The Man Who Knew Infinity

by Robert Kanigel

  I vowed that I would dedicate my powers

  To thee and thine; have I not kept the vow?

  For the layman, to be sure, this is an ultimately unsatisfying way to confront Ramanujan’s mathematics, for it keeps us at several removes from what he did, leaves us having to take others’ word for it, looking at his mathematical achievements through a blurry film of metaphor, poetry, and, yes, ignorance. True, the composition of a sonata may be equally mysterious; but the result more intimately involves the five senses.

  What Ramanujan did will live forever. It will not, to be sure, live in the hearts of the masses of men, like the work of Gandhi, Shakespeare, or Bach. Still, his ideas and discoveries, percolating through those few minds tuned to them, will mingle with the intellectual energy of the cosmos, and thence into the deep, broad pool of human knowledge. “What we do may be small, but it has a certain character of permanence,” wrote Hardy of the work of pure mathematicians, “and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men.”

  • • •

  By the time of the centennial of his birth in 1987, Ramanujan’s reputation shone with a new luster. In India, he was compared to Nehru and Nobel Prize-winning physicist C. V. Raman, both of whose centennials were being celebrated at about the same time. Three Indian films were made about his life. A Ramanujan Mathematical Society, started in 1986, published the first volume of its journal.

  Celebrations were held all across South India. Andrews, Askey, and Berndt, the three American mathematicians who had most contributed to the restoration of Ramanujan’s name, were kept busy shuttling all over the country, giving lectures at Annamalainagar, and Bombay, and Pune, and Gorakhpur and Madras.

  In Madras, when the Narosa Publishing House issued The Lost Notebook, Prime Minister Rajiv Gandhi was there to sign the first copy and present it to Janaki.

  In Kumbakonam, the framed and garlanded poster-sized portrait of Ramanujan, fat again and wearing the mortarboard he wore when he received his Cambridge degree, was borne through the streets atop a gaily decorated elephant, to the accompaniment of traditional street musicians. The National Cadet Corps was there, and girl scouts in pink blouses and rose-colored skirts, and traditional dancers, all of them showered with flower blossoms as they paraded down the street in front of Ramanujan’s house. Loudspeakers shouted praise of Kumbakonam’s favorite son to the assembled throngs in the street.

  At Anna University, which named its computer center for Ramanujan, Andrews, his voice choked with emotion, presented Janaki with a shawl. It was she who deserved the credit for the Lost Notebooks, he said, since she had kept his papers together while he lay dying.

  After World War II, the university had noticed that Janaki’s 20-rupee-per-month pension no longer went very far and raised it to 125. Janaki financed her son Narayanan’s way through college. He later got a job with the State Bank of India, married, and had three children. Recently, he retired from the bank job he held for twenty-five years and began to spend more time caring for his mother.

  After a hard life and years of anonymity, Janaki herself began to garner attention as her husband was rediscovered. Along the way, she grew more outspoken. At one point, presented a pension by the University of Madras, she remarked that while the cash was fine, it would have done her more good sixty years earlier. A little earlier, in 1981, she had told an Indian newspaper reporter, “They said years ago a statue would be erected in honor of my husband. Where is the statue?”

  Dick Askey learned of Janaki’s lament. “If she wants a bust of her husband,” he thought, “we owe that much to Ramanujan, and to her.” We meant the mathematicians of the world. Askey knew the Minnesota sculptor Paul Granlund, from whom he had bought some works, and contacted him. Granlund agreed to do it, provided at least three busts would materialize from the project. (Ultimately, ten did.) Askey and his wife would buy one. So would Chandrasekhar, the astrophysicist, to whom Askey had written about the idea. But where would the $3000 come for Janaki’s? Askey got some of it from institutions, including Trinity College. But most came in individual $25 contributions from mathematicians around the world. Today, Granlund’s bronze bust of Ramanujan, based on the passport photograph, stands on a pedestal in Janaki’s house in Madras.

