The Man Who Knew Infinity

Robert Kanigel

• Publisher: Washington Square Press
• Year: 2013
• ISBN:
  9781439121863
• Topic: History
• Subtopic: Historical Biographies
• Index: History

NOW A MAJOR MOTION PICTURE STARRING JEREMY IRONS AND DEV PATEL! A moving and enlightening look at the unbelievable true story of how gifted prodigy Ramanujan stunned the scholars of Cambridge University and revolutionized mathematics. In 1913, a young unschooled Indian clerk wrote a letter to G H Hardy, begging the preeminent English mathematician's opinion on several ideas he had about numbers. Realizing the letter was the work of a genius, Hardy arranged for Srinivasa Ramanujan to come to England.Thus began one of the most improbable and productive collaborations ever chronicled. With a passion for rich and evocative detail, Robert Kanigel takes us from the temples and slums of Madras to the courts and chapels of Cambridge University, where the devout Hindu Ramanujan, "the Prince of Intuition, " tested his brilliant theories alongside the sophisticated and eccentric Hardy, "the Apostle of Proof."In time, Ramanujan's creative intensity took its toll: he died at the age of thirty-two, but left behind a magical and inspired legacy that is still being plumbed for its secrets today.

CHAPTER ONE

In the Temple’s Coolness

[1887 to 1903]

1. DAKSHIN GANGE

He heard it all his life—the slow, measured thwap . . . thwap . . . thwap . . . of wet clothes being pounded clean on rocks jutting up from the waters of the Cauvery River. Born almost within sight of the river, Ramanujan heard it even as an infant. Growing up, he heard it as he fetched water from the Cauvery, or bathed in it, or played on its sandy banks after school. Later, back in India after years abroad, fevered, sick, and close to death, he would hear that rhythmic slapping sound once more.

The Cauvery was a familiar, recurring constant of Ramanujan’s life. At some places along its length, palm trees, their trunks heavy with fruit, leaned over the river at rakish angles. At others, leafy trees formed a canopy of green over it, their gnarled, knotted roots snaking along the riverbank. During the monsoon, its waters might rise ten, fifteen, twenty feet, sometimes drowning cattle allowed to graze too long beside it. Come the dry season, the torrent became a memory, the riverbanks wide sandy beaches, and the Cauvery itself but a feeble trickle tracing the deepest channels of the riverbed.

But always it was there. Drawing its waters from the Coorg Mountains five hundred miles to the west, branching and rebranching across the peninsula, its flow channeled by dams and canals some of which went back fifteen hundred years, the Cauvery painted the surrounding countryside an intense, unforgettable green. And that single fact, more than any other, made Ramanujan’s world what it was.

Kumbakonam, his hometown, flanked by the Cauvery and one of its tributaries, lay in the heartland of staunchly traditional South India, 160 miles south of Madras, in the district then known as Tanjore. Half the district’s thirty-seven hundred square miles, an area the size of the state of Delaware, was watered directly by the river, which fell gently, three feet per mile, to the sea, spreading its rich alluvial soil across the delta.

The Cauvery conferred almost unalloyed blessing. Even back in 1853, when it flooded, covering the delta with water and causing immense damage, few lives were lost. More typically, the great river made the surrounding land immune to year-to-year variation in the monsoon, upon whose caprices most of the rest of India hung. In 1877, in the wake of two straight years of failed monsoons, South India had been visited by drought, leaving thousands dead. But Tanjore District, nourished by the unfailing Cauvery, had been scarcely touched; indeed, the rise in grain prices accompanying the famine had brought the delta unprecedented prosperity.

No wonder that the Cauvery, like the Ganges a thousand miles north, was one of India’s sacred rivers. India’s legendary puranas told of a mortal known as Kavera-muni who adopted one of Brahma’s daughters. In filial devotion to him, she turned herself into a river whose water would purify from all sin. Even the holy Ganges, it was said, periodically joined the Cauvery through some hidden underground link, so as to purge itself of pollution borne of sinners bathing in its waters.

