Hardy's Lectures

In lectures, his enthusiasm and delight in the subject fairly spilled over. “One felt,” wrote one of his later students, E. C. Titchmarsh, “that nothing else in the world but the proof of these theorems really mattered.” Norbert Wiener, the American mathematical prodigy who would later create the field known as “cybernetics,” attended Hardy’s lectures. “In all my years of listening to lectures in mathematics,” he would write, “I have never heard the equal of Hardy for clarity, for interest, or for intellectual power.” Around this time, a pupil of E. W. Barnes, director of mathematical studies at Trinity, sought Barnes’s advice about what lectures to attend. Go to Hardy’s, he recommended. The pupil hesitated. “Well,” replied Barnes, “you need not go to Hardy’s lectures if you don’t want, but you will regret it—as indeed,” recalled the pupil many years later, “I have.” Others who missed his lectures may not, in retrospect, have felt such regret: so great was Hardy’s personal magnetism and enthusiasm, it was said, that he sometimes diverted to mathematics those without the necessary ability and temperament.

But as lucid as were his lectures, it was his writing that probably had more impact. Later, speculating about what career he might have chosen other than mathematics, Hardy noted that “Journalism is the only profession, outside academic life, in which I should have felt really confident of my chances.” Indeed, no field demanding literary craftsmanship could fail to have profited from his attention. “He wrote, in his own clear and unadorned fashion, some of the most perfect English of his time,” C. P. Snow once said of him. That Hardy’s impressions of Ramanujan would be so relentlessly quoted, and would go so far toward fixing Ramanujan’s place in history, owes not alone to his close relationship with Ramanujan but to the sheer grace with which he wrote about him.

**

Thought, Hardy used to say, was for him impossible without words. The very act of writing out his lecture notes and mathematical papers gave him pleasure, merged his aesthetic and purely intellectual sides. Why, if you didn’t know math was supposed to be dry and cold, and had only a page from one of his manuscripts to go on, you might think you’d stumbled on a specimen of some new art form beholden to Chinese calligraphy. Here were inequality symbols that slashed across the page, sweeping integral signs an inch and a quarter high, sigmas that resonated like the key signatures on a musical staff. There was a spaciousness about how he wrote out mathematics, a lightness, as if rejecting the cramped, ungenerous formalities of the printed notation. He was like a French impressionist, intimating worlds with a few splashes of color, not a maker of austere English miniatures.

British Math vs European Math

Since the seventeenth century, Britain had stood, mathematically, with its back toward Europe, scarcely deigning to glance over its shoulder at it. Back then, Isaac Newton and the German mathematician Gottfried Wilhelm von Leibniz had each, more or less independently, discovered calculus. Controversy over who deserved the credit erupted even while both men lived, then mushroomed after their deaths, with mathematicians in England and on the Continent each championing their compatriots. Newton was the premier genius of his age, the most fertile mind, with the possible exception of Shakespeare’s, ever to issue from English soil. And yet he would later be called “the greatest disaster that ever befell not merely Cambridge mathematics in particular but British mathematical science as a whole.” For to defend his intellectual honor, as it were, generations of English mathematicians boycotted Europe—steadfastly clung to Newton’s awkward notational system, ignored mathematical trails blazed abroad, professed disregard for the Continent’s achievements. “The Great Sulk,” one chronicler of these events would call it.

In calculus as in mathematics generally, the effects were felt all through the eighteenth and nineteenth centuries and on into the twentieth. Continental mathematics laid stress on what mathematicians call “rigor,” the kind to which Hardy had first been exposed through Jordan’s Cours d’analyse and which insisted on refining mathematical concepts intuitively “obvious” but often littered with hidden intellectual pitfalls. Perhaps reinforced by a strain in their national character that sniffed at Germanic theorizing and hairsplitting, the English had largely spurned this new rigor. Looking back on his Cambridge preparation, Bertrand Russell, who ranked as Seventh Wrangler in the Tripos of 1893, noted that “those who taught me the infinitesimal Calculus did not know the valid proofs of its fundamental theorems and tried to persuade me to accept the official sophistries as an act of faith. I realized that the Calculus works in practice but I was at a loss to understand why it should do so.” So, it is safe to say, were most other Cambridge undergraduates.

