The Man Who Knew Infinity

by Robert Kanigel

  “A gem… . What Mozart was to music and Einstein was to physics, Ramanujan was to math… .”

  —Clifford Stoll, author of The Cuckoo’s Egg and Silicon Snake Oil

  EXTRAORDINARY PRAISE FOR ROBERT KANIGEL’S

  “ENLIGHTENING… . a magic, tragic ugly-duckling fable… .Ramanujan’s remarkable story comes through… .”

  —The New York Times

  “The most luminous expression ever of … genius interacting with genius … I’ve seen nothing to compare with it.”

  —Hugh Kenner, BYTE

  “ENTHRALLING … one of the best scientific biographies I’ve ever seen.”

  —Dr. John Gribbin, author of In Search of Shrödinger’s Cat

  “COMPELLING … a work of arduous research and rare insight … Kanigel deserves high praise.”

  —Booklist

  “… a REMARKABLE book… . a model of the biographer’s art: Kanigel has taken a man, a social context and a specialist field and made each accessible and convincing. He has done so with a rare combination of skills—encyclopedic thoroughness, meticulous research, genuine sympathy for his subjects and first-rate writing of exceptional lucidity and verve. THOUGHTFUL, COMPASSIONATE AND CLEAR, THE MAN WHO KNEW INFINITY IS A MASTERPIECE… . BREATHTAKING.”

  —The Washingon Post Book World

  A BOOK-OF-THE-MONTH-CLUB

  FEATURED SELECTION

  FINALIST FOR THE LOS ANGELES TIMES BOOK AWARD

  “BRILLIANTLY REALIZED… . [the] fascinating story of a difficult but astoundingly fruitful cross-cultural collaboration.”

  —Kirkus Reviews

  “THE MAN WHO KNEW INFINITY is an accessible look at an almost romantic episode in the enormously rich intellectual world of mathematics … Robert Kanigel also gives a real sense of Ramanujan’s creative compulsion which, like Mozart’s, contained the seeds of both success and tragedy.”

  —Baltimore Evening Sun

  “ … more fascinating than a novel … a verbal portrait, A VIRTUAL MASTERPIECE, complete with vibrant scenes from all the places graced by the presence of Ramanujan… . ENCHANTING.”

  —Lexington Herald-Leader (Kentucky)

  “THE MAN WHO KNEW INFINITY tells of the plight of unrecognized genius… . this story of romance with mathematics makes for lively reading … with a heartbreaking end.”

  —Christian Science Monitor

  “SPLENDID … One of Robert Kanigel’s achievements in THE MAN WHO KNEW INFINITY is to make the math magic … accessible… . a very human story… . EXCITING.”

  —San Diego Union

  “[A] SUPERBLY CRAFTED biography… . Kanigel succeed[s] in giving a taste of Ramanujan the mathematician, but his exceptional triumph is in the telling of this wonderful human story… . a pleasure to read … THE MAN WHO KNEW INFINITY is a thoughtful and deeply moving account of a signal life.”

  —Science

  “A simple story VIVIDLY TOLD… . Kanigel excels in descriptions that will appeal to both the lay and scholarly reader.”

  —San Francisco Chronicle

  “PERSPICACIOUS, INFORMED, IMAGINATIVE, THE MAN WHO KNEW INFINITY is … the best mathematical biography I have ever read.”

  —The New York Review of Books

  “[An] extremely well-researched and well-written biography.”

  —Library Journal

  “Mr. Kanigel has a wonderful gift… . The drama of Ramanujan’s ‘Spring’ and ‘Autumn’ comes through magnificently.”

  —Freeman Dyson, author of Disturbing the Universe

  “MOVING AND ASTONISHING.”

  —Publishers Weekly

  “THE MAN WHO KNEW INFINITY is a story at least as compelling as Brian Epstein’s discovery of the Beatles … [a] richly detailed road map to strange, wondrous foreign cultures… . Kanigel expertly intertwines the details of Ramanujan’s odd, doomed life with his soaring professional accomplishments.”

