathy’s translation of one of Pillai’s venbas, a terse, quasi-quatrain verse form:

  Chidambaram, who once bestowed largesse

  like the rain to supplicant poets,

  Now, fallen, runs around the world,

  singing venbas that don’t scan,

  his words and skin, worn thin.

  When Pillai left Cannanore jail in 1912, after serving four years, there were no crowds to greet him, no political career about to heat up, or even a law practice to continue—his jail conviction having effectively disbarred him. Moreover, his shipping concern had collapsed while he was in prison, costing him his base of subscribers’ money. Now, a man who thought resisters of his movement should be shunned was shunned himself. Waiting outside the jail was only Sivam, himself recently released from prison.

  Surveying the Swadeshi years, historians have wondered if more labor agitations might have increased the movement’s penetration, showing that Swadeshi didn’t merely represent the ambitions of an educated elite. Yet such agitations were only sporadic. In 1908, Lenin, considering a large strike of textile workers in Bombay, had written optimistically that the Indian street had begun to stand with its writers and intellectuals. That it didn’t happen on a larger scale can’t be laid entirely at the feet of those intellectuals. By 1908, the British had deported or imprisoned most of the movement’s leaders; many would never return to politics again. Sivam finally died of leprosy contracted in prison. Pillai survived for another two decades, trying to involve himself in various causes, but the world had soured on him. He never had a mass audience again.

  That would fall to Gandhi to create. The Swadeshi movement, and the acts of terrorism he feared would flow from it, prompted Gandhi to write, in 1909, his first serious work about Indian politics, Hind Swaraj, one of the aims of which was to dissuade Indians from violent struggle. Six years later, in January 1915, he disembarked in Bombay to begin his decades-long campaign to unite Indians into a national, nonviolent, and ultimately victorious struggle against British rule.

  31

  SRINIVASA RAMANUJAN

  The Elbow of Genius

  1887–1920

  Dear Sir, I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras on a salary of only £20 per annum. I am now about 23 years of age.

  When a young Indian, seemingly uncertain of his own age, mailed a letter to a Cambridge don in January 1913, it was a crucial link in a chain of influence that extended well beyond the young man’s lifetime, and will no doubt extend beyond ours.

  I have had no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics … I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as “startling” … If you are convinced that there is anything of value I would like to have my theorems published …

  The young man, who had already solicited two other famous mathematicians in vain, concluded, “Requesting to be excused from the trouble I give you.”

  The trouble caused by Ramanujan, one of the most gifted mathematicians of the twentieth century, turned out to be vast indeed. For a century now, his investigations have vexed and inspired mathematical scientists in fields ranging from number theory to particle physics and even medicine. During most of this time, the weight of emphasis was on “vexed.” With his work seen by many as barely fathomable or only narrowly relevant, the full significance of it might never have been recognized had it not been for the tragic romance of his life.

  It is a story suitable for novels, documentaries, films, or inspirational TED talks: the tale of a deeply religious savant and college dropout ostensibly rescued from a South Indian village and brought to Cambridge by the mathematician G. H. Hardy, the recipient of Ramanujan’s letter. After a few years burning bright, Ramanujan died young, his greatest potential perhaps unrealized. The narrative (cut with various quantities of exoticism and the miraculous, depending on the teller) even involves some lost notebooks, dramatically rediscovered, and a cryptic but ultimately revelatory final letter.

  In other, similar stories, math is often merely a backdrop. Yet Ramanujan’s work today is recognized as a frontier in advanced mathematics. (“Shiver in ecstasy,” a scientist recently tweeted of a connection Ramanujan made between infinite series, continued fractions, e, and pi.) It has proven integral to our highly networked and encrypted digital lives, as well as to cutting-edge attempts to cure cancer and to understand the deepest structures of the universe. Every day, researchers across the world, aided in part by those so-called lost notebooks and Ramanujan’s last letter, are sweating to find more applications. Did he hold the key to quantum gravity, which could unlock a unified theory of everything? another scientist recently wondered.

  Many questions such as that, about the significance of Ramanujan’s work, could not have been asked during his lifetime. The groundbreaking insights in at least one of the papers he published while at Trinity College, Cambridge (the unassumingly titled “On Certain Arithmetical Functions,” from 1916) remained hidden in plain view for more than thirty years. It took a new generation of mathematicians, armed with three decades of new math, to see that his results could help solve some of the most intractable problems in mathematical history. Those results even had a role in the biggest mathematical discovery of the twentieth century: the proof of Fermat’s last theorem.