Calculus rests on a strategy of dividing quantities into smaller and smaller pieces that are said to “approach,” yet never quite reach, zero. Taking a “limit,” the process is called, and it’s fundamental to an understanding of calculus—but also, typically, alien and slippery territory to students raised on the firm ground of algebra and geometry. And yet, it is possible to blithely sail on past these intellectual perils, concentrate on the many practical applications that fairly erupt out of calculus, and never look back.

In textbooks even today you can see vestiges of the split—which neatly parallels that between Britain and the Continent in the nineteenth century: the author briefly introduces the limit, assumes a hazy intuitive understanding, then spends six chapters charging ahead with standard differentiation techniques, maxima-minima problems, and all the other mainstays of Calc 101 . . . until finally, come chapter 7 or so, he steps back and reintroduces the elusive concept, this time covering mine-strewn terrain previously sidestepped, tackling conceptual difficulties—and stretching the student’s mind beyond anything he’s used to.

Well, the first six chapters of this generic calculus text, it could be said, were English mathematics without the Continental influence. Chapter 7 was the new rigor supplied by French, German, and Swiss mathematicians. “Analysis” was the generic name for this precise, fine-grained approach. It was a world of Greek letters, of epsilons and deltas representing infinitesimally small quantities that nonetheless the mathematicians found a way to work with. It was a world in which mathematics, logic, and Talmudic hairsplitting merged.

First Gauss, Abel, and Cauchy had risen above the looser, intuitive nostrums of the past; later in the century, Weierstrass and Dedekind went further yet. None of them were English. And the English professed not to care. Why, before the turn of the century, Cauchy—the Cauchy, Augustin Louis Cauchy, the Cauchy who had launched the French school of analysis, the Cauchy of the Cauchy integral formula—was commonly referred to around Cambridge as “Corky.”

Since Newton’s time, British mathematics had diverged off on a decidedly applied road. Mathematical physics had become the British specialty, dominated by such names as Kelvin, Maxwell, Rayleigh, and J. J. Thomson. Pure math, though, had stultified, with the whole nineteenth century leaving England with few figures of note. “Rigor in argument,” J. E. Littlewood would recall, “was generally regarded—there were rare exceptions—with what it is no exaggeration to call contempt; niggling over trifles instead of getting on with the real job.” Newton had said it all; why resurrect these arcane fine points? Calculus, and the whole architecture of mathematical physics that emanated from it, worked.

And so, England slept in the dead calm of its Tripos system, where Newton was enshrined as God, his Principia Mathematica the Bible. “In my own Tripos in 1881, we were expected to know any lemma [a theorem needed to prove another theorem] in that great work by its number alone,” wrote one prominent mathematician later, “as if it were one of the commandments or the 100th Psalm. . . . 

Cambridge became a school that was self-satisfied, self-supporting, self-content, almost marooned in its limitations.” Replied a distinguished European mathematician when asked whether he had seen recent work by an Englishman: “Oh, we never read anything the English mathematicians do.”

The first winds of change came in the person of Andrew Russell Forsyth, whose Theory of Functions had begun, in 1893, to introduce some of the new thinking—though by this time it wasn’t so new anymore—from Paris, Göttingen, and Berlin. Written in a magisterial style, it burst on Cambridge, as E. H. Neville once wrote, “with the splendour of a revelation”; some would argue it had as great an influence on British mathematics as any work since Newton’s Principia. By the standards of the Continent, however, it was hopelessly sloppy and was soundly condemned there. “Forsyth was not very good at delta and epsilon,” Littlewood once said of him, referring to the Greek letters normally used for dealing with infinitesimally small quantities. Still, it helped redirect the gaze of English mathematicians toward the Continent. It charted a course to the future, but did not actually follow it.