  —Los Angeles Times Book Review

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  Contents

  Prologue

  One/IN THE TEMPLE’S COOLNESS/1887 to 1903

  1. Dakshin Gange

  2. Sarangapani Sannidhi Street

  3. A Brahmin Boyhood

  4. Off-scale

  5. The Goddess of Namakkal

  Two/RANGING WITH DELIGHT/1903 to 1908

  1. The Book of Carr

  2. The Cambridge of South India

  3. Flight

  4. Another Try

  5. The Notebooks

  6. A Thought of God

  7. Enough is Enough

  Three/THE SEARCH FOR PATRONS/1908 to 1913

  1. Janaki

  2. Door-to-Door

  3. “Leisure” in Madras

  4. Jacob Bernoulli and His Numbers

  5. The Port Trust

  6. The British Raj

  7. The Letter

  Four/HARDY/G. H. Hardy to 1913

  1. Forever Young

  2. Horseshoe Lane

  3. Flint and Stone

  4. A Fellow of Trinity

  5. “The Magic Air”

  6. The Hardy School

  Five/“I BEG TO INTRODUCE MYSELF …”/1913 to 1914

  1. The Letter

  2. “I Have Found in You a Friend …”

  3. “Does Ramanujan Know Polish?”

  4. A Dream at Namakkal

  5. At the Dock

  Six/RAMANUJAN’S SPRING/1914 to 1916

  1. Out of India

  2. Together

  3. The Flames of Louvain

  4. The Zeroes of the Zeta Function

  5. S. Ramanujan, B.A.

  Seven/THE ENGLISH CHILL/1916 to 1918

  1. High Table

  2. An Indian in England

  3. “A Singularly Happy Collaboration”

  4. Deepening the Hole

  5. “All Us Big Steamers”

  6. The Danish Phenomenon

  7. Trouble Back Home

  8. The Nelson Monument

  9. Ramanujan, Mathematics, and God

  10. Singularities at X = 1

  11. Slipped from Memory

  Eight/“IN SOMEWHAT INDIFFERENT HEALTH”/From 1918

  1. “All the World Seemed Young Again”

  2. Return to the Cauvery

  3. The Final Problem

  4. A Son of India

  5. Ramanujan Reborn

  6. Better Blast Furnaces?

  7. Svayambhu

  Epilogue

  Photographs

  About Robert Kanigel

  Notes

  Selected Bibliography

  Author’s Note and Acknowledgments

  Index

  For Mom and Dad

  with love and thanks

  Prologue

  One day in the summer of 1913, a twenty-year-old Bengali from an old and prosperous Calcutta family stood in the chapel of King’s College in the medieval university town of Cambridge, England. A glorious, grandly proportioned place, more cathedral than chapel, it was the work of three kings of England going back to 1446. Light streamed in through stained glass panels ranging across the south wall. Great fluted columns reached heavenward, flaring out into the massive splayed vault of the roof.

  Prasantha Chandra Mahalanobis was smitten. Scarcely off the boat from India and planning to study in London, he had come up on the train for the day to sightsee. But now, having missed the last
train back to London and staying with friends, he couldn’t stop talking about the chapel and its splendors, how moved he’d been, how …

  Perhaps, proposed a friend, he should forget London and come to King’s instead. That was all Mahalanobis needed to hear. The next day he met with the provost, and soon, to his astonishment and delight, he was a student at King’s College, Cambridge.

  He had been at Cambridge for about six months when his mathematics tutor asked him, “Have you met your wonderful countryman Ramanujan?”