  With the approach of the centennial, the house became a pilgrimage site. Mathematicians passing through Madras paid her homage. She appeared in a British television special about Ramanujan, Letters from an Indian Clerk, later shown in America as well. In August of the centennial year, a foundation presented her with a purse of twenty thousand rupees and a monthly pension of one thousand rupees; she asked that a Srinivasa Ramanujan Trust be created for awards and scholarships to bright young mathematics students. Early the following year, Trinity College made its own gesture, its council in February 1988 agreeing to “a grant of £2,000 a year until further notice.”

  As the centennial approached, T. V. Rangaswami, a Tamil language journalist in Madras, set out on what became a thirty-one-part series of articles on Ramanujan. He spent months collecting letters, documents, and photographs, and interviewing Janaki, who lived near him in Triplicane. Each afternoon they would meet and talk. One afternoon, he showed her a photograph of “Gometra,” the house off Harrington Road where she had nursed Ramanujan and in which he had died. The wrinkled old woman, removed by more than sixty years from the events that took place there, broke down and cried.

  7. SVAYAMBHU

  A bittersweet tang sometimes slipped into the encomiums India lavished on Ramanujan over the years, sad reminders of the poverty, bureaucracy, and institutional rigidity that almost crushed him in 1905. Ramanujan was an inspiration to India, yes—but also a rebuke. How could India let him come so close to being lost to the world? Why hadn’t he gotten more encouragement? Why was it left to foreigners to make him famous?

  J. B. S. Haldane, the distinguished English biologist who lived in India toward the end of his life, in the early 1960s complained that

  today in India Ramanujan could not get even a lectureship in a rural college because he had no degree. Much less could he get a post through the Union Public Service Commission. This fact is a disgrace to India. I am aware that he was offered a chair in India after becoming a Fellow of the Royal Society. But it is scandalous that India’s great men should have to wait for foreign recognition. If Ramanujan’s work had been recognized in India as early as it was in England, he might never have emigrated and might be alive today. We can cast the blame for Ramanujan’s non-recognition on the British Raj. We cannot do so when similar cases occur today… .

  On his birthday in 1974, a Professor Srinivasa Ramanujan International Memorial Committee published a commemoration volume littered with advertisements expressing “respectful homage” and like sentiments by every little South Indian company that wanted to briefly bask in Ramanujan’s reflected glory, from Madras Aluminum Co. in Coimbatore to Smart Dresses on Ranganathan Street in Madras. Prime Minister Indira Gandhi wrote from New Delhi that Ramanujan’s “untutored genius” dazzled science and that “his achievement will inspire successive generations of Indian youth.” But editor S. Ramakrishnan added: “Let not Free India lose sight of her living Ramanujans, languishing in obscurity.”

  Languishing in obscurity. There was another side to Ramanujan’s service as symbol of India and, in 1946, Nehru himself had referred to it in his Discovery of India:

  Ramanujan’s brief life and death are symbolic of conditions in India. Of our millions how few get any education at all; how many live on the verge of starvation … If life opened its gates to them and offered them food and healthy conditions of living and education and opportunities of growth, how many among these millions would be eminent scientists, educationists, technicians, industrialists, writers, and artists, helping to build a new India and a new world?

  R. Viswanathan, a later headmaster of Ra
manujan’s alma mater, Town High School in Kumbakonam, would insist that, given the resources, he could turn out many Ramanujans. Taken literally, he was quite wrong; all the wealth of the British Empire, all the rich intellectual tradition of Europe, all the freedom and opportunity of America, have made for but a handful of Ramanujans through the centuries. Still, Viswanathan had expressed a larger truth—that India held vast stores of talent and ability denied the means to develop fully. Ramanujan represented his country’s intellectual and spiritual strengths—but also its untapped potential.

  • • •

  But didn’t Ramanujan’s story prove, quite to the contrary, that genius in the end overcomes? If Ramanujan, with all his disadvantages, could command the attention of the world and leave so indelible a mark on it, couldn’t anyone endowed with special gifts do it, too?

  Not so. So long did Ramanujan languish, so many times did his future hang on a knife edge, so close did he come to dying unknown—and so plainly was his full promise never realized—that his life’s lesson bears as much on the stumbling blocks he faced as on his success, such as it was, in overcoming them.