That was left to Hardy.

Cambridge, A Society of Bachelors

That Hardy’s life was spent almost exclusively in the company of other men, that he scarcely ever saw a woman, was, in those days, not uncommon. After all, among Havelock Ellis’s thousand or so British “geniuses,” 26 percent never married. In the academic and intellectual circles of which Hardy was a part, such a monastic sort of life actually represented one pole of common practice.

Thus, at Cranleigh School, all the teachers, except for the House staff, were men, most of them bachelors; dormitory masters had to be bachelors. Winchester was the same way. So was Cambridge. “In my day we were a society of bachelors,” wrote Leslie Stephen in Some Early Impressions of his time at Cambridge during the early 1860s. “I do not remember during my career to have spoken to a single woman at Cambridge except my bed-maker and the wives of one or two heads of houses.”

Not much had changed by the time Hardy reached Cambridge a generation later. Among the twenty or so colleges, two—Girton and Newnham—had been established for women in the previous two decades. But though women, with the lecturer’s consent and chaperoned by a woman don, could attend university lectures, by 1913 they still kept mostly to themselves and played little part in undergraduate life. Until 1882, college fellows couldn’t marry, but even after that most fellows remained bachelors. In 1887, a proposal was made to offer degrees to women; it was soundly defeated. Ten years later, on a May day in 1897, a straw-hatted mob thronged outside the Senate House, where the matter was again being taken up, demonstrating against the measure. A woman was hanged in effigy. A large banner advised (after Act II, Scene I of Much Ado About Nothing) “Get you to Girton, Beatrice. Get you to Newnham. Here’s no place for you maids.”

It was an almost laughably artificial environment, with dons left woefully ignorant of domestic life. One time at St. John’s College, the story goes, an elderly bachelor at High Table congratulated someone on the birth of his son. “How old is the little man?” he asked.

“Six weeks,” came the reply.

“Ah,” said the bachelor don, “just beginning to string little sentences together, I suppose.”

About the only time Hardy and other fellows encountered women was among the bedmakers who tidied up college rooms—and they were said to be selected for their plainness, age, and safely married status, presumably so as to minimize the distraction they represented to students and fellows of the colleges.

**

There was a hauntedness to Hardy that you could see in his eyes. “I suspect,” remembered an Oxford economist, Lionel Charles Robbins, who knew him later, that “Hardy found many forms of contact with life very painful and that, from a very early stage, he had taken extensive measures to guard himself against them. Certainly in his friendlier moments—and he could be very friendly indeed—one was conscious of immense reserves.” Always, he kept the world at bay. The obsession with cricket, the bright conversation, the studied eccentricity, the fierce devotion to mathematics—all of these made for a beguiling public persona; but none encouraged real closeness. He was a friend of many in Cambridge, an intimate of few.

In the years after 1913, Hardy would befriend a poor Indian clerk. Their friendship, too, would never ripen into intimacy.

Hardy

Hardy was forever judging, weighing, comparing. He rated mathematicians, the work they did, the books and papers they wrote. He held firm opinions on everything, and expressed them. When a Cambridge club to which he’d belonged moved to change its official colors, Hardy took six pages to attack the plan. He faulted a sacrosanct academic tradition of almost two centuries’ standing, and condemned it, unrelentingly, for more than twenty years. All his enthusiasms, peeves, and idiosyncrasies were like that—sharp, unwavering, vehement. He hated war, politicians as a class, and the English climate. He loved the sun. He loved cats, hated dogs. He hated watches and fountain pens, loved The Times of London crossword puzzles

Lack of Paper

“Once, the story goes, a friend found him around the docks during working hours, prowling for packing paper on which to work calculations. Another time, Sir Francis called Narayana Iyer into his office. How, he demanded to know, sternly regarding his aide, had these pages of mathematical results gotten mixed into this important file? Was he, perhaps, using office time to dabble in mathematics? Narayana Iyer pleaded innocent, claimed the math wasn’t in his handwriting at all, that perhaps it was Ramanujan’s work. Sir Francis laughed. Of course it was Ramanujan’s work. He’d known as much all along.”

