The Man Who Knew Infinity Read online

  Most often, it was a Brahmin male’s wife who prepared and served his meals. But he never ate with her—another example of heathen ways the English cited as repugnant to proper Christians: women prepared the meals of the men and children of the household, serving them from vessels of silver, copper, and brass (not china, which was deemed insufficiently clean), and hovering over them during mealtime to dispense fresh helpings. The men would eat, largely oblivious to them, then rise together at meal’s end. Only then, once having cleaned up, would the women retreat to the kitchen and eat whatever remained.

  Ramanujan ate while seated on the floor, from a round metal tray or, more often, banana leaves set before him and later discarded, like paper plates. He ate with his hands. This did not mean using bread to scoop or sop up food. The staple food up North was wheat, that of the South rice; bread played little role in its diet. So Ramanujan ate precisely as every Western toddler learns not to eat—with his fingers.

  Into the center of the banana leaf would be ladled a helping of rice. Toward the periphery of the leaf—about the size of a place mat in a Western household and still green and fresh, with a thick, muscular rib running down the middle—would go dollops of sharply pickled fruits or vegetables, like mangos, onions, or oranges; spiced fruit chutneys; sambhar, a thick lentil soup stocked with potatoes; and yogurt. Sometimes just a few selections, sometimes, for a festive meal, as many as a dozen. With the fingers of his right hand (and only his right hand), Ramanujan would mix rice with one or several other foods. Then, with four fingers and thumb formed into a pincer, he’d shape some of the loose mixture into a pasty ball and plop it onto his tongue.

  South Indian cuisine was tasty and nutritious, if not always subtle. It was never bland; the curried dishes were sharp and spicy, the others almost maddeningly sweet. Rice and yogurt, beyond their nutritive value, softened and blunted the bite of the spices themselves. Coconuts and bananas (or actually plantains, a shorter, stubbier variety, tasting much the same) were the main fruits, along with mango and guava.

  That Ramanujan never ate meat, then, was no act of painful self-denial. Like virtually all Brahmins, he was a strict vegetarian. And yet to say meat was “prohibited” to him subtly misses the point. It scarcely needed to be prohibited, and for the same simple, invisible reason an orthodox Jew or Muslim needn’t be told not to eat pork: you just didn’t do it. Others ate meat; he didn’t. He would have gagged at the thought. Some of his friends even avoided ingredients, like beetroot, that gave food a reddish cast reminiscent of blood.

  Ramanujan absorbed such dos and don’ts of Brahmin life as naturally as he learned to walk and talk. “As the child learned to accept responsibility for its own bodily cleanliness, it was also taught the importance of avoiding the invisible pollution conferred by the touch of members of the lowest castes,” is how one scholar, G. Morris Carstairs, would later depict the Indian socializing process at work. “The mother or grandmother would call him in and make him bathe and change his clothes if this should happen, until his repugnance for a low caste person’s touch became as involuntary as his disgust for the smell and touch of feces.”

  Every morning a Hindu male underwent an elaborate cleansing ritual. He defecated, using his left hand only to clean himself with water. Then he bathed, preferably in a holy river like the Cauvery, but always paying special heed to ears, eyes, and nostrils. In drinking, he never brought a cup to his lips but rather spilled water from it into his mouth. After a meal, he got up, left the eating area, and ceremoniously poured water over his hands. For all the dirt and lack of modern sanitary facilities which so bothered English visitors, there was a fastidiousness about Hindu life that no one observed more scrupulously than orthodox Brahmins.

  Though sometimes scorned as haughty, Brahmins felt pride that, in their own estimation, even the poorest among them were cleaner and purer than others; that the least educated Brahmin knew some Sanskrit, the ancient language of Hinduism’s sacred texts; that normally they were accorded deference and respect by others; that educationally and professionally, they excelled. All this contributed to a sense almost universal among them—and nothing suggests Ramanujan failed to share it—that Brahmins were, in a real sense, chosen.