  If Ramanujan has helped us understand our universe, the relationship has not been entirely reciprocal. The mathematician Ken Ono, a professor at Emory University who has spent the last thirteen years trying to unpack three pages of Ramanujan’s handwritten enigmas, says that the more he studies Ramanujan’s pap
ers, the less he is able to grasp the mind of the man. Part of this mystery is Ramanujan’s apparent indifference to Western mathematical conventions: much of his most far-seeing work doesn’t include proofs. Perhaps that is because he learned with chalk and a tablet, erasing figures with his elbow as he moved on—“My elbow has become rough and black in making a genius of me!” he reportedly once remarked. Or maybe he felt, as he sometimes indicated, that proofs would help others steal his work. So his exquisitely terse results, and not his reasoning, are what mathematicians and scientists have to work with: stand-alone puzzles, some of universal dimensions, to which even the occasional scientist has been known to impute a mystical, essentially Indian power.

  * * *

  “I did not invent him,” Hardy famously said, late in life, about Ramanujan; “like other great men, he invented himself.” But Ramanujan didn’t flourish in a vacuum. Aiding his self-invention were the sophisticated South Indian traditions in which he was raised; sources of classical mathematics that he was able to beg, borrow, or find; and the encouragement of a determined mother.

  Ramanujan’s hometown, Kumbakonam, in Tamil Nadu, is sometimes portrayed as the distant, desperate sticks, the better to foreground a Cambridge-bestowed deliverance. In reality, Ramanujan’s Vaishnavite Brahmin community, part of a town that had the highest percentage of professionals outside Madras, was the sort Annie Besant (29) had in mind when she went all eugenical and talked about superior beings. The Vaishnavite tradition was strict, erudite, ascetic, devout, and, crucially, treated with veneration by others in the society. Ramanujan was born, in other words, into a hothouse of intellectual self-belief.

  Not that status translated into rupees. His father was a clerk, tallying up accounts for a mediocre living, while his educated, self-possessed mother, Komalatammal, taught their only son. A singer of devotional songs in the local temple, she dabbled in numerology and astrology and believed in the spiritual and predictive power of math. Neighbors considered her a sort of psychic. Yet when the Ramanujan biographer Robert Kanigel went to Kumbakonam and interviewed relatives, he turned up no one before Ramanujan with an unusual gift for numbers.

  Komalatammal, strong-willed, noticed early her son’s desire for imposing order, through behavior we might now call “on the spectrum”: when he was barely walking, he aligned the cooking vessels against the wall with absolute precision. Nursing him through several illnesses, including smallpox, his mother noted how quickly he mathematized one of their time-pass games, in order to trounce her. From then on, she became what Ono calls an Indian Tiger Mom.

  It is often said that Ramanujan grew up in two parallel but distinct intellectual worlds: the spiritually rich but rationally deficient sacred precincts of the Hindu temple, and the rational but soul-crumbling rote classrooms of the Raj. The reality was less neat. The mathematical culture of the South Indian Brahmin was fundamentally a utilitarian one, using algebra, trigonometry, and geometry to make practical astronomical calculations, albeit to regulate religious life. So Ramanujan would hardly have been the first to spend afternoons doing math in chalk on the floor of the temple where his mother sang.

  Nor did the Madras school curriculum of the day conspicuously stifle Ramanujan’s talent. Though aimed at producing competent and honest junior-level public servants, not geniuses, the system acquitted itself reasonably well when confronted by an adolescent anomaly. Corpulent and hard to understand when he bothered to talk, he could easily have been bullied. Instead, he was recognized as both a star and a practical resource: administrators recruited him to solve such problems as scheduling the movement of twelve hundred students through various classrooms across the day.

  Once he’d exceeded the limits of his teachers’ mathematical knowledge, he studied higher-level textbooks borrowed from a local library and from college students whom his family took in as boarders. After mastering advanced trigonometry from a book by S. L. Loney, at around the age of thirteen, he progressed to G. S. Carr’s A Synopsis of Elementary Results in Pure and Applied Mathematics (1880), a nineteenth-century compendium of theorems and formulae. In Carr, mathematical facts were stated baldly, without proof or extrapolation; the inner logic was left to the reader to puzzle out. Ramanujan may have absorbed something of that style as he worked his way, problem by problem, through Carr’s version of mathematical history.

  An obsession with numbers at the expense of everything else brought him the highest honors at matriculation, but also led the protected teenager to his life’s first crisis. In 1904 he enrolled on a scholarship at Kumbakonam’s small, well-respected Government College. But he lost the scholarship by failing English, and ran away from home in the depths of his shame. Later he tried again at Madras University, where inattention to nonmath subjects caused him to fail his finals three times. His school career in India was over. His parents married him to a ten-year-old village girl named Janaki, and now expected him to start earning his living.