Ramanujan

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.

It was into this nascent new world that Ramanujan “came out,” as it were, as a mathematician in 1911.”

“An equation has no meaning unless it expresses a thought of God”

“In the West, there was an old debate as to whether mathematical reality was made by mathematicians or, existing independently, was merely discovered by them. Ramanujan was squarely in the latter camp; for him, numbers and their mathematical relationships fairly threw off clues to how the universe fit together. Each new theorem was one more piece of the Infinite unfathomed. So he wasn’t being silly, or sly, or cute when later he told a friend, “An equation for me has no meaning unless it expresses a thought of God.”

Ramanujan's Notebooks

“The first of the published Notebooks that come down to us today, which Ramanujan may have prepared around the time he left Pachaiyappa’s College in 1907, was written in what someone later called “a peculiar green ink,” its more than two hundred large pages stuffed with formulas on hypergeometric series, continued fractions, singular moduli . . .

But this “first” notebook, which was later expanded and revised into a second, is much more than mere odd notes. Broken into discrete chapters devoted to particular topics, its theorems numbered consecutively, it suggests Ramanujan looking back on what he has done and prettying it up for formal presentation, perhaps to help him find a job. It is, in other words, edited. It contains few outright errors; mostly, Ramanujan caught them earlier. And most of its contents, arrayed across fifteen or twenty lines per page, are entirely legible; one needn’t squint to make out what they say. No, this is no impromptu record, no pile of sketches or snapshots; rather, it is like a museum retrospective, the viewer being guided through well-marked galleries lined with the artist’s work.

Or so they were intended. At first, Ramanujan proceeded methodically, in neatly organized chapters, writing only on the right-hand side of the page. But ultimately, it seems, his resolve broke down. He began to use the reverse sides of some pages for scratch work, or for results he’d not yet categorized.

“Mathematical jottings piled up, now in a more impetuous hand, with some of it struck out, and sometimes with script marching up and down the page rather than across it. One can imagine Ramanujan vowing that, yes, this time he is going to keep his notebook pristine . . . when, working on an idea and finding neither scratch paper nor slate at hand, he abruptly reaches for the notebook with its beckoning blank sheets—the result coming down to us today as flurries of thought transmuted into paper and ink.

In those flurries, we can imagine the very earliest notebooks, those predating the published ones, coming into being. Ramanujan had set out to prove the theorems in Carr’s book but soon left his remote mentor behind. Experimenting, he saw new theorems, went where Carr had never—or, in many cases, no one had ever—gone before. At some point, as his mind daily spun off new theorems, he thought to record them. Only over the course of years, and subsequent editions, did those early, haphazard scribblings evolve into the published Notebooks that today sustain a veritable cottage industry of mathematicians devoted to their study.”

**

“Two monkeys having robbed an orchard of 3 times as many plantains as guavas, are about to begin their feast when they espy the injured owner of the fruits stealthily approaching with a stick. They calculate that it will take him 2 1/4 minutes to reach them. One monkey who can eat 10 guavas per minute finishes them in 2/3 of the time, and then helps the other to eat the plantains. They just finish in time. If the first monkey eats plantains twice as fast as guavas, how fast can the second monkey eat plantains?”

This charming little problem had appeared some years before Ramanujan’s time in an Indian mathematical textbook. Exotic as it might seem at first, one has but to change the monkeys to foxes, and the guavas to grapes, to recognize one of those exercises, beloved of some educators, supposed to inject life and color into mathematics’ presumably airless tracts. Needless to say, this sort of trifle, however tricky to solve, bears no kinship to the brand of mathematics that filled Ramanujan’s notebooks.

