Rajagopalachari was just a few months older than Ramanujan, had grown up in the same town, frequented the same temple, attended Town High with him. One afternoon back in 1902, during recess, an older student, said to be the smartest in his class, handed him a math problem. Ramanujan was so smart? Well, then, let him solve this:
At first glance falling under the familiar heading of “two simultaneous equations in two unknowns,” the problem actually confronted Ramanujan with a difficult fourth-degree equation and meant recalling a theorem applicable to a particular class of them. To any ordinarily smart fourteen-year-old, it would be exceedingly difficult. “To my astonishment,” Rajagopalachari remembered later, “Ramanujan worked it out in half a minute and arrived at the answer by two steps.”
In fact, he probably didn’t “work it out” at all, but simply looked at it, guessed the answer might be one where each was a square, tried a couple of possibilities in his head, and saw the solution, x = 9 and y = 4, jump out at him; in other words, it was a piece of fancy footwork, nothing mathematically profound. Still, it impressed Rajagopalachari, and he and Ramanujan became friends.
Over the years, Rajagopalachari had followed a straight career trajectory toward becoming a lawyer, while Ramanujan floundered. The two lost contact. But now, in 1910, almost a decade later, they met again by chance in Madras. Despondent, Ramanujan told Rajagopalachari about his school failure. He had no future, he said. No one appreciated him. He’d written a famous mathematician in Bombay, Professor Saldhana, with samples of his work. He’d written the Indian Mathematical Society. Nothing had come of any of it. So, thanks to a friend who was supplying the ticket, he was taking a train back to Kumbakonam that very night.
Don’t go, said Rajagopalachari. Ramanujan may have mentioned he had a letter of introduction to Ramachandra Rao, but had not yet acted on it. In any case, Rajagopalachari said that he would take him to meet Ramachandra Rao. When Ramanujan protested that he had no money to remain in Madras, his friend said he’d foot the expenses.
The meeting occurred. Ramachandra Rao wrote about it later, in these words:
Several years ago, a nephew of mine, perfectly innocent of mathematics, spoke to me, “Uncle, I have a visitor who talks of mathematics; I do not understand him; can you see if there is anything to his talk?” And in the plenitude of my mathematical wisdom, I condescended to permit Ramanujan to walk into my presence. A short uncouth figure, stout, unshaved, not overclean, with one conspicuous feature—shining eyes—walked in, with a frayed notebook under his arm.
Three times, according to Rajagopalachari, Ramanujan met with the great man. The first time, Ramachandra Rao asked to keep Ramanujan’s papers a few days. The second time, having perused them, he said he’d never seen anything like Ramanujan’s theorems, but since he could make nothing of them, he hoped they would not trouble him again. They did, of course, so now, on this third occasion, Ramachandra Rao put things more plainly. Perhaps Ramanujan was sincere, he allowed; but if no moral fraud, he was more than likely an intellectual one. In other words, he doubted that Ramanujan knew what he was talking about.
As the two friends left, Ramanujan mentioned that with him he had his correspondence with Professor Saldhana, the eminent Bombay mathematician. Saldhana, too, had concluded that he couldn’t help him. But many of Ramanujan’s formulas, he’d written in the margins of the sheet of paper Ramanujan had sent him, seemed intriguing indeed. It was just that he could hardly throw the weight of his reputation behind someone working in areas so unfamiliar to him.
This was hardly a ringing endorsement; indeed it differed only slightly from what Ramanujan would hear all through his early years—that his work was not well enough understood to classify as either the fulminations of a crank or the outpourings of a genius. Ramachandra Rao himself, in so many words, had said that; dubious, he’d erred on the side of caution, and decided not to take up Ramanujan’s case. But Saldhana, erring even further on the side of caution, had at least made clear that, whatever else he was, Ramanujan was no crank.