  Fortunately, as the degree-less, socially awkward Ramanujan struggled to hold down work as a tutor and clerk, word of his intelligence reached the leaders of the newly founded Indian Mathematical Society. One of them, a wealthy district collector, secured him a bursary, even though Ramanujan’s work was beyond his ken. An intense period of independent study ensued.

  Ironically, given the decades it would take his mathematical successors to appreciate the depth of his later insights, some of the problems he worked hardest on had been solved generations before. When he learned that Leonhard Euler, the legendary eighteenth-century mathematician, had beaten him to a “discovery” (the series that yielded the basic trigonometric functions sine and cosine), he took no pleasure in having matched one of the greatest minds of the Enlightenment. Instead, shaken and ashamed, he hid some of his results in the roof of the family house.

  Where he lurched ahead of even Euler was on the related subject of infinite series—that is, functions whose terms go on indefinitely, but which can often be expressed in unexpectedly simple ways. The ability to grapple almost tangibly with the infinite was becoming a hallmark of Ramanujan’s thought. He once told a fellow Indian mathematician, “An equation has no meaning for me unless it expresses a thought of GOD.” He claimed his most impressive results came to him in a dream, inscribed on his tongue by the Hindu goddess Namagiri, an important force in the life of his family.

  This claim has since become a fallback for those unable to account for Ramanujan’s genius: a sort of South Indian Hindu longhand for what others call “intuition,” or a power more profound. Yet I wonder if Namagiri wasn’t a way, conscious or otherwise, for Ramanujan to mediate between his family and himself on the one hand, and the demands of his extraordinary abilities on the other. He seems to have felt, partly on the advice of others, that his talents could be validated and developed only in the West. So at the same time that he was claiming inspiration from Namagiri, he was pursuing recognition and mentorship from British mathematicians. And he eventually declared that Namagiri had given him permission to break caste taboos and pollute himself by leaving India to take up the invitation of G. H. Hardy.

  * * *

  Franz Ferdinand was assassinated two months after Ramanujan arrived in Cambridge. At the same time that the twenty-one-year-old was caught up in the collective anxiety of war, he was also struggling to absorb shocks of a more intimate scale: aching in a cold he had never before felt, unhappy at letters from home reporting fights between his mother and his wife, and miserably hungry in the face of the vile collations that passed in Britain for vegetarian food. Once, overcome with one of the bouts of mortification that he had endured since adolescence, he attempted suicide. Still, he worked.

  Given Hardy’s renown, the collegial stance he took toward a laden twenty-one-year-old college failure was striking and sensitive, and rooted perhaps in Hardy’s own history. He’d been a prodigy himself, and being homosexual, he had grown up to be a social nonstarter in a different way from Ramanujan. On first browsing the young Indian’s work, he
had had an initial reaction similar to that of some members of the Indian Mathematical Society a few years before: a fraudster was wasting his valuable time. Yet with deeper engagement in the work, Hardy had come to see a level of confidence and idiosyncratic genius that might be squashed by heavy-handed intervention.

  Freedom and collaboration were what Hardy offered instead. With these, Ramanujan would in the course of five years at Cambridge make significant contributions to subjects ranging from probabilistic number theory and hypergeometric series to the distribution of prime numbers and the theory of partitions. On the basis of this work alone, he should be considered one of the greatest mathematicians of his generation. Yet these were merely the fields in which his contemporaries could grasp the importance of his results.

  Experts tell me that it’s difficult to appreciate Ramanujan’s achievements without a PhD in mathematics or theoretical physics—and even then, noted his biographer Robert Kanigel, it has to be a PhD in the right type of math or physics. (I’ll take their word for it.) Still, there are a few areas in which the rest of us can glimpse the power of his mind. In 1914, for instance, Ramanujan published work on the irrational number pi, the ratio of a circle’s circumference to its diameter. Expressed as a decimal, pi’s digits extend onward forever in a totally random fashion. For millennia, mathematicians had striven to approximate this number as closely as possible. Until the nineteenth century, the nearest they had got was roughly one hundred digits. Ramanujan eventually tamed the chaos, creating not just one but two beautiful expressions of the value of pi. According to Ono, Ramanujan’s innovation was to stop thinking of pi as a decimal, and to conceive of it instead as a complex but elegant fraction. Today, supercomputers, using a version of one of Ramanujan’s formulae, have calculated the value to more than twelve trillion digits.