  Ramanujan had much more going for him than millions of others in India did. His family was poor but hardly destitute. He was a Brahmin, part of a culture that encouraged learning. His mother was tolerant of his whims and forceful in advancing his interests. His innocent charm won over those his eccentricities might otherwise have put off. And he enjoyed a peculiarly stubborn faith in himself and his powers.

  What, one must ask, if he had had none of these? What if he had been every inch the genius he was, with just as much to give the world, but his mother had been a little less supportive? Or he had been the barest bit less likeable or less sure of his abilities? Doubtless he would have wound up like his brothers, an anonymous government bureaucrat, or otherwise consigned to obscurity. For those who have biographies written about them, the System by definition works; the measure of its failure lies in those who never bask in the warm glow of the world’s acclaim. Those you never hear about.

  Ramanujan, then, was an embarrassment to India as well as an inspiration, a reminder of the gauntlet India’s other Ramanujans must run in order to achieve anything. As symbol of South Indian genius, he was a delight to contemplate. In the sometimes harsh reality of his life, much less so.

  When in November 1968, on receiving the Srinivasa Ramanujan Medal of the Indian National Science Academy, S. Chandrasekhar revealed that Ramanujan had tried to commit suicide, his comments sparked a furor. “I was shocked and surprised,” he wrote later, “that I was accused by several [including his uncle, C. V. Raman] of defaming Ramanujan’s name.” Someone charged him with trying to enhance his own reputation at Ramanujan’s expense. Chandrasekhar had sinned: he had torn down Ramanujan as icon, replaced him with Ramanujan the man.

  Today, as in Ramanujan’s day and in all the years in between, many of India’s best minds leave to go overseas, where they are nourished by Western ideas and sidestep the sort of “inefficient and inelastic” educational system that stifled Ramanujan. India, a poor country, can lavish praise on the long-dead Ramanujan more easily than it can lavish resources on finding and nurturing new Ramanujans.

  In 1951, a wealthy merchant and patron of higher education, Alagappa Chettiar, founded the Ramanujan Institute. After his death, the institute faced severe financial problems and almost shut down. In 1957, it was absorbed by the University of Madras, where it became the Centre for Advanced Studies in Mathematics. In 1972, it moved into a low-slung modern building just across a little concrete bridge spanning the Buckingham Canal from the main university campus. The institute, with nineteen teachers, lecturers, and research students, remains there today. But it does not specialize in areas of mathematics Ramanujan pursued, nor does its name bear anything like the luster of its namesake.

  Even the centennial festivities were marred by reminders of the limited opportunities India offered its Ramanujans and the obstacles it placed in their way. Why, some wondered, were Ramanujan’s research reports from 1914 lost while in Indian care? Why was it left to American, more than Indian, mathematicians to restore Ramanujan’s reputation? “I want you all to sit back and think about this,” one speaker, S. Ramaseshan, asked his listeners at a centennial event in Kumbakonam:

  How many registrars in this country today, or for that matter how many vice chancellors of today, 100 years after Ramanujan was born, would give a failed pre-university student a research scholarship of what is now equivalent of Rs. 2000/- or Rs. 2500/- today? This is after 40 years of independence, when we can no longer blame a colonial power for not encouraging Indian talent.

  A writer for the Illustrated Weekly of India, referring to Ramanujan, suggested that “perhaps the luminescence of his mind is too harsh for Indians in this age of their intellectual bleakness… .”

  • • •

  Ramanujan as inspiration. Ramanujan as rebuke. Ramanujan as … ? Ramanujan’s life can be made to serve as parable for almost any lesson you want to draw from it. At an early Indian Mathematical Society conference, his name was invoked to point up the society’s meager resources: “When the famous mathematician, Mr. Ramanujan, F.R.S., sought some modest help from our Society to enable him to devote his attention to mathematical studies and research, our bankruptcy was made manifest… .” In the 1950s, a library director recounted Ramanujan’s story for readers of Wilson Library Bulletin, emphasizing the impact on him of Carr’s Synopsis. Ramanujan’s life, he was saying, was a testimonial to the books that had nurtured him. All across the years and up to the present, it was like that—Ramanujan invoked as model, inspiration, warning, or instructive case history. Ramachandra Rao had done it. Hardy had. Nehru had.