That was enough for the tenacious Rajagopalachari, who saw in Saldhana’s comments a way to allay Ramachandra Rao’s doubts. Back they went—on so fine a knife edge did Ramanujan’s fate hinge—a fourth time. At first, Ramachandra Rao was angry. Here again? Just a few minutes later? But then he was shown the Saldhana correspondence, as well as some of Ramanujan’s easier, more accessible results. “These,” he wrote later, “transcended existing books and I had no doubt that he was a remarkable man. Then, step by step he led me to elliptic integrals, and hypergeometric series. At last, his theory of divergent series, not yet announced to the world, converted me. I asked him what he wanted.”
What he wanted, Ramanujan replied, was a pittance on which to live and work. Or, as Ramachandra Rao later put it, “He wanted leisure, in other words, simple food to be provided to him without exertion on his part, and that he should be allowed to dream on.”
3. “LEISURE” IN MADRAS
He wanted leisure …
The word leisure has undergone a shift since the time Ramachandra Rao used it in this context. Today, in phrases like leisure activity or leisure suit, it implies recreation or play. But the word actually goes back to the Middle English leisour, meaning freedom or opportunity. And as the Oxford English Dictionary makes clear, it’s freedom not from but “to do something specified or implied” [emphasis added]. Thus, E. T. Bell writes of a famous seventeenth-century French mathematician, Pierre de Fermat, that he found in the King’s service “plenty of leisure”—leisure, that is, for mathematics.
So it was with Ramanujan. It was not self-indulgence that fueled his quest for leisure; rather, he sought freedom to employ his gifts. In his Report on Canara, Malabar and Ceded Districts, Thackeray spoke of the “leisure, independence and high ideals” that had propelled Britain to its cultural heights. The European “gentleman of leisure,” free from the need to earn a livelihood, presumably channeled his time and energy into higher moral and intellectual realms. Ramanujan did not belong to such an aristocracy of birth, but he claimed membership in an aristocracy of the intellect. In seeking “leisure,” he sought nothing more than what thousands born to elite status around the world took as their due.
And remarkably—in a testament to his stubbornness as much as his brains—he found it.
That he was a Brahmin probably helped. Ramanujan was poor, from a family that sometimes lacked enough to eat. But in India, economic class counted for less than caste. Being a Brahmin gave him access to circles otherwise closed to him. In fact, virtually all those whom Ramanujan met during these years were Brahmins. Ramaswami Iyer was a Brahmin. So was Seshu Iyer. So was Ramachandra Rao. Had Ramanujan been of another caste, he might likewise have sought, and received, help from wealthy and influential castemen. But in no other caste did prestige, connections, and a taste for the life of the mind merge so naturally as they did among Brahmins.
As a Brahmin, Ramanujan may also have felt freer to seek the sort of constructive idleness he thought he needed—and perhaps even, in some measure, conceived as his due. Traditionally, Brahmins were recipients of alms and temple sacrifices; earning a livelihood was for them never quite the high and urgent calling it was for others. Uncharitably, it might be said that Ramanujan exhibited a prima donna-like self-importance that left him unwilling to study what he had no wish to study, or to work for any reason but to support his mathematics. Less harshly—and, on balance, with greater justice—he was a secular sanyasi.
• • •
Ramachandra Rao sent Ramanujan back to Seshu Iyer, saying it would be cruel to let him rot in a backwater like Nellore. No, he would not give him a job in the local taluk office but rather would seek for him some scholarship to which, despite his penchant for failing examinations, he might be eligible. Meanwhile, let him stay in Madras; he, Ramachandra Rao, would pay his way.
Monthly, from then on, Ramanujan began receiving a money order for twenty-five rupees. It wasn’t much. But it was e
nough to free him from economic cares. Life opened up for him. Now, more decisively than before, he left the Kumbakonam of his youth behind and, from early 1911 and for the next three years, stepped into the wider world of South India’s capital, Madras.
• • •
It was the fifth-largest city in the British Empire and, after Calcutta and Bombay, third-largest on the subcontinent. Some traced its name to the legend of a fisherman named Madarasen; others to a corruption of Mandarajya, meaning realm of the stupid, or even Madre de Dios, Portuguese for mother of God. The city itself, however, was an invention of British colonial policy. The British East India Company bought land at the mouth of the Cooum River, and Fort St. George, which they constructed there in 1642, became the administrative hub of the British presence in South India.
