The Man Who Knew Infinity

by Robert Kanigel

  Meanwhile, he ignored the physiology, the English, the Greek and Roman history he was supposed to be studying; he was no longer, if he’d ever been, “well-rounded.” Back in 1897, his high standing on the Primary Examination had depended on excelling in many subjects, including English. Letters known to be written by him later, while showing no special grace, were competent enough, as were his mathematics notebooks when he used words, rather than symbols, to explain something. Yet now, at Government College, he failed English composition. “To the college authorities,” E. H. Neville observed later, “he was just a student who was neglecting flagrantly all but one of the subjects he was supposed to be studying. The penalty was inevitable: his scholarship was taken away.”

  His mother, of course, was incensed and went to see the principal. How could he refuse her son a scholarship? He was unequaled in mathematics. They had never seen his like. The principal was polite, but firm. Rules were rules. Her son had failed the English composition paper, and miserably so. That was that.

  Ramanujan’s scholarship was no matter of mere prestige to him. Tuition was thirty-two rupees per term—as much as his father made in a month and a half. The scholarship insulated him from it; it enabled him to attend. He needed it.

  Still, he managed to hang on for a few months, showing up for class enough to earn a certificate in July 1905 attesting to his attendance. The effort must have taxed him. He’d lost the scholarship, and everybody knew it. His parents were under a heavy financial burden; he knew that, too. He felt pressure to do well in his other subjects, yet he didn’t want to lay mathematics aside for their sake. He was torn and miserable.

  He endured the situation until he could endure it no longer. In early August 1905, Ramanujan, seventeen years old, ran away from home.

  3. FLIGHT

  As the hot breeze poured through the open windows of the railway car, Ramanujan watched the South Indian countryside slip by at twenty-five miles an hour. Villages of thatched roofs weathered to a dull barn-gray; intense pink flowers poking out from bushes and trees; palm trees, like exclamation points, punctuating the rice field flatness. From a distance, the men in the fields beside the tracks were little more than brown sticks, their dhotis and turbans white cotton puffs. The women were bright splashes of color, their orange and red saris set off against the startling green of the rice fields.

  A snapshot might have recorded the scene as a charming bucolic tableau, but Ramanujan saw people everywhere engaged in purposeful activity. Men tending cattle. Women, stooped over in the fields, nursing the crops. Sometimes they worked alone, sometimes together in groups of a dozen or more, baskets perched atop their heads, fetching water from streams. Occasionally, a child with its mother would glance up from the surrounding fields and wave at the train bearing Ramanujan north to Vizagapatnam.

  • • •

  For eons, transportation in India, by bullock cart or the one-horse vehicle known as a jutka, had been painfully slow. Roads were terrible. Even by Ramanujan’s time, only about an eighth of Tanjore District’s seventeen hundred miles of road were “metalled,” or paved with limestone or other rock. The difference was considerable. Cart drivers forced to travel on bumpy dirt roads thickly covered by dust or mud, rather than a metalled one, normally planned on carrying two-thirds the load, at two-thirds the speed. Twenty-five miles was a good day’s journey.

  The coming of the railroad had changed Indian life. It was the crowning engineering achievement of the British Raj, emerging in the midnineteenth century to knit the far-flung country together. In the South, the first lines had been laid in 1853, and in 1874 they began pushing south from Madras. In 1892, with the line to Vizagapatnam still unfinished, to get there from Kumbakonam could still take three weeks by train, bullock cart, and canal boat. By the following year, construction now complete, the trip took one day.

  The railroads were the great leveler; everyone used them, irrespective of caste. “When you get to the third-class railway carriage you override even such a tough obstacle as caste,” an English writer from this period noted. “Into it are bundled Brahmin and Pariah; they sit on the same seat; they rub shoulders who might not mingle shadows. ‘You must drop your caste,’ says the railway, ‘if you want to travel at a farthing a mile’; and it is dropped—to be resumed again outside the station.”