Dakshin Gange, the Cauvery was called—the Ganges of the South. And it made the delta the most densely populated and richest region in all of South India. The whole edifice of the region’s life, its wealth as well as the rich spiritual and intellectual lives its wealth encouraged, all depended on its waters. The Cauvery was a place for spiritual cleansing; for agricultural surfeit; for drawing water and bathing each morning; for cattle, led into its shallow waters by men in white dhotis and turbans, to drink; and always, for women, standing knee-deep in its waters, to let their snaking ribbons of cotton or silk drift out behind them into the gentle current, then gather them up into sodden clumps of cloth and slap them slowly, relentlessly, against the water-worn rocks.

2. SARANGAPANI SANNIDHI STREET

In September 1887, two months before her child was due to be born, a nineteen-year-old Kumbakonam girl named Komalatammal traveled to Erode, her parental home, 150 miles upriver, to prepare for the birth of the child she carried. That a woman returned to her native home for the birth of her first child was a tradition so widely observed that officials charged with monitoring vital statistics made a point of allowing for it.

Erode, a county seat home to about fifteen thousand people, was located at the confluence of the Cauvery and one of its tributaries, the Bhavani, about 250 miles southwest of Madras. At Erode—the word means “wet skull,” recalling a Hindu legend in which an enraged Siva tears off one of Brahma’s five heads—the Cauvery is broad, its stream bed littered with great slabs of protruding rock. Not far from the river, in “the fort,” as the town’s original trading area was known, was the little house, on Teppukulam Street, that belonged to Komalatammal’s father.

It was here that a son was born to her and her husband Srinivasa, just after sunset on the ninth day of the Indian month of Margasirsha—or Thursday, December 22, 1887. On his eleventh day of life, again in accordance with tradition, the child was formally named, and a year almost to the day after his birth, Srinivasa Ramanujan Iyengar and his mother returned to Kumbakonam, where he would spend most of the next twenty years of his life.

“Srinivasa”—its initial syllable pronounced shri—was just his father’s name, automatically bestowed and rarely used; indeed, on formal documents, and when he signed his name, it usually atrophied into an initial “S.” “Iyengar,” meanwhile, was a caste name, referring to the particular branch of South Indian Brahmins to which he and his family belonged. Thus, with one name that of his father and another that of his caste, only “Ramanujan” was his alone. As he would later explain to a Westerner, “I have no proper surname.” His mother often called him Chinnaswami, or “little lord.” But otherwise he was, simply, Ramanujan.

He got the name, by some accounts, because the Vaishnavite saint Ramanuja, who lived around A.D. 1100 and whose theological doctrines injected new spiritual vitality into a withered Hinduism, was also born on a Thursday and shared with him other astrological likenesses. “Ramanujan”—pronounced Rah-MAH-na-jun, with only light stress on the second syllable, and the last syllable sometimes closer to jum—means younger brother (anuja) of Rama, that model of Indian manhood whose story has been handed down from generation to generation through the Ramayana, India’s national epic.

• • •

Ramanujan’s mother, Komalatammal, sang bhajans, or devotional songs, at a nearby temple. Half the proceeds from her group’s performances went to the temple, the other half to the singers. With her husband earning only about twenty rupees per month, the five or ten she earned this way mattered; never would she miss a rehearsal.

Yet now, in December 1889, she was missing them, four or five in a row. So one day, the head of the singing group showed up at Komalatammal’s house to investigate.

There she found, piled near the front door, leaves of the margosa tree; someone, it was plain to her, had smallpox. Stepping inside, she saw a small, dark figure lying atop a bed of margosa leaves. His mother, chanting all the while, dipped the leaves in water laced with ground turmeric, and gently scoured two-year-old Ramanujan’s pox-ridden body—both to relieve the infernal itching and, South Indian herbalists believed, subdue the fever.