Madras was not a compact city. The 550,000 people who inhabited it in 1910 were spread up and down along the Bay of Bengal for miles, dispersed in quite distinct population centers—Georgetown, Triplicane, Mylapore, Chepauk, and others. Many of these places went back hundreds or thousands of years. Three and a half miles south of the ragged center of town, for example, was Mylapore, site of the revered Kapalaswara Temple. There, St. Thomas the Apostle, patron saint of India, had settled in the first century A.D. But the area was known to the ancient Greeks and Romans, as a port, long before that.
The modern city of Madras slung low over the land, only the occasional gopuram of a thousand-year-old temple punctuating the flatness; no part of the city rose more than fifty feet above sea level. Spread all across it, especially at the sites of old villages, were clusters of “hutments,” one-room dwellings of mud and thatch, tens of thousands of them. But even the more substantial structures with red tile roofs almost never rose higher than the second floor. Over the years, the city had expanded horizontally, not vertically; you’d add an extension to the front or back of the house rather than build another story. Madras, then, was more like a leisurely, sprawling Phoenix or San Diego than a restless, densely packed New York.
There were still large rural tracts within the city, with palm trees and paddy fields, buffalo and washermen in rivers and lagoons, fishermen’s thatched huts and catamarans idled on the beach. Save for a few more crowded districts, the crush of people squeezed onto every square inch that the Westerner today associates with Indian cities was still in the future. The city retained an easygoing village slowness.
It was possible to gaze down from the top of the lighthouse overlooking the harbor and note, as one English visitor did around the turn of the century, that
Madras is more lost in green than the greenest city further north. Under your feet the red huddled roofs of the Black Town [the adjacent native quarter] are only a speck. On one side is the bosom of the turquoise sea, the white line of surf, the leagues of broad, empty, yellow beach; on the other, the forest of European Madras, dense, round-polled green rolling away southwards and inland till you can hardly see where it passes into the paler green of the fields.
That was a European perspective, of course. But among Indians, too, Madras was regarded as slower and more congenial, greener and more spacious than a Calcutta or Bombay. It was hard being poor anywhere in India. But it was a little easier in Madras. There was never the cold to bear. And being so removed from the North, so much a regional capital, so much South Indian, the city felt comfortable and familiar to the thousands who, like Ramanujan, had moved to it from towns and villages across the South.
• • •
In May 1911, Ramanujan left the place he shared on Venkatanarayan Lane and moved to a little alley boarding house, on Swami Pillai Street, bearing the inflated name “Summer House.” There he lived for the rest of the year and much of 1912 with close to a dozen others, mostly students, who frequented a Brahmin-run restaurant on Pycroft’s Road, the main street of a neighborhood known as Triplicane.
A few minutes’ walk down Pycroft’s, right beside Presidency College, lay the beach. Even then it was a Madras landmark, a place anyone who’d visited the city for even a few days always remembered. It was not just a beach, but a freak of nature, a sweep of sand piled up by the roaring surf over the eons, that then had been refined, manicured, and developed by an otherwise obscure Madras governor, one Mountstuart George Grant-Duff, back in the 1880s. At the end of the long sloping sand, the breakers rumbled. Yet so deep was the beach that, having once stepped onto it, it was as if you still had a great desert to cross to reach them.
It was here that Ramanujan would come, letting his mathematical ruminations percolate as he strolled along by the sea. Or else, come the cooler hours of the evening, he would come with his friends, plunking himself down on the light brown sand, flecked with tiny fragments of seashell, and spin occult stories until long after dark.
There was an openness out here, away from the hot, dusty streets of Triplicane, a delightful coolness. Looking inland, Ramanujan could see the domed clock tower of Presidency College, made gold by the setting sun. Looking out to sea, he could spy merchant vessels—distant gray shapes, and others, closer to shore, all cargo booms and bright paint—plying their way up the coast from Colombo, in Ceylon, and from around the southern tip of India, bound for Madras.