  Ramanujan had grown up with the railways—as when, a child, he’d been shuttled among schools in Kumbakonam, Kanchipuram, and Madras. And now, in 1905, in the wake of losing his scholarship at Government College, the rails facilitated his flight.

  Madras was 194 miles up the tracks of the South Indian Railways from Kumbakonam. And Vizagapatnam, following the main line along the coast, was 484 miles beyond that. A town of about forty thousand, it lay in an angle of the Bay of Bengal formed by a promontory known as the “Dolphin’s Nose.” Boasting the only natural harbor on India’s east coast, it was a flourishing seaport; through it, yarn and piece goods entered India and manganese ore and raw sugar left. A new lighthouse had just been built near the anchorage. Now the engineers were planning to dredge the backwater and river and build new docks. Vizagapatnam was on the move.

  And it was for this largely Telugu-speaking town halfway up the coast to Calcutta that Ramanujan, informing no one, set out. Fragmentary accounts from the period variously give as reasons the influence of a friend, the pursuit of a scholarship, the wish to find a patron, or—under pressure from his father—a job. But invariably, they also use language like “owing to disappointment,” “ran away,” and “too sensitive to ask his parents for help,” and it’s plain that whatever Ramanujan may have sought in Vizagapatnam, he was running from something, too.

  There is evidence that the family, distraught over their son’s disappearance, advertised in newspapers for him; that his father went house to house in Madras and Trichinopoly, looking for him. Otherwise, details of Ramanujan’s impetuous flight are scanty. Except that soon, probably by September, his parents had him safely back in Kumbakonam.

  • • •

  It was the first of the Great Disappearances, the first of numerous such occasions on which Ramanujan would abruptly vanish, and about which little subsequently became known. But it was not the first time he’d taken abrupt and heedless action in the wake of what he deemed an intolerable blow to his self-esteem.

  Back in 1897, aged nine, when he took his primary exam at Town Hall in Kumbakonam, he had scored a 42 out of 45 on the arithmetic portion, while a friend, K. Sarangapani Iyengar, got a 43. Hurt and angry, Ramanujan refused to speak to him. Sarangapani was mystified; what was the big deal? Trying to mollify him, he pointed out that in the other subjects Ramanujan had scored higher. Didn’t matter, grumbled Ramanujan—in arithmetic he always scored highest. This time he had not, and everyone knew it. It was all too much to bear—whereupon he ran home crying to his mother.

  Later, in high school, Ramanujan saw how trigonometric functions could be expressed in a form unrelated to the right triangles in which, superficially, they were rooted. It was a stunning discovery. But it turned out that the great Swiss mathematician Leonhard Euler had anticipated it by 150 years. When Ramanujan found out, he was so mortified that he secreted the papers on which he had recorded the results in the roof of his house.

  Adolescent behavior quirks, irrelevant in the broad sweep of a genius’s life? Perhaps. But together, and coupled with many other such instances later, they suggest an almost pathological sensitivity to the slightest breath of public humiliation. When, years later, Ramanujan stopped getting letters from a once-close friend, he wrote to the friend’s brother that perhaps “he is too sorry for his failure in the Exam to write to me.” Plainly, it was behavior to which he was keenly sensitive.

  Shame is what psychologists call this sensitivity to public disgrace, something quite distinct from “guilt.” Guilt, roughly speaking, comes from doing wrong, shame at being discovered, or at the prospect of being discovered, in some failure or vice; you’re caught masturbating, say, o
r with your hand in the till. “An obligatory aspect of shame is the role discovery plays,” writes Leon Wurmser, a University of Maryland psychiatrist, in The Mask of Shame. “It is usually a more or less sudden exposure, and exposure that abruptly brings to light the discrepancy between expectation and failure.” The feeling is that of sudden, sharp, inescapable humiliation—of a yawning gap between who you say you are and who your failures reveal you to be, of an ugly stain upon your public face.

  It is not necessary to actually be discovered, Wurmser points out; one can feel shame before oneself, at the mere thought of discovery. “We may wince at ourselves in the mirror and despise and degrade ourselves for the dishonor we feel within… . No one else has to see this stain—the shame remains.”