Ramanujan needed no vision of monkeys chomping on guavas to spur his interest. For him, it wasn’t what his equation stood for that mattered, but the equation itself, as pattern and form. And his pleasure lay not in finding in it a numerical answer, but from turning it upside down and inside out, seeing in it new possibilities, playing with it as the poet does words and images, the artist color and line, the philosopher ideas.

Ramanujan’s world was one in which numbers had properties built into them. Chemistry students learn the properties of the various elements, the positions in the periodic table they occupy, the classes to which they belong, and just how their chemical properties arise from their atomic structure. Numbers, too, have properties which place them in distinct classes and categories.

For starters, there are even numbers, like 2, 4, and 6; and odd numbers, like 1, 3, and 5.

There are the integers—whole numbers, like 2, 3, and 17; and nonintegers, like 17 1/4 and 3.778.

Numbers like 4, 9, 16, and 25 are the product of multiplying the integers 2, 3, 4, and 5 by themselves; they are “squares,” whereas 3, 10, and 24, for example, are not.

A 6 differs fundamentally from a 5, in that you can get it by multiplying two other numbers, 2 and 3; whereas a 5 is the product only of itself and 1. Mathematicians call 5 and numbers like it (2, 3, 7, and 11, but not 9) “prime.” Meanwhile, 6 and other numbers built up from primes are termed “composite.”

That happens often in mathematics; a notion at first glance arbitrary, or trivial, or paradoxical turns out to be mathematically profound, or even of practical value. After an innocent childhood of ordinary numbers like 1, 2, and 7, one’s initial exposure to negative numbers, like − 1 or − 11, can be unsettling. Here, it doesn’t require much arm-twisting to accept the idea: If t represents a temperature rise, but the temperature drops 6 degrees, you certainly couldn’t assign the same t = 6 that you would for an equivalent temperature rise; some other number, − 6, seems demanded. Somewhat analogously, imaginary numbers—as well as many other seemingly arbitrary or downright bizarre mathematical concepts—turn out to make solid sense.

Ramanujan’s notebooks ranged over vast terrain. But this terrain was virtually all “pure” mathematics. Whatever use to which it might one day be put, Ramanujan gave no thought to its practical applications. He might have laughed out loud over the monkey and the guava problem, but he thought not at all, it is safe to say, about raising the yield of South Indian rice. Or improving the water system. Or even making an impact on theoretical physics; that, too, was “applied.”

Rather, he did it just to do it. Ramanujan was an artist. And numbers—and the mathematical language expressing their relationships—were his medium.”

Ramanujan's Failure

“Except for math he did poorly in all his subjects, but in physiology he reached particularly impressive lows, often scoring less than 10 percent on exams. He’d take the three-hour math exam and finish it in thirty minutes. But that got him exactly nowhere. In December 1906, he appeared again for the F.A. examination and failed. The following year, he took it again. And failed again.

Government College, Kumbakonam, 1904 and 1905 . . . Pachaiyappa’s College, Madras, 1906 and 1907 . . . In the first decade of the twentieth century, there was no room for Srinivasa Ramanujan in the higher education system of South India. He was gifted, and everyone knew it. But that hardly sufficed to keep him in school or get him a degree.

The System wouldn’t budge.

**

“To bring in money, Ramanujan approached friends of the family; perhaps they had accounts to post, or books to reconcile? Or a son to tutor? One student, for seven rupees a month, was Viswanatha Sastri, son of a Government College philosophy professor. Early each morning, Ramanujan would walk to the boy’s house on Solaiappa Mudali Street, at the other end of town, to coach him in algebra, geometry, and trigonometry. The only trouble was, he couldn’t stick to the course material. He’d teach the standard method today and then, if Viswanatha forgot it, would improvise a wholly new one tomorrow. Soon he’d be lost in areas the boy’s regular teacher never touched.