  4. OFF-SCALE

  Among Brahmins, traditionally, a sanyasi, or itinerant beggar who gave up worldly interests for spiritual, was not deemed a failure. An ascetic streak ran through Brahmin culture. As Sanskrit scholar Daniel Ingalls has written in an essay, “The Brahmin Tradition,” “Asceticism and mysticism have been, for many centuries now, to the respectable Indian classes what art has been for the last century and a half to the bourgeoisie of Western Europe”—something to which, whether aspiring to it themselves or not, they at least gave lip service, and respected.

  This tradition lifted an eyebrow toward any too-fevered a rush toward worldly success, lauded a life rich in mind and spirit, bereft though it might be of physical comfort. Even wealthy Brahmin families often kept homes that, both by Western standards and those of other well-off Indians, were conspicuous by their simplicity and spartan grace, with bare floors, the meanest of furniture. “Simple living and high thinking,” is how one South Indian Brahmin would, years later, characterize the tradition.

  But in the years Ramanujan was growing up, things were changing. Brahmins were still the priests and gurus, the logicians and poets, the Sanskrit scholars and sanyasis of Hindu life. But now the old contemplative bent was taking new form; the spiritual was being transmuted into the secular. Like Jews in Europe and America at about the same time (with whom South Indian Brahmins would, almost a century later, routinely compare themselves), they were becoming professionals.

  The census following Ramanujan’s birth noted that of South India’s six hundred thousand male Brahmins, some 15 percent—an extraordinarily high number—held positions in the civil service, the learned professions, and minor professional fields. They already dominated the ranks of the college educated, and within a generation, by 1914, of 650 graduates of the University of Madras no fewer than 452 would be Brahmins—more than ten times their proportion of the population. The old middle class of traders and barristers had traditionally been drawn from their own distinct castes. But the British had helped build a new middle class of brokers, agents, teachers, civil servants, journalists, writers, and government clerks. And these positions Brahmins now began to fill.

  In Brahminically steeped Kumbakonam, one in five adult males could read and write, more than anywhere else in South India with the possible exception of Tanjore, the district seat, and Madras itself. Kumbakonam Brahmins had a taste for philosophical and intellectual inquiry, a delight in mental exercise, that led one English observer to pronounce them “proverbial for ability and subtlety.” Ramanujan’s parents, when not mired in outright poverty, clung to the nethermost reaches of the middle class and were illiterate in English, though not in their native Tamil; his friends, however, mostly came from better-off families and were bound for positions as lawyers, engineers, and government officials.

  In doing so, they trod career paths with one thing in common: the way was always marked in English.

  Ramanujan’s native language was Tamil, one of a family of Dravidian languages that includes Malayalam, Canarese, and the musical-sounding Telugu. European scholars acclaimed Tamil for its clear-cut logic; “a language made by lawyers and grammarians,” someone once called it. Spoken from just north of Madras within a broad, kidney-shaped region west to the Nilgiri Hills and south to Cape Comorin at the tip of the subcontinent, as well as in northern Ceylon, Tamil represented no out-of-the-way linguistic outpost. It had its own rich literature, distinct from the Hindi of the north, going back to the fifth century B.C., boasted a verse form reminiscent of ancient Greek, and was spoken by almost twenty million people.

  But in the early 1900s, as now, English was ascendant in India. It was the language of the country’s rulers. It fueled the machinery of government. It was the lingua franca to which Indians, who spok
e more than a dozen distinct languages, turned when they did not otherwise understand one another. Among Indians as a whole, to be sure, the proportion who spoke English was small. Even among relatively well-educated Tamil Brahmin males, only about 11 percent were (in 1911) literate in it. So, those who did speak and read it were, in obedience to the law of supply and demand, propelled onto the fast track. As a clerk, even a smattering of it got you an extra few rupees’ pay. It was the ticket of admission to the professions.

  • • •

  While a pupil at Kangayan Primary School, Ramanujan studied English from an early age, and in November 1897, just shy of ten, he passed his primary examinations—in English, Tamil, arithmetic, and geography—scoring first in the district. The following January, he enrolled in the English language high school, Town High.