  The single most reliable marker of the shame syndrome is the impulse to flee. Writes Wurmser: “Hiding is intrinsic to and inseparable from the concept of shame.” One experiences “the wish to hide, to flee, to ‘cover one’s face,’ to ‘sink into the ground.’ ” And that’s just what Ramanujan did when faced with the ignominy of scoring only second in the arithmetic exam; in hiding evidence that his discovery was in fact rediscovery; and in running off to Vizagapatnam. One account has Ramanujan suffering a “mental aberration” during this period. Another calls it “a temporary unsoundness of mind.” Whatever it was, acutely felt shame may have triggered it.

  Years later, the memory of his school failure would make Ramanujan seek assurance that a scholarship he had been offered would not leave him with another examination to pass. The Government College fiasco humiliated him, apparently to the point of psychic trauma. His impulse, as it would be all his life, was to escape. And in fleeing to Vizagapatnam, he yielded to it.

  Nor was it incongruous that one who, as mathematician, would prove so free from the intellectual blinders of the crowd should care so deeply how the crowd perceived him. Ramanujan was supremely self-assured about his mathematical gifts. Yet socially, he was a thoroughgoing conformist. If he cared not at all to follow mathematical paths others had trod, he cared deeply how others esteemed the path he had chosen.

  Later, while in England and learning of a mathematics prize, he breathlessly inquired whether he might apply for it; formal, outward acknowledgment was no matter of indifference to him, and he never pretended otherwise. Similarly, when the British awarded him a high honor, his letter acknowledging word of it fairly bubbled over with excitement.

  Was he respected as a mathematician? Was he deemed a dutiful son, a good Brahmin? Did he hold an important scholarship? Had he won a prize? The answers, as outward markers of acceptance or success, counted—and certainly never more so than now, as a teenager, at an age of exquisite sensitivity to the opinions of others.

  Tales of Ramanujan’s youth reveal a boy content to camp out on the pial of his house and work at mathematics, outwardly oblivious to the raucous play of his friends out on the street. Often, wrapped up in mathematics, he was oblivious. At other times, though, he must have wanted to be part of it. His thirst for public acknowledgment of his gifts, his pain when denied it, and his sensitivity to social slight, show how deeply, at another level, he really cared.

  4. ANOTHER TRY

  Pachaiyappa Mudaliar, born in 1784 of a destitute rural family, was a dubash, a master of two languages, who thereby served as a vital link in commerce with the British. By the time he was twenty-one he had amassed a fortune. At his death, aged forty-six, he left great heaps of it to charity. The college bearing his name, founded in 1889 and open only to Hindus, was by 1906 a respectable institution. Surely the building in which it was housed did nothing to sully its reputation—a great columned structure modeled on the Temple of Theseus in Athens, located on what was then known as China Bazaar Road in the busy Georgetown section of Madras.

  It was to Pachaiyappa’s—pronounced Pa-shay-a-pas—College that Ramanujan was bound when, one day early in 1906, he arrived at Egmore Station in Madras, so tired and disoriented that he fell asleep in the waiting room. A man woke him, took him back to his house, fed him, gave him directions, and sent him on his way to the college.

  In India a college degree was no mere prerequisite for a good job; it virtually guaranteed you one, and a good start in your career. You earned a degree not by taking so many courses, or accumulating so many credits, but by passing an examination administered by the University of Madras; the “university” was not teachers and students, but merely an examining body. “To appear and succeed at the university examinations has been the ambition of every youth of promise,” an English writer from the period noted. Some of Ramanujan’s contemporaries at the college in Kumbakonam transferred to Presidency College in Madras, the crown jewel of the South Indian educational system, in hopes of better preparing for the all-important examination.