Sometimes he would fly off onto philosophical tangents. They’d be discussing the height of a wall, perhaps for a trigonometry problem, and Ramanujan would insist that its height was, of course, only relative: who could say how high it seemed to an ant or a buffalo? One time he asked how the world would look when first created, before there was anyone to view it. He took delight, too, in posing sly little problems: If you take a belt, he asked Viswanatha and his father, and cinch it tight around the earth’s twenty-five-thousand-mile-long equator, then let it out just 2π feet—about two yards—how far off the earth’s surface would it stand? Some tiny fraction of an inch? Nope, one foot.”

“Viswanatha Sastri found Ramanujan inspiring; other students, however, did not. One classmate from high school, N. Govindaraja Iyengar, asked Ramanujan to help him with differential calculus for his B.A. exam. The arrangement lasted all of two weeks. You can think of calculus as a set of powerful mathematical tools; that’s how most students learn it and what most exams require. Or else you can appreciate it for the subtle questions it poses about the nature of the infinitesimally small and the infinitely large. Ramanujan, either unmindful of his students’ practical needs or unwilling to cater to them, stressed the latter. “He would talk only of infinity and infinitesimals,” wrote Govindaraja, who was no slouch intellectually and wound up as chairman of India’s public service commission. “I felt that his tuition [teaching] might not be of real use to me in the examination, and so I gave it up.”

Ramanujan had lost all his scholarships. He had failed in school. Even as a tutor of the subject he loved most, he’d been found wanting.

He had nothing.

And yet, viewed a little differently, he had everything. For now there was nothing to distract him from his notebooks—notebooks, crammed with theorems, that each day, each week, bulged wider.”

Ramanujan's Monologues

Illustration: R Rajesh

When he was twenty-one, he showed up at the house of a teacher, got drawn into conversation, and soon was expatiating on the ties he saw between God, zero, and infinity—keeping everyone spellbound till two in the morning. It was that way often for Ramanujan. Losing himself in philosophical and mystical monologues, he’d make bizarre, fanciful leaps of the imagination that his friends did not understand but found fascinating anyway. So absorbed would they become that later all they could recall was the penetrating set of his eyes.

**

It had been Namagiri to whom Ramanujan’s mother and father, childless for some years after they married, had prayed for a child. Ramanujan’s maternal grandmother, Rangammal, was a devotee of Namagiri and was said to enter a trance to speak to her. One time, a vision of Namagiri warned her of a bizarre murder plot involving teachers at the local school. Another time, many years earlier, before Ramanujan’s birth, Namagiri revealed to her that the goddess would one day speak through her daughter’s son. Ramanujan grew up hearing this story. And he, too, would utter Namagiri’s name all his life, invoke her blessings, seek her counsel. It was goddess Namagiri, he would tell friends, to whom he owed his mathematical gifts. Namagiri would write the equations on his tongue. Namagiri would bestow mathematical insights in his dreams.

So he told his friends. Did he believe it?

His grandmother did, and so did his mother.

The Off-Scale Student

http://www.indiaart.com/Art-Marketplace/painting-details/19977/Ramanujan

“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.”

The Brahmin Tradition

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.

Locked Away Ramanujans

It is a story of one man and his stubborn faith in his own abilities. But it is not a story that concludes, Genius will out—though Ramanujan’s, in the main, did. Because so nearly did events turn out otherwise that we need no imagination to see how the least bit less persistence, or the least bit less luck, might have consigned him to obscurity. In a way, then, this is also a story about social and educational systems, and about how they matter, and how they can sometimes nurture talent and sometimes crush it. How many Ramanujans, his life begs us to ask, dwell in India today, unknown and unrecognized? And how many in America and Britain, locked away in racial or economic ghettos, scarcely aware of worlds outside their own?