  Town High School had its origins in 1864 in two houses on Big Street, a main thoroughfare near the heart of town. When, some years later, the local college dropped its lower classes, a group of public-spirited citizens rushed to fill the vacant academic niche from below, through an expanded Town High. They would tear down the old buildings, erect a new one on the existing site … No, pronounced Thambuswami Mudaliar, a magnificently mustachioed eminence on the school’s managing committee, better to start afresh. And for the school’s new campus, he offered seven prime acres then harboring a banana orchard. There, he personally supervised construction of the first buildings.

  Today, Town High’s cluster of handsome white buildings occupies an oasis of tropical charm insulated from the noisy street out front by a sandy field shaded by tall margosa trees. At the time Ramanujan attended, however, the first block of classrooms, with its roof of densely layered red clay tiles and porch overhangs of palm leaf thatching, had gone up just a few years before. Its classrooms were laid end-to-end, making for a building one room wide, with windows on both sides to catch any hint of breeze.

  The windows would have caught any adolescent clamor, too, but there was probably little to carry. Years later an alumnus would recall the long coats and turbans of the teachers and the respect they commanded among the students. Headmaster during Ramanujan’s time, and for twenty-two years in all, was S. Krishnaswami Iyer, a severe-faced man partial to impromptu strolls between classes. The tapping of his walking stick would alert both teachers and students to his coming. Sometimes he’d step into a class, take over from the teacher, question students, and teach the rest of the class—with enough flair, it seems, that when he taught Grey’s “Eton College” one student imagined little Town High as Eton, the irrigation ditch crossing the campus as the Thames.

  The school, which stood about a five-minute walk from Ramanujan’s house, drew the cream of Kumbakonam youth and launched them into college and career. Alumni would later recall it with genuine fondness. And it nourished Ramanujan for six years, bringing him as close as he’d ever come to a satisfying academic experience.

  Even allowing for the retrospective halo that sees in every schoolboy exploit of the famous a harbinger of future greatness, it’s plain that Ramanujan’s gifts became apparent early. Ramanujan entered Town High’s first form at the age of ten, corresponding to about an American seventh grade. And already while he was in the second form, his classmates were coming to him for help with mathematics problems.

  Soon, certainly by the third form, he was challenging his teachers. One day, the math teacher pointed out that anything divided by itself was one: Divide three fruits among three people, he was saying, and each would get one. Divide a thousand fruits among a thousand people, and each would get one. So Ramanujan piped up: “But is zero divided by zero also one? If no fruits are divided among no one, will each still get one?”

  Ramanujan’s family, always strapped for cash, often took in boarders. Around the time he was eleven, there were two of them, Brahmin boys, one from the neighboring district of Trichinopoly, one from Tirunelveli far to the south, studying at the nearby Government College. Noticing Ramanujan’s interest in mathematics, they fed it with whatever they knew. Within months he had exhausted their knowledge and was pestering them for math texts from the college library. Among those they brought to him was an 1893 English textbook popular in South Indian colleges and English preparatory schools, S. L. Loney’s Trigonometry, which actually ranged into more advanced realms. By the time Ramanujan was thirteen, he had mastered it.

  Ramanujan learned from an older boy how to solve cubic equations. He came to understand trigonometric functions not as the ratios of the sides in a right triangle, as usually taught in school, but as far more sophisticated concepts involving infinite series. He’d rattle off the numerical values of π and e, “transcendental” numbers appearing frequently in higher mathematics, to any number of decimal places. He’d take exams and finish in half the allotted time. Classmates two years ahead would hand him problems they thought difficult, only to watch him solve them at a glance.

  Occasionally, his powers were put to good use. Some twelve hundred students attended the school and each had to be assigned to classrooms, and to the school’s three dozen or so teachers, while satisfying any special circumstances peculiar to particular students. At Town High, the senior math teacher, Ganapathi Subbier, was regularly shackled with the maddening job—and he would give it to Ramanujan.