  For most who sought a degree, though, it was all in vain. Of those taking the matriculation exam—equivalent to a high school diploma but more eagerly sought—half failed. A similar proportion fell out at each degree step along the way; failures of Pachaiyappa’s students on the F.A. exam ran to 80 percent. In 1904, fewer than five thousand boys—and just forty-nine girls—were enrolled in the presidency’s colleges and professional schools. And among all its forty-three million people, the number earning an F.A. degree each year came to barely a thousand.

  Ramanujan, eighteen years old now, aimed to be one of them. A year after his failure in Kumbakonam, he was giving college another try in Madras.

  For a time, he lived a few blocks away from Pachaiyappa’s in a small lane off the fruit bazaar on Broadway in his grandmother’s house. It was dingy and dark. And the air seemed to hang, static and close. But at least he was back in school.

  Ramanujan’s new math teacher, shown his notebooks, came away so impressed that he introduced him to the principal—who, on the spot, awarded him a partial scholarship. Though interrupted by a bad bout of dysentery that brought him back to Kumbakonam for three months, Ramanujan’s early days at Pachaiyappa’s College seemed filled with new promise.

  N. Ramanujachariar, the math teacher, would take two sliding blackboards to work out a problem in algebra or trigonometry, reaching the solution in a dozen scrawled mathematical steps; Ramanujan would get up and show how to solve it in three or four. “Uh, what was that?” Ramanujachariar, who was a little deaf, would have to ask. So Ramanujan would obligingly run through it again. Sometimes the teacher would interrupt the lecture, turn to Ramanujan, and ask, “And what do you think, Ramanujan?” The prodigy from Kumbakonam tended to jump around the problem, working out key steps in his head but omitting them from his exposition—leaving his classmates thoroughly confused.

  Sometimes he’d get together with the college’s senior math professor, P. Singaravelu Mudaliar. Singaravelu—something of a catch for Pachaiyappa’s, having formerly been an assistant professor of mathematics at the more prestigious Presidency College across town—was struck by Ramanujan’s gifts. Together the two of them would tackle problems appearing in mathematical journals. If Ramanujan couldn’t crack one of them, he’d give it to Singaravelu to work on overnight; invariably the professor couldn’t solve it, either.

  Everyone was struck by Ramanujan’s gifts; but there was nothing new in that. Nor was there anything new in that nothing tangible came of it. For his experience in Kumbakonam now repeated itself at Pachaiyappa’s. At Government College, it was English that had been his undoing. Now, among other subjects remote from mathematics he had to master, there was physiology. And this he found not merely boring, but repellent.

  The text was a small book, Physiology for Beginners, written by two Cambridge dons, Michael Foster and Lewis E. Shore, published in 1894, and consisting mostly of the kind of flat descriptive accounts that passed for science in the late nineteenth century: “At the upper left-hand part of the stomach is the opening into it of the esophagus, a tube which passes from the mouth down the neck, through the thorax, and piercing the diaphragm, enters the stomach.” It was full of elaborate drawings s
howing a rabbit with its skin peeled back, its internal organs revealed in graphic detail; a sheep’s heart filling most of one page, a cutaway of a human mouth and tongue on another.

  This was as far from the abstract heights of mathematics as you could get; if mathematics was art deco, with its cool geometric elegance, physiology was a kind of art nouveau, fluid and sumptuous. It was a world for which Ramanujan, as a strict vegetarian, could scarcely have had much taste: “Procure a rabbit which has been recently killed, but not skinned,” chapter 3 of the text began. “Fasten the rabbit on its back by its four limbs to a board, and then, with a small sharp and pointed knife and a pair of scissors …”

  Ramanujan reacted to all this with a skittish—and uncharacteristic—sarcasm. The professor would dissect a big, anesthetized frog, earnestly pointing out physiological similarities to humans, only to have Ramanujan pipe up with, And where is the serpent in this frog?—apparently a reference to the nade, or serpent power, that Hindu tradition ascribes to human nature. Another time, on an exam covering the digestive system, Ramanujan simply wrote a few lines in the answer book and handed it back unsigned: “Sir, this is my undigested product of the Digestion chapter.” The professor had no trouble figuring whose it was.