  Cut cruelly short, Ramanujan’s life bore something of the frustration that a checked swing does in baseball; it lacked follow-through, roundedness, completion. It never had a second half to give it shape. So we continue to give it shape now, years after his death.

  His life was truncated, like a cone sliced off short of its vertex. Or like an economic graph that stops with the present, leaving forecasters to fill in a vast and uncertain future. Ramanujan’s life, littered with what-might-have-beens, was like that: it was so easy to see in it what you wanted to see. Its bare facts fairly cried out for interpretation.

  Was his failure in school testimony to India’s failure to nurture its own? Or was his rescue by Ramachandra Rao and Narayana Iyer proof that, in the end, India recognized and appreciated him?

  Was he an example of the oppressiveness of the raj, a case of native genius nearly quashed—then making its contribution, when it did emerge, to “English mathematics”? Or was his discovery a testament to British beneficence?

  Would he have achieved more had he found mentors early on? Would he have become the next Gauss or Newton? Or did working on his own, under less than ideal conditions, make him more mathematically resourceful, even contribute to his stunning originality?

  Was his genius the product of sheer intellectual power, different only in degree from other brilliant mathematicians? Or was it steeped in something of the mystical or the supernatural?

  Was Ramanujan’s life a tragedy of unfulfilled promise? Or did his five years in Cambridge redeem it?

  In each case, the evidence left ample room to see it either way. In this sense, Ramanujan’s life was like the Bible, or Shakespeare—a rich fund of data, lush with ambiguity, that holds up a mirror to ourselves or our age.

  • • •

  There were no mathematicians in Ramanujan’s family, no strain of unusual mathematical aptitude. So where did he come from?

  Legion are those who have taken credit for discovering Ramanujan or for otherwise figuring largely in his life. Ramaswami Iyer would later say he was proud of two things—starting the Indian Mathematical Society and discovering Ramanujan. Narayana Iyer’s family today points with pride to its patriarch’s role in rescuing Ramanujan from oblivion, and numberless people later claimed credit fo
r convincing him to go to England. Then, too, many saw Ramanujan as the creation of his mother; the two of them, plainly, were made from the same cloth, and her heart was bound up in his success.

  Among the English, Hardy was not alone in savoring his role in Ramanujan’s life; Neville, too, would sweetly recall his days with him in Madras a quarter century before, and point out that had he “failed to win the confidence of Ramanujan and his friends,” Ramanujan might never have reached England. But Hardy remains the prime candidate. Paul Erdos has recorded that when Hardy was asked about his greatest contribution to mathematics, he unhesitatingly replied, “The discovery of Ramanujan.” At another time, indeed, Hardy went on record as calling him “my discovery.”

  In a sense, of course, he was. But a more satisfying way to explain Ramanujan’s emergence as a figure on the world mathematical stage was given in an article appearing in India during the centennial, by a writer for The Illustrated Weekly of India known only as “RGK.” Ramanujan, he suggested, was svayambhu—“self-born.” He had sprouted up out of the soil of India of his own accord. He had created himself.

  You cannot say much about Ramanujan without resorting to the word self He was self-willed, self-directed, self-made. Indeed, some might conceivably label him “selfish” for his preoccupation with doing the mathematics he loved without any great concern for the betterment of his family or his country.

  Ramanujan did what he wished to do, went his own way. It was only later, after he had indulged in an orgy of mathematical creation, that he might wake up and realize how far he had strayed from the common run of human intercourse. Only then might he begin to care, sometimes painfully much, how others thought of him.

  When he was a teenager, he lent support to the local crazy man, though the whole rest of Kumbakonam dismissed him as a crank. He gave himself over to mathematics, throwing aside everything else, even the degree-as-meal-ticket his mother so much wanted for him. He knocked on doors all over South India, introducing himself to one mathematician after another. Then, when he had exhausted the mathematical resources of India, he turned to England. He wrote Baker. He wrote Hobson. He wrote Hardy.