  He had not yet met him, but he had heard of him. Ramanujan was a self-taught mathematical prodigy from a town outside Madras, in South India, a thousand miles from the sophisticated Calcutta that Mahalanobis knew best, a world as different from his own as Mahalanobis’s was from England. The South, as educated North Indians were wont to see it, was backward and superstitious, scarcely brushed by the enlightened rationality of Bombay and Calcutta. And yet, somehow, out of such a place, from a poor family, came a mathematician so alive with genius that the English had practically hand-delivered him to Cambridge, there to share his gifts with the scholars of Trinity College and learn whatever they could teach him.

  Among the colleges of Cambridge University, Trinity was the largest, with the most lustrous heritage, home to kings, poets, geniuses. Isaac Newton himself had studied there; since 1755, his marble likeness, holding the prism he’d used to explore the polychromatic nature of light, stood in its chapel. Lord Byron had gone to Trinity. So had Tennyson, Thackeray, and Fitzgerald. So had the historian Macaulay, and the physicist Rutherford, and the philosopher Bertrand Russell. So had five English prime ministers.

  And now, Ramanujan was at Trinity, too.

  Soon Mahalanobis did meet him, and the two became friends; on Sunday mornings, after breakfast, they’d go for long walks, talk about life, philosophy, mathematics. Later, looking back, Mahalanobis would date the flowering of their friendship to one day in the fall following Ramanujan’s arrival. He’d gone to see him at his place in Whewell’s Court, a three-story stone warren of rooms built around a grassy quadrangle laced with arched Gothic windows and pierced at intervals by staircases leading to rooms. One such portal led to Ramanujan’s small suite, on the ground floor, a step or two off the court.

  It had turned cold in Cambridge and as Mahalanobis came in, he saw Ramanujan, with his fleshy, pockmarked face, sitting huddled by the fire. Here was the pride of India, the man whom the English had moved heaven and earth to bring to Cambridge. But well-laid plans had gone awry. It was the shameful year of 1914, and Europe had gone to war. The graceful arched cloisters of Nevile’s Court, Sir Christopher Wren’s eternal stamp on Trinity, had become an open-air hospital. Thousands had already left for the front. Cambridge was deserted. And cold.

  Are you warm at night? asked Mahalanobis, seeing Ramanujan beside the fire. No, replied the mathematician from always-warm Madras, he slept with his overcoat on, wrapped in a shawl. Figuring his friend hadn’t enough blankets, Mahalanobis stepped back into the little sleeping alcove on the other side of the fireplace from the sitting room. The bedspread was loose, as if Ramanujan had just gotten up. Yet the blankets lay perfectly undisturbed, tucked neatly under the mattress.

  Yes, Ramanujan had enough blankets; he just didn’t know what to do with them. Gently, patiently, Mahalanobis showed him how you peeled them back, made a little hollow for yourself, slipped inside …

  • • •

  For five years, walled off from India by the war, Ramanujan would remain in strange, cold, distant England, fashioning, through twenty-one major papers, an enduring mathematical legacy. Then, he would go home to India, to a hero’s welcome, and die.

  “Srinivasa Ramanujan,” an Englishman would later say of him, “was a mathematician so great that his name transcends jealousies, the one superlatively great mathematician whom India has produced in the last thousand years.” His leaps of intuition confound mathematicians even today, seven decades after his death. His papers are still plumbed for their secrets. His theorems are being applied in areas—polymer chemistry, computers, even (it has recently been suggested) cancer—scarcely imaginable during his lifetime. And always the nagging question: What might have been, had he been discovered a few years earlier, or lived a few years longer?

  Ramanujan was a simple man. His needs were simple. So were his manners, his humor. He was no idiot savant; he was intelligent in realms outside mathematics, persistent, hardworking, and even, in his own way, charming. But by the lights of Cambridge or, for that matter, of Calcutta or Bombay, he was supremely narrow and naive. Something so small as Mahalanobis’s lesson in the art of blanketing could leave him “extremely touched.” He was shamed by the most insignificant slight. His letters, outside their mathematical content, are barren of grace or subtlety.

  In this book I propose to tell Ramanujan’s story, the story of an inscrutable intellect and a simple heart.