Ramanujan would bear the scars of his childhood smallpox all his life. But he recovered, and in that was fortunate. For in Tanjore District, around the time he was growing up, a bad year for smallpox meant four thousand deaths. Fewer than one person in five was vaccinated. A cholera epidemic when Ramanujan was ten killed fifteen thousand people. Three or four children in every ten died before they’d lived a year.

Ramanujan’s family was a case study in the damning statistics. When he was a year and a half, his mother bore a son, Sadagopan. Three months later, Sadagopan was dead.

When Ramanujan was almost four, in November 1891, a girl was born. By the following February, she, too, was dead.

When Ramanujan was six and a half, his mother gave birth to yet another child, Seshan—who also died before the year was out.

Much later, two brothers did survive—Lakshmi Narasimhan, born in 1898, when Ramanujan was ten, and Tirunarayanan, born when he was seventeen. But the death of his infant brothers and sister during those early years meant that he grew up with the solicitous regard and central position of an only child.

After the death of his paternal grandfather, who had suffered from leprosy, Ramanujan, seven at the time, broke out in a bad case of itching and boils. But this was not the first hint of a temperament inclined to extreme and unexpected reactions to stress. Indeed, Ramanujan was a sensitive, stubborn, and—if a word more often reserved for adults in their prime can be applied to a little boy—eccentric child. While yet an infant back in Erode, he wouldn’t eat except at the temple. Later, in Kumbakonam, he’d take all the brass and copper vessels in the house and line them up from one wall to the other. If he didn’t get what he wanted to eat, he was known to roll in the mud in frustration.

For Ramanujan’s first three years, he scarcely spoke. Perhaps, it is tempting to think, because he simply didn’t choose to; he was an enormously self-willed child. It was common in those days for a young wife to shuttle back and forth between her husband’s house and that of her parents, and Komalatammal, worried by her son’s muteness, took Ramanujan to see her father, then living in Kanchipuram, near Madras. There, at the urging of an elderly friend of her father’s, Ramanujan began the ritual practice of Akshara Abhyasam: his hand, held and guided by his grandfather, was made to trace out Tamil characters in a thick bed of rice spread across the floor, as each character was spoken aloud.

Soon fears of Ramanujan’s dumbness were dispelled and he began to learn the 12 vowels, 18 consonants, and 216 combined consonant-vowel forms of the Tamil alphabet. On October 1, 1892, the traditional opening day of school, known as Vijayathasami, he was enrolled, to the accompaniment of ancient Vedic chants, in the local pial school. A pial is the little porch in front of most South Indian houses; a pial school was just a teacher meeting there with half a dozen or so pupils.

But five-year-old Ramanujan, disliking the teacher, bristled at attending. Even as a child, he was so self-directed that, it was fair to say, unless he was ready to do something on his own, in his own time, he was scarcely capable of doing it at all; school for him often meant not keys to knowledge but shackles to throw off.

Quiet and contemplative, Ramanujan was fond of asking questions like, Who was the first man in the world? Or, How far is it between clouds? He liked to be by himself, a tendency abetted by parents who, when friends called, discouraged him from going out to play; so he’d talk to them from the window overlooking the street. He lacked all interest in sports. And in a world where obesity was virtually unknown, where bones protruded from humans and animals alike, he was, first as a child and then for most of his life, fat. He used to say—whether as boast, joke, or lament remains unclear—that if he got into a fight with another boy he had only to fall on him to crush him to pieces.

For about two years, Ramanujan was shuffled between schools. Beginning in March 1894, while still at his mother’s parents’ house in Kanchipuram, he briefly attended a school in which the language of instruction was not his native Tamil but the related but distinct Telugu. There, sometimes punished by having to sit with his arms folded in front of him and one finger turned up to his lips in silence, he would at times stalk out of class in a huff.