Lightened by the load Ramachandra Rao’s generosity had lifted from his shoulders, Ramanujan was happy, or something close to it. Now, after that anxious, groping two years following his marriage, he was surrounded by friends, doing what he liked to do, carefree and cheerful. C. R. Krishnaswami Iyer, who’d known him at Pachaiyappa’s and now shared a room with him in Summer House, remembered how once Ramanujan stayed up exclaiming on astronomical wonders till late into the night. Finally, Krishnaswami’s cousin, his sleep shattered by Ramanujan’s monologue, poured a pot of water over him; that would cool his fevered brain, he said. But Ramanujan took it all in stride. Ah, yes, a refreshing Gangasnanam—a purging bath in the River Ganges; could he have another?
1911 was a good and hopeful year. It was the year the capital of India was shifted, with great pomp and ceremony, from Calcutta to Delhi. The year a new sewer system, complete with underground conduits, sand filters, and pumps, was being installed in Madras. The year its oil-lit streets began to give way to electricity. And it was the year Srinivasa Ramanujan’s first paper appeared, in the Journal of the Indian Mathematical Society—representing his initial step onto the stage of Indian mathematics, and the world’s.
4. JACOB BERNOULLI AND HIS NUMBERS
Five years before, in late 1906, several dozen professors at colleges in Madras, Mysore, Coimbatore, and elsewhere in South India received a letter from V. Ramaswami Iyer, in which he proposed the formation of a mathematical society. Behind the idea lay simple want. Just as Ramanujan had so depended on whatever few mathematical books had come his way, so did Indian mathematicians generally suffer a lack of books and journals from Europe and America. The society, in Ramaswami’s conception, would subscribe to journals and buy books, then circulate them to members. Twenty-five rupees per year from even half a dozen members would be enough to get the society off the ground.
He wound up with 20 founding members, all hungry for mathematical fellowship, and what was known first as the Analytical Club, then the Indian Mathematical Society, was born. Soon it was publishing a journal of its own. Just a dozen years later, at its second conference in Bombay, it would claim 197 members and be circulating 35 European and American journals.
These events awaited modern times. But a thousand years before the British came, Indians were doing mathematics. Before the seventh century, while the West was still mired in awkward Roman numerals, India had introduced the numerals we use today. The zero, a symbol expressing nothingness, represented a particular triumph; it may go back to as early as the second century B.C. but definitely appeared in a book in the third century and on the wall of a temple near Gwalior, in central India, in the ninth (where it helped specify a flower garden as 270 units long).
Many of India’s contributions to mathematics were spurred by
the need to know, based on astronomical factors, the correct times for Vedic ceremonies. Algebra, geometry, and trigonometry were all thereby enriched. Figures like Aryabhata, born in A.D. 476, who established one of the earliest and best values for π, and Brahmagupta, 150 years later, left theorems even now associated with their names.
It was a rich tradition, but one quite different from that of Greece, the cradle of Western mathematics. Whereas the Greeks, especially Euclid, emphasized formal proof, as in the step-by-step process high school students first encounter in geometry, Indian mathematics stressed the results themselves, however obtained. And without that winnowing out of mathematical dross that formal proof achieved, Indian mathematics was wildly uneven; some of it was just plain wrong. One Muslim writer noted in a book about India that Hindu mathematics was “a mixture of pearl shells and sour dates … of costly crystal and common pebbles.”
By the twentieth century, the pearl shells and crystal had long lain buried in the dust of time. For centuries, India had stood its mathematical ground against the rest of the world. But now, that was ancient history; of late it had added little to the world’s mathematical treasure. Only a line of brilliant mathematicians in Kerala, on the subcontinent’s southwest tip, broke the gloom that otherwise extended back to the great Bhaskara of the twelfth century. The birth of the Mathematical Society could not ensure a rebirth. But its founders—hungry to connect with the West, proud of their country’s heritage yet soberly aware that reverence for the past was no substitute for present achievement—surely hoped it did.
The Man Who Knew Infinity Page 11