  It is a story of the clash of cultures between India and the West—between the world of Sarangapani Sannidhi Street in Kumbakonam in South India, where Ramanujan grew up, and the glittering world of Cambridge; between the pristine proofs of the Western mathematical tradition and the mysterious powers of intuition with which Ramanujan dazzled East and West alike.

  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?

  This is a story, too, about what you do with genius once you find it. Ramanujan was brought to Cambridge by an English mathematician of aristocratic mien and peerless academic credentials, G. H. Hardy, to whom he had written for help. Hardy saw that Ramanujan was a rare flower, one not apt to tolerate being stuffed methodically full of all the mathematical knowledge he’d never acquired in India. “I was afraid,” he wrote, “that if I insisted unduly on matters which Ramanujan found irksome, I might destroy his confidence and break the spell of his inspiration.”

  Ramanujan was a man who grew up praying to stone deities; who for most of his life took counsel from a family goddess, declaring it was she to whom his mathematical insights were owed; whose theorems would, at intellectually backbreaking cost, be proved true—yet leave mathematicians baffled that anyone could divine them in the first place. This is also a book, then, about an uncommon and individual mind, and what its quirks may suggest about creativity, intuition, and intelligence.

  • • •

  Like most books, this one started with an idea. Sadly, it was not mine, but that of Barbara Grossman, then senior editor at Crown Publishers, now publisher at Scribners. Barbara first encountered the name of Ramanujan in late 1987, a time when magazines and newspapers in the United States, India, and Britain were full of articles marking the hundredth anniversary of his birth. Like Mahalanobis in King’s College Chapel, Barbara was smitten. First, with the sheer romance of his life—the story in it. But also with how today, years after his death and long into the computer age, some of his theorems were, as she put it later, being “snatched back from history.”

  “Ramanujan who?” I said when my agent, Vicky Bijur, told me of Barbara’s interest in a biography of him. Though skeptical, I did some preliminary research into his life, as recorded by his Indian biographers. And the more I learned, the more I, too, came under Ramanujan’s spell. His was a rags-to-intellectual-riches story. Parts of it, wrote an English mathematician, B. M. Wilson, in the 1930s, “might be lifted almost unchanged by a scenario-writer for the talkies.�
�� My doubts fell away. My excitement mounted at the prospect of delving into the life of this strange genius.

  Early on, I viewed a documentary about Ramanujan’s life by the British filmmaker Christopher Sykes. Released by the BBC the previous year as Letters from an Indian Clerk, Sykes’s film superbly distilled, into a single hour, something of the romance of Ramanujan’s life. But watching it, I grew beguiled by G. H. Hardy, too. Hardy, it turned out, was the third English mathematician to whom Ramanujan had appealed; the other two declined to help. And Hardy did not just recognize Ramanujan’s gifts; he went to great lengths to bring him to England, school him in the mathematics he had missed, and bring him to the attention of the world.

  Why Hardy?

  Was it sheer mathematical acumen? Probably not; the other two mathematicians were equally distinguished. There must have been other, less purely intellectual traits demanded of him—a special openness, perhaps, a willingness to disrupt his life and stake his reputation on someone he’d never seen.

  Hardy, I learned, was a bizarre and fascinating character—a cricket aficionado, a masterful prose stylist, a man blessed with gorgeous good looks who to his own eyes was so repulsively ugly he couldn’t look at himself in the mirror. And this enfant terrible of English mathematics was, at the time he heard from Ramanujan, working a revolution on his field that would be felt for generations to come.

  One is, of course, moved to praise Hardy’s ability to see genius in the tattered garb in which it was clothed, and to agree that the world was enriched as a result. But, it struck me, Hardy was enriched, too. His whole life was shaped by his time with Ramanujan, which he called “the one romantic incident in my life.” The story of Ramanujan, then, is a story about two men, and what they meant to each other.