In a dispute over a loan, his grandfather quit his job and left Kanchipuram. Ramanujan and his mother returned to Kumbakonam, where he enrolled in the Kangayan Primary School. But when his other grandfather died, Ramanujan was bounced back to his maternal grandparents, who by now were in Madras. There he so fiercely fought attending school that the family enlisted a local constable to scare him back to class.

By mid-1895, after an unhappy six months in Madras, Ramanujan was once more back in Kumbakonam.

• • •

Kumbakonam was flanked by the Cauvery and the Arasalar, its tributary. Most streets ran parallel to these rivers or else marched straight down to their banks, perpendicular to the first set, making for a surprisingly regular grid system. And there, near the middle of this compact grid, on Sarangapani Sannidhi Street, a dirt road about thirty feet wide with squat little buildings close packed on either side, was Ramanujan’s house.

The one-story structure, thatched with palm leaves, stood back about ten feet from the street, insulated, as it were, by its two-tiered, covered pial: it was a step or two up from the dusty (or muddy) street, another few up to the little porch. The stucco house faced the street with a twelve-foot-wide wall broken by a window to the left and a door to the right. A bystander in the street, peering through the open door and into the gloom of the interior, could sight all the way through to the back, where his gaze would be arrested by a splash of sunlight from the open rear court. The rest of the house, meanwhile, was offset to the left, behind the front window. Here was the main living area and, behind it, a small kitchen, redolent with years of cooking smells.

South India was not always hot; but it was never cold. At a latitude of about eleven degrees north. Kumbakonam lay comfortably within the tropics; even on a January winter’s night, the thermometer dropped, on average, only to seventy degrees. And that climatological fact established an architectural fact, for it gave South Indian homes a kind of permeability; their interiors always savored a little of the outside (a feeling familiar to Americans with screened-in porches). Windows there were, but these were merely cutouts in the wall, perhaps with bars or shutters, never space-sealing panes of glass that left you conscious of being on one side or another. In the middle of most houses was a small courtyard, the muttam, open to the sky—like a skylight but again without the glass—that brought rain into the center of the house, where it was funneled to a drain that led back outside. In Ramanujan’s house, smells from outside wafted inside. Lizards crawled, mosquitos flew unimpeded. The soft South Indian air, fragrant with roses, with incense, with cow dung burned as a fuel, wafted over everything.

Just outside the door lay Kumbakonam, an ancient capital of the Chola Empire. The Cholas had reached their zenith around A.D. 1000, when Europe wallowed in the Dark Ages, and had ruled, along with northern Ceylon, most of what, during Ramanujan’s day, was known as the Madras Presidency (which, with those of Bombay and Calcutta, constituted the chief administrative and political units of British-ruled India). The dozen or so major temples dating from this period made Kumbakonam a magnet to pilgrims from throughout South India.

Every twelve years, around February or March, they came for the Mahammakham festival, commemorating a legendary post-Deluge event in which the seeds of creation, drifting upon the waters in a sacred pot—or kumba, source of the town’s name—was pierced by the god Siva’s arrow. The nectar thus freed, it was said, had collected in the Mahammakham “tank,” the outdoor pool for ritual bathing that was part of every temple. At such times—as in 1897, when Ramanujan was nine—three-quarters of a million pilgrims might descend on the town. And the great tank, surrounded by picturesque mandapams, or halls, and covering an expanse of twenty acres, would be so filled with pilgrims that its water level was said to rise several inches.

When not in use, temple tanks could seem anything but spiritually uplifting. Open, stone-lined reservoirs, sometimes stocked with fish, frequently green with algae, they often served as breeding grounds for malarial mosquitos. Situated on low ground between two rivers, Kumbakonam was notorious for its bad water, its mosquitos, and its filarial elephantiasis, a mosquito-borne disease that left its victims with grotesquely deformed limbs, sometimes with scrota the size of basketballs. When Ramanujan was six, the town completed a drainage system. But this was designed to carry off only surface water, not sewage, and most of the town’s health problems continued unabated.

Kumbakonam, a day’s train ride from Madras, which was...