  By the time he was fourteen and in the fourth form, some of his classmates had begun to write Ramanujan off as someone off in the clouds with whom they could scarcely hope to communicate. “We, including teachers, rarely understood him,” remembered one of his contemporaries half a century later. Some of his teachers may already have felt uncomfortable in the face of his powers. But most of the school apparently stood in something like respectful awe of him, whether they knew what he was talking about or not.

  He became something of a minor celebrity. All through his school years, he walked off with merit certificates and volumes of English poetry as scholastic prizes. Finally, at a ceremony in 1904, when Ramanujan was being awarded the K. Ranganatha Rao prize for mathematics, headmaster Krishnaswami Iyer introduced him to the audience as a student who, were it possible, deserved higher than the maximum possible marks.

  An A-plus, or 100 percent, wouldn’t do to rate him. Ramanujan, he was saying, was off-scale.

  Still, during most of his time in school, Ramanujan’s life remained in rough balance. At graduation, he was his mother’s son, motivated and successful in school, getting set to enroll the following year, with a scholarship, in the Government College at the other end of town, looking ahead to academic achievement, a career, marriage …

  But soon, very soon, that uneasy balance would be destroyed, and Ramanujan would be led out into a new, mentally unsettling realm of intellectual passion and fierce, unbending intensity that would rule the rest of his life.

  For beside the reasoned, rational side of Ramanujan lay an intuitive, even irrational streak that most of his Western friends later could never understand—but with which he was at ease, and to which he happily surrendered himself.

  5. THE GODDESS OF NAMAKKAL

  It would take a few minutes for his eyes to adjust to the shadows. There, in the Sarangapani temple’s outer hall, it seemed gloomy after the bright sun outside. What light there was swept in from the side, softly modeling the intricate sculpted shapes, the lions and geometrically cut stone, of the hall’s closely spaced columns.

  Away further from the light, nestled among the columns, were areas favored by bats for nesting. Sometimes Ramanujan could hear the quick, nervous swatting of their wings. Or even see them hanging from the ceiling, chirping away, then abruptly fluttering into flight.

  Unlike Western churches which, architecturally, drew you higher and higher, here the devout were pulled, as it were, inner and inner. Within the high stone walls of the temple complex stood a broad court, open to the sky and, within that, the roofed columned area. In further yet, you came to the great chariot, its enormous wheels, several feet in diameter, drawn by sculpted horses and elephants. Within
the building-within-a-building that was the chariot stood, in a dark stone cell where a lamp burned night and day, the sanctum sanctorum, the primary deity himself—the great god Vishnu, rising up from his slumber beside the many-headed serpent representing Eternity.

  Always the temple stirred with little bright devotional fires, the chanting of mantras, the smell of incense in small shrines and dark niches devoted to secondary deities. The closer one approached to the central shrine itself, the darker it grew—more mysterious, more intimately scaled, progressively smaller, tighter, closer. What from the noisy street beyond the temple walls might have seemed a fit site for great public spectacles, here, inside, within stone grottos blackened by centuries of ritual fire presided over by bare-chested Brahmin priests, was a place for one man and his gods.

  From the outside, the gopuram, or entrance tower, of this great temple built by Nayak kings sometime before A.D. 1350 was a massive twelve-story trapezoid of intricately sculpted figures, 90 feet across at its base and rising 146 into the sky. It was so high you could scarcely discern the images at the top, much less the facial expressions upon which their sculptors had lavished attention. There were figures clothed and naked, figures sitting and standing, with human shapes and animal, realistic and utterly fantastic. There were figures dancing, on horseback, making love, strumming instruments—a full panoply of human activity, densely realized in stone.

  To Ramanujan, growing up within sight of the temple, these were not neutral images. Each represented legends onto which, since his earliest childhood, layers of imagery and significance had been heaped up—scenes and stories he had heard at his mother’s knee, stories from the great epics, the Ramayana and the Mahabharata, stories meant to edify, or amuse. Every Hindu child learned of mischievous little Krishna—a child now, not yet a god—coming upon a group of women bathing, stealing their saris, and escaping up a tree with them, the women frantically imploring him for their return. Here, Ramanujan had only to lift his gaze to the wall of the gopuram to see Krishna perched in the legendary tree.